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We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three strategies (rock–paper–scissors) higher order interaction terms allow travelling waves to emerge in non-declining finite populations. We show that these travelling waves arise from diffusion stabilisation of an unstable interior equilibrium point that is present in the aspatial dynamics. Based on these observations and prior results, we offer two conjectures whose proofs would fully generalise our results to all odd cyclic games, both with and without higher order interactions, assuming a spatial replicator dynamic. Intriguingly, these generalisations for N ⩾ 5 strategies seem to require declining populations, as we show in our discussion. [ABSTRACT FROM AUTHOR]

Motivated by the consideration of integrable systems in three spatial dimensions in Euclidean space with integrals quadratic in the momenta we classify three-dimensional Abelian subalgebras of quadratic elements in the universal enveloping algebra of the Euclidean algebra under the assumption that the Casimir invariant p â†' â‹... l â†' vanishes in the relevant representation. We show by means of an explicit example that in the presence of magnetic field, i.e. terms linear in the momenta in the Hamiltonian, this classification allows for pairs of commuting integrals whose leading order terms cannot be written in the famous classical form of Makarov et al [17]. We consider limits simplifying the structure of the magnetic field in this example and corresponding reductions of integrals, demonstrating that singularities in the integrals may arise, forcing structural changes of the leading order terms. [ABSTRACT FROM AUTHOR]

In this paper, the qualitative behaviors of an important four-dimensional Lorenz system with wild pseudohyperbolic attractor that proposed in (Gonchenko et al 2021 Nonlinearity 34 2018–47) are considered. Here, we prove that the four-dimensional Lorenz system with varying parameters is global bounded according to Lyapunov's direct method. Furthermore, we provide a collection of global absorbing sets, where in addition we obtain the rate of the trajectories going from the exterior to the global absorbing set. In particular, we solve the critical case k → 0 + that cannot be resolved by using the previous methods. The fundamental qualitative behaviors are analyzed theoretically and numerically. We present bifurcation diagrams to further explore the complicated dynamical behaviors of this system. The period-doubling bifurcation phenomenon is found. To illustrate the efficiency of our method, we present numerical simulations to show the validity of our research results. Finally, we present some applications of our research results in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a novel quantization scheme for cooperative games is proposed. The circuit is inspired by the Eisert–Wilkens–Lewenstein protocol, which was modified to represent cooperation between players and extended to 3–qubit states. The framework of Clifford algebra is used to perform necessary computations. In particular, we use a direct analogy between Dirac formalism and Quantum Register Algebra (QRA) to represent circuits. This analogy enables us to perform automated proofs of the circuit equivalence in a simple fashion. The expected value of the Shapley value concerning quantum probabilities is employed to distribute players' payoffs after the measurement. We study how entanglement, representing the level of pre-agreement between players, affects the final utility distribution. The paper also demonstrates how the QRA and GAALOP software can automate all necessary calculations. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions for the existence of strongly (uniformly and exponentially) quasi-mixing limits of one-dimensional diffusion processes with killing. As a by-product, these conditions also ensure that the considered processes have strong quasi-ergodicity, strong fractional quasi-ergodicity and uniform mean-ratio quasi-ergodicity. Moreover, the quasi-ergodic speeds of these three quasi-ergodicities are also characterized. [ABSTRACT FROM AUTHOR]

The authors of the paper (Vitali et al 2022 J. Phys. A: Math. Theor. 55 224012) analyzed a simple CTRW model with a waiting time distribution defined as the weighted sum of two exponential distributions. They showed that their model meets many paradigmatic features that belong to the anomalous diffusion as it is observed in living systems. This comment point out the previous paper that considers a similar model and improves on the authors' result regarding the time dependence of the mean-square displacement. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the simple current orbifold of a rational Narain CFT (Narain RCFT). This is a method of constructing other rational CFTs from a given rational CFT, by 'orbifolding' the global symmetry formed by a particular primary fields (called the simple current). Our main result is that a Narain RCFT satisfying certain conditions can be described in the form of a simple current orbifold of another Narain RCFT, and we have shown how the discrete torsion in taking that orbifold is obtained. Additionally, the partition function can be considered a simple current orbifold with discrete torsion, which is determined by the lattice and the B-field. We establish that the partition function can be expressed as a polynomial, with the variables substituted by certain q -series. In a specific scenario, this polynomial corresponds to the weight enumerator polynomial of an error-correcting code. Using this correspondence to the code theory, we can relate the B-field, the discrete torsion, and the B-form to each other. [ABSTRACT FROM AUTHOR]

We consider two-dimensional, non-relativistic quantum system with asymptotically straight soft waveguide. We show that the local deformation of the symmetric waveguide can lead to the emerging of the embedded eigenvalues living in the continuous spectrum. The main problem of this paper is devoted to the analysis of weak perturbation of the symmetric system. We show that the original embedded eigenvalues turn to the second sheet of the resolvent analytic continuation and constitute resonances. We describe the asymptotics of the real and imaginary components of the complex resonant pole depending on deformation. Finally, we generalize the problem to three dimensional system equipped with a soft layer. [ABSTRACT FROM AUTHOR]

