Search

We recognize certain special hypergeometric motives, related to and inspired by the discoveries of Ramanujan more than a century ago, as arising from Asai $L$-functions of Hilbert modular forms., Comment: 18 pages

We present a basis of eigenvectors for the graph building operators acting along the mirror channel of planar fishnet Feynman integrals in $d$-dimensions. The eigenvectors of a fishnet lattice of length $L$ depend on a set of $L$ quantum numbers $(u_k,l_k)$, each associated with the rapidity and bound-state index of a lattice excitation. Each excitation is a particle in $(1+1)$-dimensions with $O(d)$ internal symmetry, and the wave-functions are formally constructed with a set of creation/annihilation operators that satisfy the corresponding Zamolodchikovs-Faddeev algebra. These properties are proved via the representation - new to our knowledge - of the matrix elements of the fused R-matrix with $O(d)$ symmetry as integral operators on the functions of two spacetime points. The spectral decomposition of a fishnet integral we achieved can be applied to the computation of Basso-Dixon integrals in higher dimensions., 51 pages, 19 figures

We revisit the Riemann-Hilbert problem determined by Donaldson-Thomas invariants for the resolved conifold and for other small crepant resolutions. While this problem can be recast as a system of TBA-type equations in the conformal limit, solutions are ill-defined due to divergences in the sum over infinite trajectories in the spectrum of D2-D0-brane bound states. We explore various prescriptions to make the sum well-defined, show that one of them reproduces the existing solution in the literature, and identify an alternative solution which is better behaved in a certain limit. Furthermore, we show that a suitable asymptotic expansion of the $\tau$ function reproduces the genus expansion of the topological string partition function for any small crepant resolution. As a by-product, we conjecture new integral representations for the triple sine function, similar to Woronowicz' integral representation for Faddeev's quantum dilogarithm., Comment: 25+14 pages; added proof for integral representation of the double sine function and a similar conjecture for the triple sine; version accepted for publication in Annales Henri Poincar\'e

International audience; This paper presents a model of capital accumulation for a large number of heterogenous producer-consumers in an exchange space in which interactions depend on agents' positions. Each agent is described by his production, consumption, stock of capital, as well as the position he occupies in this abstract space. Each agent produces one differentiated good whose price is fixed by market clearing conditions. Production functions are Cobb-Douglas, and capital stocks follow the standard capital accumulation dynamic equation. Agents consume all goods but have a preference for goods produced by their closest neighbors. Agents in the exchange space are subject both to attractive and repulsive forces. Exchanges drive agents closer, but beyond a certain level of proximity, agents will tend to crowd out more distant agents. The present model uses a formalism based on statistical field theory developed earlier by the authors. This approach allows the analytical treatment of economic models with an arbitrary number of agents, while preserving the system's interactions and complexity at the individual level. Our results show that the dynamics of capital accumulation and agents' position in the exchange space are correlated. Interactions in the exchange space induce several phases of the system. A first phase appears when attractive forces are limited. In this phase, an initial central position in the exchange space favors capital accumulation in average and leads to a higher level of capital, while agents far from the center will experience a slower accumulation process. A high level of initial capital drives agents towards a central position, i.e. improve the terms of their exchanges: they experience a higher demand and higher prices for their product. As usual, high capital productivity favors capital accumulation, while higher rates of capital depreciation reduce capital stock. In a second phase, attractive forces are predominant. The previous results remain, but an additional threshold effect appears. Even though no restriction was imposed initially on the system, two types of agents emerge, depending on their initial stock of capital. One type of agents will remain above the capital threshold and occupy and benefit from a central position. The other type will remain below the threshold, will not be able to break it and will remain at the periphery of the exchange space. In this phase, capital distribution is less homogenous than in the first phase.

International audience; In this article, we develop an extension of the Fourier transform solution method in order to solve conduction equation with nonperiodic boundary conditions (BC). The periodic Lippmann-Schwinger equation for porous materials is extended to the case of non-periodicity with relevant source terms on the boundary. The method is formulated in Fourier space based on the temperature as unknown, using the exact periodic Green function and form factors to describe the boundaries. Different types of BC: flux, temperature, mixed and combined with periodicity can be treated by the method. Numerical simulations show that the method does not encounter convergence issues due to the infinite contrast and yields accurate results for both local fields and effective conductivity.