This document is our reply to the Comment (Miloslav Znojil 2023 J. Phys. A: Math. Theor. 56 038001) on our recent work titled 'The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'. The original Comment consists of three addenda to our work. The first addendum claims that our work is ill-motivated as the motivating question, namely whether PT-symmetric quantum theory extends the standard quantum theory, was already answered in the literature. The second addendum points to some missing references in our work, and the third addendum suggests what constraints could lead to an extension of standard quantum theory. In our reply, we explain that the claim in the first addendum is a result of a misinterpretation of our motivating question. When interpreted correctly, the third addendum in the Comment in itself elaborates on why our motivating question is interesting and relevant. We also briefly comment on the prospects of an extension of standard quantum theory along the lines suggested in the third addendum. As our response to the second addendum, we explain our rationale behind citing certain references while leaving out others. [ABSTRACT FROM AUTHOR]

Criticisms and a claim in the recent paper Backflow in relativistic wave equations by Bialynicki-Birula et al 2022 J. Phys. A: Math. Theor. 55 255702 are addressed, and it is emphasized again that the widely discussed phenomenon of quantum probability backflow has no classical counterpart. It is pointed out that backflow for the relativistic Dirac Equation has been treated in depth by us some years ago and by others since. [ABSTRACT FROM AUTHOR]

It turns out that harmonic analysis on the superspace R m | 2 n is quite parallel to the classical theory on the Euclidean space R m unless the superdimension M := m − 2 n is even and non-positive. The underlying symmetry is given by the orthosymplectic superalgebra o s p (m | 2 n) . In this paper, when the symmetry is reduced to o s p (m − 1 | 2 n) we describe explicitly the corresponding branching laws for spherical harmonics on R m | 2 n also in exceptional cases, i.e, when M − 1 ∈ − 2 N 0 . In unexceptional cases, these branching laws are well-known and quite analogous as in the Euclidean framework. [ABSTRACT FROM AUTHOR]

Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental statistical limits represents a true challenge, and despite a decade-long history of efforts in the community, there is still no closed formula able to describe its optimal performances in the case where the rank of the matrix scales linearly with its size. In the present paper, we study this extensive rank problem, extending the alternative 'decimation' procedure that was recently introduced by Camilli and Mézard, and carry out a thorough study of its performance. Decimation aims at recovering one column/line of the factors at a time, by mapping the problem into a sequence of neural network models of associative memory at a tunable temperature. The main advantage of decimation is that its theoretical performance can be studied using statistical physics techniques. In this paper we provide the general analysis applying to a large class of compactly supported priors and we show that the replica symmetric free entropy of the neural network models takes a universal form in the low temperature limit. We then study the decimation phase diagrams in two concrete cases, the sparse Ising prior and the uniform prior, for which we show that matrix factorization is theoretically possible when the ration P / N of rank to variable is below a certain threshold. This suggest that a possible route to solving algorithmically the matrix factorization problem could be to find efficient decimation algorithms; in this respect, we show that simple simulated annealing, though being effective for limited signal sizes, is not scalable. [ABSTRACT FROM AUTHOR]

This paper examines networks of n measuring parties sharing m nonsignaling resources that can be locally wired together: that is, each party follows a scheme to measure the resources in a cascaded fashion with inputs to later resources possibly depending on outputs of earlier-measured ones. A specific framework is provided for studying probability distributions arising in such networks, and this framework is used to directly prove some accepted, but often only implicitly invoked, facts: there is a uniquely determined and well-defined joint probability distribution for the outputs of all resources shared by the parties, and this joint distribution is nonsignaling. It is furthermore shown that is often sufficient to restrict consideration to only extremal nonsignaling resources when considering features and properties of such networks. Finally, the framework illustrates how the physical theory of nonsignaling boxes and local wirings is causal, supporting the applicability of the inflation technique to constrain such models. For an application, we probe the example of (3 , 2 , 2) inequalities that witness genuine three-party nonlocality according to the local-operations-shared-randomness definition, and show how all other examples can be derived from that of Mao et al (2022 Phys. Rev. Lett. 129 150401). [ABSTRACT FROM AUTHOR]

We consider discrete dynamical systems obtained as deformations of mutations in cluster algebras associated with finite-dimensional simple Lie algebras. The original (undeformed) dynamical systems provide the simplest examples of Zamolodchikov periodicity: they are affine birational maps for which every orbit is periodic with the same period. Following on from preliminary work by one of us with Kouloukas, here we present integrable maps obtained from deformations of cluster mutations related to the simple root systems A 3 , C 2 , B 3 and D 4 . We further show how new cluster algebras arise, by considering Laurentification, that is, a lifting to a higher-dimensional map expressed in a set of new variables (tau functions), for which the dynamics exhibits the Laurent property. For the integrable map obtained by deformation of type A 3 , which already appeared in our previous work, we show that there is a commuting map of Quispel–Roberts–Thompson (QRT) type which is built from a composition of mutations and a permutation applied to the same cluster algebra of rank 6, with an additional 2 frozen variables. Furthermore, both the deformed A 3 map and the QRT map correspond to translation by a generator in the Mordell-Weil group of a rational elliptic surface of rank two, and the underlying cluster algebra comes from a quiver that is mutation equivalent to the q -Painlevé III quiver found by Okubo. The deformed integrable maps of types C 2 , B 3 and D 4 are also related to elliptic surfaces. From a dynamical systems viewpoint, the message of the paper is that special families of birational maps with completely periodic dynamics under iteration admit natural deformations that are aperiodic yet completely integrable. [ABSTRACT FROM AUTHOR]

Many-body quantum dynamics defined on a spatial lattice and in discrete time—either as stroboscopic Floquet systems or quantum circuits—has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with q states per site, defined on the square lattice by a complex partition function and paremeterized in terms of q × q Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata (Schlingemann et al 2008 J. Math. Phys. 49 112104) and in the q → ∞ limit to the classical spatiotemporal cat model of many body chaos (Gutkin et al 2021 Nonlinearity 34 2800). We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper (Lotkov et al 2022 Phys. Rev. B 105 144306) can be reinterpreted in purely graphical terms and directly applied here. [ABSTRACT FROM AUTHOR]

In this paper, a generalized version of dynamic asymmetric simple exclusion process (ASEP) is introduced, and it is shown that the process has a Markov duality property with the same process on the reversed lattice. The duality functions are multivariate q -Racah polynomials, and the corresponding orthogonality measure is the reversible measure of the process. By taking limits in the generator of dynamic ASEP, its reversible measure, and the duality functions, we obtain orthogonal and triangular dualities for several other interacting particle systems. In this sense, the duality of dynamic ASEP sits on top of a hierarchy of many dualities. For the construction of the process, we rely on representation theory of the quantum algebra U q (sl 2) . In the standard representation, the generator of generalized ASEP can be constructed from the coproduct of the Casimir. After a suitable change of representation, we obtain the generator of dynamic ASEP. The corresponding intertwiner is constructed from q -Krawtchouk polynomials, which arise as eigenfunctions of twisted primitive elements. This gives a duality between dynamic ASEP and generalized ASEP with q -Krawtchouk polynomials as duality functions. Using this duality, we show the (almost) self-duality of dynamic ASEP. [ABSTRACT FROM AUTHOR]

We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well founded quantity to optimize when training autoencoders for problems where the inputs and outputs are fully quantum. We provide a rigorous algorithm for computing the value of the quantum information bottleneck quantity within error ε that requires O (log 2 ⁡ (1 / ϵ) + 1 / δ 2) queries to a purification of the input density operator if its spectrum is supported on { 0 } ⋃ [ δ , 1 − δ ] for δ > 0 and the kernels of the relevant density matrices are disjoint. We further provide algorithms for estimating the derivatives of the QIB function, showing that quantum neural networks can be trained efficiently using the QIB quantity given that the number of gradient steps required is polynomial. [ABSTRACT FROM AUTHOR]

Our aim in this paper is two-fold. We establish a novel geometric characterization of the Robertson–Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an arbitrary space frame. A known characterization establishes that a spacetime foliated by constant curvature leaves whose orthogonal flow (the cosmological flow) is geodesic, shear-free, and with constant expansion on each leaf, is RW. We generalize this characterization by relaxing the condition on the expansion. We show it suffices to demand that the spatial gradient and Laplacian of the cosmological expansion on a single arbitrary timelike curve vanish. In General Relativity these local conditions are equivalent to demanding that the energy flux measured by the cosmological flow, as well as its divergence, are zero on a single arbitrary timelike curve. The proof allows us to construct canonically adapted coordinates to the arbitrary curve, thus well-fitted to an observer with an arbitrary motion with respect to the cosmological flow. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behaviour of a Caginalp-type phase field system derived from a heat conduction law which is a generalization of the Maxwell–Cattanéo law and whose potential is singular. This type of law has the advantage of correcting the paradox of heat conduction that appears when the Fourier law is considered. The potential considered is typically logarithmic. Using such a potential makes the model much more relevant from a physical point of view. However, from a theoretical point of view, it is essential to obtain the strict separation property of the phase field in order to give sense of the equations. We first prove the existence and uniqueness of the solution thanks to the separation property. We also address the question of the dissipativity of the system. Finally, we obtain the existence of the global attractor. [ABSTRACT FROM AUTHOR]

The Ablowitz–Ladik equations, hereafter called A L + and A L − , are distinguished integrable discretizations of respectively the focusing and defocusing nonlinear Schrödinger (NLS) equations. In this paper we first study the modulation instability of the homogeneous background solutions of A L ± in the periodic setting, showing in particular that the background solution of A L − is unstable under a monochromatic perturbation of any wave number if the amplitude of the background is greater than 1, unlike its continuous limit, the defocusing NLS. Then we use Darboux transformations to construct the exact periodic solutions of A L ± describing such instabilities, in the case of one and two unstable modes, and we show that the solutions of A L − are always singular on curves of spacetime, if they live on a background of sufficiently large amplitude, and we construct a different continuous limit describing this regime: a NLS equation with a nonlinear and weak dispersion. At last, using matched asymptotic expansion techniques, we describe in terms of elementary functions how a generic periodic perturbation of the background solution (i) evolves according to A L + into a recurrence of the above exact solutions, in the case of one and two unstable modes, and (ii) evolves according to A L − into a singularity in finite time if the amplitude of the background is greater than 1. The quantitative agreement between the analytic formulas of this paper and numerical experiments is perfect. [ABSTRACT FROM AUTHOR]