The centralizer of the image of the diagonal embedding of $U_q(\mathfrak{sl}_2)$ in the tensor product of three irreducible representations is examined in a Schur-Weyl duality spirit. The aim is to offer a description in terms of generators and relations. A conjecture in this respect is offered with the centralizers presented as quotients of the Askey-Wilson algebra. Support for the conjecture is provided by an examination of the representations of the quotients. The conjecture is also shown to be true in a number of cases thereby exhibiting in particular the Temperley-Lieb, Birman-Murakami-Wenzl and one-boundary Temperley-Lieb algebras as quotients of the Askey-Wilson algebra., 26 pages

A bipolar charge transport model with two levels of traps (shallow and deep traps) is employed to describe and investigate the dynamic behavior of the space charge in low-density polyethylene (LDPE). This kind of model requires some initial experimental conditions alongside a set of parameters. An optimization method is used in order to provide the best precision for model parameters. Furthermore, the sensitivity of these parameters has been analyzed using an approach based on Sobol's method. In essence, this paper proposes a specific protocol that contributes to producing a global set of parameters able to provide the best approximate fit between experimental and simulated results. Net charge density is measured by the pulse electro-acoustic method (PEA) along with what is known as external charging current measurements. The simulated data are obtained by a bipolar charge transport model, which is developed for low-sensity polyethylene.

For a complex finite-dimensional simple Lie algebra $\mathfrak{g}$, we introduce the notion of Q-datum, which generalizes the notion of a Dynkin quiver with a height function from the viewpoint of Weyl group combinatorics. Using this notion, we develop a unified theory describing the twisted Auslander-Reiten quivers and the twisted adapted classes introduced in [O.-Suh, J. Algebra, 2019] with an appropriate notion of the generalized Coxeter elements. As a consequence, we obtain a combinatorial formula expressing the inverse of the quantum Cartan matrix of $\mathfrak{g}$, which generalizes the result of [Hernandez-Leclerc, J. Reine Angew. Math., 2015] in the simply-laced case. We also find several applications of our combinatorial theory of Q-data to the finite-dimensional representation theory of the untwisted quantum affine algebra of $\mathfrak{g}$. In particular, in terms of Q-data and the inverse of the quantum Cartan matrix, (i) we give an alternative description of the block decomposition results due to [Chari-Moura, Int. Math. Res. Not., 2005] and [Kashiwara-Kim-O.-Park, arXiv:2003.03265], (ii) we present a unified (partially conjectural) formula of the denominators of the normalized R-matrices between all the Kirillov-Reshetikhin modules, and (iii) we compute the invariants $\Lambda(V,W)$ and $\Lambda^\infty(V, W)$ introduced in [Kashiwara-Kim-O.-Park, Compos. Math., 2020] for each pair of simple modules $V$ and $W$., Comment: v2: 52 pages, a considerable revision. v3 : 52 pages, minor revision, final version

International audience; We prove three fundamental properties of counting holomorphic cylinders in logCalabi–Yau surfaces: positivity, integrality and the gluing formula. Positivity andintegrality assert that the numbers of cylinders, defined via virtual techniques, are infact nonnegative integers. The gluing formula roughly says that cylinderscan be glued together to form longer cylinders, and the number of longercylinders equals the product of the numbers of shorter cylinders. Our approachuses Berkovich geometry, tropical geometry, deformation theory and theideas in the proof of associativity relations of Gromov–Witten invariants byMaxim Kontsevich. These three properties provide evidence for a conjecturalrelation between counting cylinders and the broken lines of Gross, Hacking andKeel.

We study 4dN = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories., SCOPUS: ar.j, info:eu-repo/semantics/published

In the study of integrable non-linear $\sigma$-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central role. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function., Comment: v1: 1+47 pages, Latex, v2: JHEP version

Consider the Coulomb potential $-\mu\ast|x|^{-1}$ generated by a non-negative finite measure $\mu$. It is well known that the lowest eigenvalue of the corresponding Schr\"odinger operator $-\Delta/2-\mu\ast|x|^{-1}$ is minimized, at fixed mass $\mu(\mathbb{R}^3)=\nu$, when $\mu$ is proportional to a delta. In this paper we investigate the conjecture that the same holds for the Dirac operator $-i\alpha\cdot\nabla+\beta-\mu\ast|x|^{-1}$. In a previous work on the subject we proved that this operator is self-adjoint when $\mu$ has no atom of mass larger than or equal to 1, and that its eigenvalues are given by min-max formulas. Here we consider the critical mass $\nu_1$, below which the lowest eigenvalue does not dive into the lower continuum spectrum for all $\mu\geq0$ with $\mu(\mathbb{R}^3), Comment: Final version to appear in Proc. London Math. Soc