This paper presents two methods for topological analysis of the complex Hermitian Su–Schrieffer–Heeger (SSH) model using the quantum geometric tensor: Berry phase and topological data analysis. We demonstrate how both methods can effectively generate topological phase diagrams for the model, revealing two distinct regions based on the relative magnitudes of the parameters | v | and | w | . Specifically, when | v | > | w | , the system is found to be topologically trivial, whereas for | v | < | w | , it exhibits topologically non-trivial behavior. Our results contribute to building the groundwork for topological analysis of more complicated SSH-type models. [ABSTRACT FROM AUTHOR]

The asymmetric quantum Rabi model (AQRM) is a fundamental model in quantum optics describing the interaction of light and matter. Besides its immediate physical interest, the AQRM possesses an intriguing mathematical structure which is far from being completely understood. In this paper, we focus on the distribution of the level spacing, the difference between consecutive eigenvalues of the AQRM in the limit of high energies, i.e. large quantum numbers. In the symmetric case, that is the quantum Rabi model (QRM), the spacing distribution for each parity (given by the Z 2 -symmetry) is fully clarified by an asymptotic expression derived by de Monvel and Zielinski, though some questions remain for the full spectrum spacing. However, in the general AQRM case, there is no parity decomposition for the eigenvalues. In connection with numerically exact studies and recent theoretical results, we describe the spacing distribution for the AQRM which is characterized by a new type of periodicity and symmetric behavior of the distribution with respect to the bias parameter, reflecting the hidden symmetry of the AQRM. In addition, we observe in the AQRM the excited state quantum phase transition for large values of the bias parameter, analogous to the QRM with large qubit energy, and an internal symmetry of the level spacing distribution for fixed bias. This novel symmetry is independent from the symmetry for half-integer bias and not explained by current theoretical knowledge. [ABSTRACT FROM AUTHOR]

Currently, the focus of stochastic resonance (SR) research is primarily on bistable systems, and classical bistable SR systems have the problems of low dimension, inconvenient parameter adjustment, and high threshold for SR effects. In this paper, based on the classic bistable system, a class of multi-dimensional single potential well SR systems without transition threshold is proposed and applied to signal processing. Firstly, the mechanism of double potential well SR and single potential well SR is studied. On this basis, a kind of multi-dimensional single potential well SR system is defined and its theoretical conditions are analyzed. Then a specific four-dimensional single potential well SR system is constructed, and the dynamics of the system is analyzed. The gain range and the approximate relationship between the system input and the four-dimensional output are derived. Finally, the four-dimensional single potential well SR system is applied to the processing of various signals. The experimental results show that the constructed system has good noise reduction and feature amplification effects on noisy signals through the advantages of multi-dimensional output, and can be used to highlight the fault feature frequency in bearing fault signals. [ABSTRACT FROM AUTHOR]

In this paper, we provide the mathematical foundation for an explicit and universal feature of cover time for a large class of random work processes, which was previously observed by Chupeau et al (2015 Nat. Phys. 11 844–7). Specifically, we rigorously establish that the fluctuations of the cover time, normalized by the mean first passage time, follow a Gumbel distribution, for finite-range, symmetric, irreducible random walks on a torus of dimension three or higher. The result contributes to a better understanding of cover-time behavior in random search processes, especially on the efficiency of exhaustive searches. Our approach builds upon the work of Belius (2013 Probab. Theory Relat. Fields 157 635–89) on cover times for simple random walks, leveraging a strong coupling between the random walk and random interlacements. [ABSTRACT FROM AUTHOR]

In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field T T ― —constructed out of the components of the stress-energy tensor—and its generalisations—built from higher-spin conserved currents. The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated. In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices—extensively analysed with the thermodynamic Bethe ansatz—provide the first step in the development of a bootstrap program. In this paper we present a systematic approach to computing matrix elements of operators in generalised T T ― -perturbed models, based on employing the standard form factor program. We show that for theories with diagonal scattering and certain types of fields the deformed form factors, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term. From these solutions, correlation functions can be obtained and their asymptotic properties studied. [ABSTRACT FROM AUTHOR]

We develop lattice eigenfunction equations of the lattice KdV equation, which are equations obeyed by auxiliary functions, or eigenfunctions, of the Lax pair of the lattice KdV equation. These equations are three-dimensionally consistent quad-equations, that are closely related to lattice equations in the Adler-Bobenko-Suris (ABS) classification. The connection between the H3(δ), Q1(δ), Q2 and Q3(δ) equations in the ABS classification and the lattice eigenfunction equations is explicitly showed. In particular, we provide a natural interpretation of the δ term in those equations. This can be understood as 'interactions' between the eigenfunctions. Other integrable properties of the eigenfunction equations, such as exact solutions, discrete zero curvature conditions are also provided. We believe that the approach presented in this paper can be used as a means to search for integrable lattice equations.> [ABSTRACT FROM AUTHOR]

In this paper, we consider the multi-dimensional distributed-order time-fractional diffusion equation with the unit density function. We introduce the new Volterra–Bessel function and give the integral representations of fundamental solutions of equations in terms of this function in the whole- and half-space. The fractional moments of fundamental solutions are also provided in the higher dimensions using the Mellin transforms. We further apply steepest descent method to find the asymptotic behaviors of solutions using the Schläfli integral of the Volterra–Bessel function. In this respect, we study the asymptotic analysis of the Volterra–Bessel function with the large parameters, and subsequently obtain the asymptotic behaviors of fundamental solutions with a discussion on the large space variable, large time variable, higher dimensions and small diffusivity constant. [ABSTRACT FROM AUTHOR]

Allee effect in models in interacting species of predator prey system has great significance in ecological context. Allee effect plays crucial role in population dynamics in ecology, where it is the challenging fact that per capita population growth rate is positively dependent on the population density of a species. In this paper, we inspect the famous Hastings and Powell (HP) (Hastings and Powell 1991 Ecology 72 896–903) model incorporating component Allee effect on top predator's reproduction. We analyse the updated model with the help of both analytical and numerical phenomena. Considering cost of Allee effect, half-saturation constant of prey as the key parameters, the Hopf bifurcations are also analysed. The directions of Hopf bifurcations at the critical values of Allee parameter and half-saturation constant of prey are studied theoretically by using normal form theory introduced by Hassard et al (1981 Theory and Applications of Hopf Bifurcation vol 41 (CUP Archive)). The formulated model indicates that the system demonstrates chaotic, periodic and stable dynamics in the variation of key parameters. The chaos can be controlled for proper application of the large values of parameter used as the cost of Allee effect and also for small values of the parameter used as the half saturation constant of prey population. The results of this study are applicable in the field of marine and wild ecosystem dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we establish a dynamical quantum state tomography framework. Under this framework, it is feasible to obtain complete knowledge of any unknown state of a d -level system via only one operator of a special type of positive operator-valued measure (POVM) in dimension d. We define a new channel, referred to as the time-dependent average channel. Utilizing this channel, we show that we can acquire a collection of projective operators that is informationally complete (IC) and thus obtain the corresponding informationally complete POVMs (IC-POVMs). Zauner conjectured that for any dimension d there exists a fiducial vector, such that all remaining d 2 − 1 elements of the desired symmetric informationally complete POVM (SIC-POVM) can be obtained by acting on said vector with unitary matrices representing elements of the Weyl-Heisenberg group. We show that under certain condition, it is possible to obtain infinite families of projective operators that are IC, and obtain infinite families of corresponding IC-POVMs; otherwise, Zauner's conjecture is incorrect. We also show how to simulate a SIC-POVM on any unknown quantum state by using the time-dependent average channel. [ABSTRACT FROM AUTHOR]

Quantum entanglement plays a key role in quantum computation and quantum information processing. It is of great significance to find efficient and experimentally friend separability criteria to detect entanglement. In this paper, we firstly propose two easily used entanglement criteria based on matrix moments. The first entanglement criterion only uses the first two realignment moments of a density matrix. The second entanglement criterion is based on the moments related to the partially transposed matrix. By detailed examples we illustrate the effectiveness of these criteria in detecting entanglement. Moreover, we provide an experimentally measurable lower bound of concurrence based on these moments. Finally, we present both bipartite and genuine tripartite entanglement measures based on the moments of the reduced states. By detailed examples, we show that our entanglement measures characterize the quantum entanglement in a more fine ways than the existing measures. [ABSTRACT FROM AUTHOR]

Some generalizations of spin Sutherland models descend from 'master integrable systems' living on Heisenberg doubles of compact semisimple Lie groups. The master systems represent Poisson–Lie counterparts of the systems of free motion modeled on the respective cotangent bundles and their reduction relies on taking quotient with respect to a suitable conjugation action of the compact Lie group. We present an enhanced exposition of the reductions and prove rigorously for the first time that the reduced systems possess the property of degenerate integrability on the dense open subset of the Poisson quotient space corresponding to the principal orbit type for the pertinent group action. After restriction to a smaller dense open subset, degenerate integrability on the generic symplectic leaves is demonstrated as well. The paper also contains a novel description of the reduced Poisson structure and a careful elaboration of the scaling limit whereby our reduced systems turn into the spin Sutherland models. [ABSTRACT FROM AUTHOR]

Sampling with the generalised atmospheric Rosenbluth method (GARM) is a technique for estimating the distributions of lattice polymer models that has had some success in the study of linear polymers and lattice polygons. In this paper we will explain how and why such sampling appears not to be effective for many models of branched polymers. Analysing the algorithm on a simple binary tree, we argue that the fundamental issue is an inherent bias towards extreme configurations that is costly to correct with reweighting techniques. We provide a solution to this by applying uniform sampling methods to the atmospheres that are central to GARM. We caution that the ensuing computational complexity often outweighs the improvements gained. [ABSTRACT FROM AUTHOR]