Quantum trajectories are Markov processes that describe the time-evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they are defined as solutions of the so-called "Stochastic Schr\"odinger Equations", which are nonlinear stochastic differential equations driven by Poisson and Wiener processes. This paper is devoted to the study of the invariant measures of quantum trajectories. Particularly, we prove that the invariant measure is unique under an ergodicity condition on the mean time evolution, and a "purification" condition on the generator of the evolution. We further show that quantum trajectories converge in law exponentially fast towards this invariant measure. We illustrate our results with examples where we can derive explicit expressions for the invariant measure., Comment: As accepted in Ann. Henri Poincar\'e

Recently, a universal formula for a non-holomorphic modular completion of the generating functions of refined BPS indices in various theories with $N=2$ supersymmetry has been suggested. It expresses the completion through the holomorphic generating functions of lower ranks. Here we show that for $U(N)$ Vafa-Witten theory on Hirzebruch and del Pezzo surfaces this formula can be used to extract the holomorphic functions themselves, thereby providing the Betti numbers of instanton moduli spaces on such surfaces. As a result, we derive a closed formula for the generating functions and their completions for all $N$. Besides, our construction reveals in a simple way instances of fiber-base duality, which can be used to derive new non-trivial identities for generalized Appell functions. It also suggests the existence of new invariants, whose meaning however remains obscure., 26+25 pages, 1 figure; a clarification added; numerous improvements of the presentation, version accepted for publication in Commun.Num.Theor.Phys; references updated

We consider multiverses as time-amalgamated multiply warped products of Lorentzian (Einstein) manifolds. We define the Local Multiverse as timely-connected component of our physical (3+1)-spacetime. It is a collection of ``parallel universes" with (mutually) synchronized timelines. Metaphysical considerations suggest that the Local Multiverse could be an extremely complex agglomeration with, at least, several hundred parallel universes in the Solar neighbourhood (and many thousands in galaxy bulks). In this paper we study a simplified time-almagamated globally hyperbolic model. Our picture implies the multiversality of elementary particles which are, actually, transcosmic (super)strings with multiple endpoints on parallel universes considered as D-branes., Comment: 7 pages, 1 figure

We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders. Numerical analysis shows that these conditions are incompatible unless the critical exponents take particular values, or more precisely that they must belong to a small island in the parameter space., Comment: 16 pages, 3 figures, accepted for publication by C.R.Physique

Using the hyperboloidal foliation method, we establish stability results for a coupled wave-Klein-Gordon system with quadratic nonlinearities. In particular, we investigate quadratic wave-Klein-Gordon interactions in which there are no derivatives on the massless wave component. By combining hyperboloidal energy estimates with appropriate transformations of our fields, we are able to show global existence of solutions for sufficiently small initial data., Comment: Published version. Both authors are grateful to the anonymous referees, whose comments improve a lot on the presentation and the precision of the article

Whenever available, refined BPS indices provide considerably more information on the spectrum of BPS states than their unrefined version. Extending earlier work on the modularity of generalized Donaldson-Thomas invariants counting D4-D2-D0 brane bound states in type IIA strings on a Calabi-Yau threefold $\mathfrak{Y}$, we construct the modular completion of generating functions of refined BPS indices supported on a divisor class. Although for compact $\mathfrak{Y}$ the refined indices are not protected, switching on the refinement considerably simplifies the construction of the modular completion. Furthermore, it leads to a non-commutative analogue of the TBA equations, which suggests a quantization of the moduli space consistent with S-duality. In contrast, for a local CY threefold given by the total space of the canonical bundle over a complex surface $S$, refined BPS indices are well-defined, and equal to Vafa-Witten invariants of $S$. Our construction provides a modular completion of the generating function of these refined invariants for arbitrary rank. In cases where all reducible components of the divisor class are collinear (which occurs e.g. when $b_2(\mathfrak{Y})=1$, or in the local case), we show that the holomorphic anomaly equation satisfied by the completed generating function truncates at quadratic order. In the local case, it agrees with an earlier proposal by Minahan et al for unrefined invariants, and extends it to the refined level using the afore-mentioned non-commutative structure. Finally, we show that these general predictions reproduce known results for $U(2)$ and $U(3)$ Vafa-Witten theory on $\mathbb{P}^2$, and make them explicit for $U(4)$., Comment: 34+24 pages, 6 figures; misprints fixed