In Alase et al (2022 J. Phys. A: Math. Theor. 55 244003), Alase et al wrote that 'the constraint of quasi-Hermiticity on observables' is not 'sufficient to extend the standard quantum theory' because 'such a system is equivalent to a standard quantum system.' Three addenda elucidating the current state of the art are found necessary. The first one concerns the project: in the related literature the original 'aim of extending standard quantum theory' has already been abandoned shortly after its formulation. The second comment concerns the method, viz., the study in 'the framework of general probabilistic theories' (GPT). It is noticed that a few other, mathematically consistent GPT-like theories are available. The authors do not mention, in particular, the progress achieved, under the quasi-Hermiticity constraint, in the approach using the effect algebras. We add that this approach already found its advanced realistic applications in the quasi-Hermitian models using the unbounded operators of observables acting in the infinite-dimensional Hilbert spaces. Thirdly, the 'intriguing open question' about 'what possible constraints, if any, could lead to such a meaningful extension' (in the future) is given an immediate tentative answer: the possibility is advocated that the desirable constraint could really be just the quasi-Hermiticity of the observables, provided only that one has in mind its recently developed non-stationary version. [ABSTRACT FROM AUTHOR]

In this paper we derive an explicit formula for the heat kernel of the asymmetric quantum Rabi model, a symmetry breaking generalization of the quantum Rabi model (QRM). The method described here is the extension of a recently developed method for the heat kernel of the QRM that uses the Trotter–Kato product formula instead of path integrals or stochastic methods. In addition to the heat kernel formula, we give applications including the explicit formula for the partition function and the Weyl law for the distribution of the eigenvalues, obtained from the corresponding spectral zeta function. [ABSTRACT FROM AUTHOR]

In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of the fact that the radial basis function is recovered when data is mapped to a complex Hilbert state represented by coherent states, non-linear coherent states can be considered as a natural generalisation of the associated kernels. In this paper, as an example of kernels based on non-linear coherent states, we propose kernel functions based on generalized hypergeometric functions, as orthogonal polynomial functions. The suggested kernel is implemented with the support vector machine (SVM) on two well known datasets (make_circles, and make_moons) and outperforms the baselines, even when the level of noise is high. In addition, we study the impact of the geometrical properties of the feature space, obtained by the non-linear coherent states, on the SVM classification task, by considering the Fubiniâ€"Study metric of the associated coherent states. [ABSTRACT FROM AUTHOR]

WZW models based on super Lie algebras play an important role for the description of string theory on AdS spaces. In particular, for the case of AdS 3 × S 3 with pure NS–NS flux the super Lie algebra of psu (1 , 1 | 2) k appears in the hybrid formalism, and higher dimensional AdS spaces can be described in terms of related supergroup cosets. In this paper we study the WZW models based on u (2 | 2) 1 and psu (2 | 2) 1 that may play a role for the worldsheet theory that is dual to free super Yang–Mills in 4D. [ABSTRACT FROM AUTHOR]

In this paper we study coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of coisotropic reduction is motivated by the fact that these dynamics can always be interpreted as Lagrangian or Legendrian submanifolds. Furthermore, Lagrangian or Legendrian submanifolds can be reduced by a coisotropic one. [ABSTRACT FROM AUTHOR]

Interaction-round the face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable IRF models, i.e. the models the Boltzmann weights of which satisfy the quantum Yang–Baxter equation, are of particular interest. In this paper, we investigate trigonometric Boltzmann weights of integrable IRF models. By using an ansatz proposed by one of the authors in some previous works, the Boltzmann weights of the restricted IRF models based on the affine Lie algebras su (2) k and su (3) k are computed for fundamental and adjoint representations for some fixed levels k. New solutions for the Boltzmann weights are obtained. We also study the vertex-IRF correspondence in the context of an unrestricted IRF model based on su (3) k (for general k) and discuss how it can be used to find Boltzmann weights in terms of the quantum R ^ matrix when the adjoint representation defines the admissibility conditions. [ABSTRACT FROM AUTHOR]

A class of left bialgebroids whose underlying algebra A ♯ H is a smash product of a bialgebra H with a braided commutative Yetter–Drinfeld H -algebra A has recently been studied in relation to models of field theories on noncommutative spaces. In Borowiec and Pachoł (2017 J. Phys. A: Math. Theor. 50 055205) a proof has been presented that the bialgebroid A F ♯ H F where HF and AF are the twists of H and A by a Drinfeld 2-cocycle F = ∑ F 1 ⊗ F 2 is isomorphic to the twist of bialgebroid A ♯ H by the bialgebroid 2-cocycle ∑ 1 ♯ F 1 ⊗ 1 ♯ F 2 induced by F. They assume H is quasitriangular, which is reasonable for many physical applications. However the proof and the entire paper take for granted that the coaction and the prebraiding are both given by special formulas involving the R-matrix. There are counterexamples of Yetter–Drinfeld modules over quasitriangular Hopf algebras which are not of this special form. Nevertheless, the main result essentially survives. We present a proof with a general coaction and the correct prebraiding, and even without the assumption of quasitriangularity. [ABSTRACT FROM AUTHOR]

In a system of heterogeneous (Abelian) Kuramoto oscillators with random or 'frustrated' interactions, transitions from states of incoherence to partial synchronization were observed. These so-called volcano transitions are characterized by a change in the shape of a local field distribution and were discussed in connection with an oscillator glass. In this paper, we consider a different class of oscillators, namely a system of (non-Abelian) SU(2)-Lohe oscillators that can also be defined on the 3-sphere, i.e. an oscillator is generalized to be defined as a unit vector in four-dimensional Euclidean space. We demonstrate that such higher-dimensional Kuramoto models with reciprocal and nonreciprocal random interactions represented by a low-rank matrix exhibit a volcano transition as well. We determine the critical coupling strength at which a volcano-like transition occurs, employing an Ott–Antonsen ansatz. Numerical simulations provide additional validations of our analytical findings and reveal the differences in observable collective dynamics prior to and following the transition. Furthermore, we show that a system of unit 3-vector oscillators on the 2-sphere does not possess a volcano transition. [ABSTRACT FROM AUTHOR]

There are many processes in cell biology that can be modelled in terms of an actively switching particle. The continuous degrees of freedom of the particle evolve according to a hybrid stochastic differential equation whose drift term depends on a discrete internal or environmental state that switches according to a continuous time Markov chain. Examples include Brownian motion in a randomly switching environment, membrane voltage fluctuations in neurons, protein synthesis in gene networks, bacterial run-and-tumble motion, and motor-driven intracellular transport. In this paper we derive generalized Dean–Kawasaki (DK) equations for a population of actively switching particles, either independently switching or subject to a common randomly switching environment. In the case of a random environment, we show that the global particle density evolves according to a hybrid DK equation. Averaging with respect to the Gaussian noise processes in the absence of particle interactions yields a hybrid partial differential equation for the one-particle density. We use this to show how a randomly switching environment induces statistical correlations between the particles. We also discuss methods for handling the moment closure problem for interacting particles, including dynamical density functional theory and mean field theory. We then develop the analogous constructions for independently switching particles. In order to derive a DK equation, we introduce a discrete set of global densities that are indexed by the single-particle internal states, and take expectations with respect to the switching process. However, the resulting DK equation is no longer closed when particle interactions are included. We conclude by deriving Martin–Siggia–Rose–Janssen–de Dominicis path integrals for the global density equations in the absence of interactions, and relate this to recent field theoretic studies of Brownian gases and run-and-tumble particles. [ABSTRACT FROM AUTHOR]

This paper focuses on characterizing the energy profile along pathways connecting different regions of configuration space in the context of a prototypical glass model, the pure spherical p -spin model with p = 3. The study investigates pairs of stationary points (local minima or rank-1 saddles), analyzing the energy profile along geodesic paths and comparing them with 'perturbed' pathways correlated to the landscape curvature. The goal is to assess the extent to which information from the local Hessian matrices around stationary points can identify paths with lower energy barriers. Surprisingly, unlike findings in other systems, the direction of softest local curvature is not a reliable predictor of low-energy paths, except in the case in which the direction of softest curvature corresponds to an isolated mode of the Hessian. However, other information encoded in the local Hessian does allow the identification of pathways associated with lower energy barriers. We conclude commenting on implications for the system's activated dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we use graph theory to solve wave scattering problems in the discrete dipole approximation. As a key result of this work, in the presence of active scatterers, we present a systematic method to find arbitrary large-order zero eigenvalue exceptional points (EPs). This is achieved by solving a set of non-linear equations that we interpret, in a graph theory picture, as vanishing sums of scattering events. We then show how the total field of the system responds to parameter perturbations at the EP. Finally, we investigate the sensitivity of the power output to imaginary perturbation in the design frequency. This perturbation can be employed to trade sensitivity for a different dissipation balance of the system. The purpose of the results of this paper is manifold. On the one hand, we aim to shed light on the link between graph theory and wave scattering. On the other hand, the results of this paper find application in all those settings where zero eigenvalue EPs play a unique role like in coherent perfect absorption structures. [ABSTRACT FROM AUTHOR]

We revisit the dimensionally deconstructed scalar quantum electrodynamics and consider the (Euclidean) propagator of the scalar field in the model. Although we have previously investigated the one-loop effect in this model by obtaining the usual heat kernel trace, we adopt discrete proper-time heat kernels in this paper and aim to construct the modified propagator, which has improved behaviors in the ultraviolet region, by changing the range of sum of the discrete heat kernels. [ABSTRACT FROM AUTHOR]