We construct three nonequivalent gradings in the algebra $$D_4\simeq so(8)$$ . The first is the standard grading obtained with the Coxeter automorphism $$C_1=S_{\alpha_2}S_{\alpha_1}S_{\alpha_3}S_{\alpha_4}$$ using its dihedral realization. In the second, we use $$C_2=C_1R$$ , where $$R$$ is the mirror automorphism. The third is $$C_3=S_{\alpha_2}S_{\alpha_1}T$$ , where $$T$$ is the external automorphism of order 3. For each of these gradings, we construct a basis in the corresponding linear subspaces $$ \mathfrak{g} ^{(k)}$$ , the orbits of the Coxeter automorphisms, and the related Lax pairs generating the corresponding modified Korteweg–de Vries (mKdV) hierarchies. We find compact expressions for each of the hierarchies in terms of recursion operators. Finally, we write the first nontrivial mKdV equations and their Hamiltonians in explicit form. For $$D_4^{(1)}$$ , these are in fact two mKdV systems because the exponent 3 has the multiplicity two in this case. Each of these mKdV systems consists of four equations of third order in $$ \partial _x$$ . For $$D_4^{(2)}$$ , we have a system of three equations of third order in $$ \partial _x$$ . For $$D_4^{(3)}$$ , we have a system of two equations of fifth order in $$ \partial _x$$ .

In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e. imposing an ultraviolet cutoff in momentum space) and with tolerance relations which provide a coarse grain approximation of geometric spaces at a finite resolution. In our new approach the traditional role played by $C^*$-algebras is taken over by operator systems. As part of the techniques we treat $C^*$-envelopes, dual operator systems and stable equivalence. We define a propagation number for operator systems, which we show to be an invariant under stable equivalence and use to compare approximations of the same space. We illustrate our methods for concrete examples obtained by spectral truncations of the circle. These are operator systems of finite-dimensional Toeplitz matrices and their dual operator systems which are given by functions in the group algebra on the integers with support in a fixed interval. It turns out that the cones of positive elements and the pure state spaces for these operator systems possess a very rich structure which we analyze including for the algebraic geometry of the boundary of the positive cone and the metric aspect i.e. the distance on the state space associated to the Dirac operator. The main property of the spectral truncation is that it keeps the isometry group intact. In contrast, if one considers the other finite approximation provided by circulant matrices the isometry group becomes discrete, even though in this case the operator system is a $C^*$-algebra. We analyze this in the context of the finite Fourier transform. The extension of noncommutative geometry to operator systems allows one to deal with metric spaces up to finite resolution by considering the relation $d(x,y), Comment: 46 pages, 5 figures. Version to appear in Commun. Math. Phys

Garay-Avenda��o \& Zamboni-Rached (2014) defined two classes of axisymmetric solutions of the free Maxwell equations. We prove that the linear combinations of these two classes of solutions cover all totally propagating time-harmonic axisymmetric free Maxwell fields -- and hence, by summation on frequencies, all totally propagating axisymmetric free Maxwell fields. It provides an explicit representation for these fields. This will be important, e.g., to have the interstellar radiation field in a disc galaxy modelled as an exact solution of the free Maxwell equations. Keywords: Maxwell equations; axial symmetry; exact solutions; electromagnetic duality, 17 pages. Journal version is open access, see DOI below

International audience; In this work, oxidation mechanisms were studied in fine-grained (FG) and coarse-grained (CG) Ti2AlC bulk samples. Results showed that the oxidation kinetics are controlled by the grain size of Ti2AlC. Bigger are the grains, faster is the oxidation. A dense and protective Al2O3 layer forms at the surface of FG-Ti2AlC samples while for the CG-Ti2AlC samples, a thick TiO2 layer forms on top of a discontinuous Al2O3. CG-Ti2AlC was observed to simultaneously transform into Ti3AlC2 and TiC instead of being directly transformed into TiC. This transformation result in the following crystallographically sandwich-like structure: (0001) Ti2AlC // (0001) Ti3AlC2 // (111) TiC. The volume shrinkage associated to this transformation produces elongated holes that are partially filled by α-Al2O3. The stress caused by the volume shrinkage generates cracks at the surface, which makes the oxygen inwards diffusion easier and thus worsens the oxidation resistance the CG-Ti2AlC bulk.