The d -dimensional Ornstein–Uhlenbeck process (OUP) describes the trajectory of a particle in a d -dimensional, spherically symmetric, quadratic potential. The OUP is composed of a drift term weighted by a constant θ ⩾ 0 and a diffusion coefficient weighted by σ > 0. In the absence of drift (i.e. θ = 0), the OUP simply becomes a standard Brownian motion (BM). This paper is concerned with estimating the mean first-exit time (MFET) of the OUP from a ball of finite radius L for large d ≫ 0. We prove that, asymptotically for d → ∞ , the OUP takes (on average) no longer to exit than BM. In other words, the mean-reverting drift of the OUP (scaled by θ ⩾ 0) has asymptotically no effect on its MFET. This finding might be surprising because, for small d ∈ N , the OUP exit time is significantly larger than BM by a margin that depends on θ. As it allows for the drift to be ignored, it might simplify the analysis of high-dimensional exit-time problems in numerous areas. Finally, our short proof for the non-asymptotic MFET of OUP, using the Andronov–Vitt–Pontryagin formula, might be of independent interest. [ABSTRACT FROM AUTHOR]

The authors replies to the comment made by Yang and Zhou (2024 J. Phys. A: Math. Theor.) on his 2015 paper entitled 'Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras' (Jacobsen 2015 J. Phys. A: Math. Theor. 48 454003). [ABSTRACT FROM AUTHOR]

We consider the jellium model of N particles on a line confined in an external harmonic potential and with a pairwise one-dimensional Coulomb repulsion of strength α > 0. Using a Coulomb gas method, we study the statistics of s = (1 / N) ∑ i = 1 N f (x i) where f (x), in principle, is an arbitrary smooth function. While the mean of s is easy to compute, the variance is nontrivial due to the long-range Coulomb interactions. In this paper we demonstrate that the fluctuations around this mean are Gaussian with a variance Var (s) ≈ b / N 3 for large N. In this paper, we provide an exact compact formula for the constant b = 1 / (4 α) ∫ − 2 α 2 α [ f ′ (x) ] 2 d x. In addition, we also calculate the full large deviation function characterizing the tails of the full distribution P (s , N) for several different examples of f (x). Our analytical predictions are confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

Light-front formulations of quantum field theories have many advantages for computing electroweak matrix elements of strongly interacting systems and other quantities that are used to study hadronic structure. The theory can be formulated in Hamiltonian form so non-perturbative calculations of the strongly interacting initial and final states are in principle reduced to linear algebra. These states are needed for calculating parton distribution functions and other types of distribution amplitudes that are used to understand the structure of hadrons. Light-front boosts are kinematic transformations so the strongly interacting states can be computed in any frame. This is useful for computing current matrix elements involving electroweak probes where the initial and final hadronic states are in different frames related by the momentum transferred by the probe. Finally in many calculations the vacuum is trivial so the calculations can be formulated in Fock space. The advantages of light front-field theory would not be interesting if the light-front formulation was not equivalent to the covariant or canonical formulations of quantum field theory. Many of the distinguishing properties of light-front quantum field theory are difficult to reconcile with canonical or covariant formulations of quantum field theory. This paper discusses the resolution of some of the apparent inconsistencies in canonical, covariant and light-front formulations of quantum field theory. The puzzles that will be discussed are (1) the problem of inequivalent representations (2) the problem of the trivial vacuum (3) the problem of ill-posed initial value problems (4) the problem of rotational covariance (5) the problem of zero modes and (6) the problem of spontaneously broken symmetries. [ABSTRACT FROM AUTHOR]

Brownian motion (BM) is the archetypal model of regular diffusion. BM is a Gaussian and Markov process, whose increments are stationary, and whose non-overlapping increments are independent. Elevating from regular diffusion to anomalous diffusion, fractional Brownian motion (FBM) and scaled Brownian motion (SBM) are arguably the two most popular Gaussian anomalous-diffusion models. Each of these two models maintains some BM properties, abandons other, and displays certain anomalous behaviors. This paper explores a Gaussian anomalous-diffusion model— Power Brownian Motion (PBM)—that is attained by a coupled amplitudal and temporal 'tinkering' with BM. The PBM model combines 'the better of FBM and SBM'. Indeed, as FBM, PBM displays the anomalous behaviors of persistence and anti-persistence. And, as SBM, PBM is a Markov process that displays the anomalous behaviors of aging and anti-aging. On their own, neither FBM nor SBM can provide the 'features package' that PBM provides. The PBM 'features package' on the one hand, and its simple construction on the other hand, render PBM a compelling anomalous-diffusion model. [ABSTRACT FROM AUTHOR]

The pretty good transmission (PGT) scenario implies that the probability of sending one excitation from one extreme of a spin chain to the other can reach values arbitrarily close to the unity just by waiting a time long enough. The conditions that ensure the appearance of this scenario are known for chains with different interactions and lengths. Sufficient conditions for the presence of PGT depend on the spectrum of the Hamiltonian of the spin chain. Some works suggest that the time t ɛ at which the PGT takes place scales as 1 / (| ε | ) f (N) , where ɛ is the difference between the probability that a single excitation propagates from one extreme of the chain to the other and the unity, while f (N) is an unknown function of the chain length. In this paper, we show that the exponent is not a simple function of the chain length but a power law of the number of linearly independent irrational eigenvalues of the one-excitation block of the Hamiltonian that enter into the expression of the probability of transmission of one excitation. We explicitly provide examples of a chain showing that the exponent changes when the couplings between the spins change while the length remains fixed. For centrosymmetric spin chains the exponent is at most N / 2. [ABSTRACT FROM AUTHOR]