International audience; The delamination processes occurring in chromia scales formed on Ni-30Cr and Fe-47Cr alloys were studied. Delamination is the result of the competition between growth stresses evolution during heating, thermal stresses during cooling, and stress release phenomena, leading to high residual stress in the oxide film. Delamination in chromia has been found to occur due to type and amount of residual stresses generated at the end of heating-induced chromia growth and subsequent cooling-induced differential shrinkage. The mapping of the residual stresses in the oxide films at the microscopic scale around the delaminations allow to classify the latter into three different groups: buckles of Type 1, buckles of Type 2, and spalls. Using the stress relaxation magnitude, an assessment of the interfacial toughness of the metal/oxide systems was carried out, thanks to the buckling and crack propagation theory in the oxide. From the value obtained, microscopic observations, and the residual stress maps, a diagram describing the spalling of the buckles for chromia scales is proposed, as well as the delamination maps of Fe-47Cr/Cr2O3 and Ni-30Cr/Cr2O3 systems specifying the conditions of existence of the obtained delamination features.

We consider an elastic manifold of internal dimension $d$ and length $L$ pinned in a $N$ dimensional random potential and confined by an additional parabolic potential of curvature $\mu$. We are interested in the mean spectral density $\rho(\lambda)$ of the Hessian matrix $K$ at the absolute minimum of the total energy. We use the replica approach to derive the system of equations for $\rho(\lambda)$ for a fixed $L^d$ in the $N \to \infty$ limit extending $d=0$ results of our previous work. A particular attention is devoted to analyzing the limit of extended lattice systems by letting $L\to \infty$. In all cases we show that for a confinement curvature $\mu$ exceeding a critical value $\mu_c$, the so-called "Larkin mass", the system is replica-symmetric and the Hessian spectrum is always gapped (from zero). The gap vanishes quadratically at $\mu\to \mu_c$. For $\mu, Comment: 44 pages, 5 figures

We consider the Klein-Gordon equation on asymptotically anti-de Sitter spacetimes subject to Neumann or Robin (or Dirichlet) boundary conditions, and prove propagation of singularities along generalized broken bicharacteristics. The result is formulated in terms of conormal regularity relative to a twisted Sobolev space. We use this to show the uniqueness, modulo regularising terms, of parametrices with prescribed b-wavefront set. Furthermore, in the context of quantum fields, we show a similar result for two-point functions satisfying a holographic Hadamard condition on the b-wavefront set., Comment: 65 pages

International audience; Fatigue crack nucleation in crystalline materials typically develops due to highly localized cyclic slip. During a fatigue cycle, reverse slip differs locally from slip in the forward direction particularly in precipitate-containing materials such as superalloys. In this paper we report the first direct measurements of irreversibility at the scale of individual slip bands by high-resolution digital image correlation (DIC) in a polycrystalline nickel-based superalloy. Quantitative measurements of the slip irreversibility are challenging for regions of material that have a size that captures the microstructure and its variability. High spatial resolution at the nanometer scale during experimental measurements is needed to observe slip localization during deformation. Moreover, large fields are also needed to obtain the material response over statistically representative populations of microstructural configurations. Recently, high resolution scanning electron microscope (SEM) digital image correlation (DIC) has been extended for quantitative analysis of discontinuities induced by slip events using the Heaviside-DIC method. This novel method provides quantitative measurements of slip localization at the specimen surface. In this paper, the Heaviside-DIC method is used to measure slip irreversibility and plastic strain accumulation in a nickel-based superalloy. The method detects bands with high levels of irreversibility early in cycling that ultimately form fatigue cracks upon further cycling. The local microstructural configurations that induce large amounts of plasticity and slip irreversibility are correlated to crack nucleation locations.

We compute the information theoretic von Neumann entropy of the state associated to the fermionic second quantization of a spectral triple. We show that this entropy is given by the spectral action of the spectral triple for a specific universal function. The main result of our paper is the surprising relation between this function and the Riemann zeta function. It manifests itself in particular by the values of the coefficients $c(d)$ by which it multiplies the $d$ dimensional terms in the heat expansion of the spectral triple. We find that $c(d)$ is the product of the Riemann xi function evaluated at $-d$ by an elementary expression. In particular $c(4)$ is a rational multiple of $\zeta(5)$ and $c(2)$ a rational multiple of $\zeta(3)$. The functional equation gives a duality between the coefficients in positive dimension, which govern the high energy expansion, and the coefficients in negative dimension, exchanging even dimension with odd dimension., Comment: 15 pages

International audience; We extend the notion of (branched) holomorphic Cartan geometry on a complex manifold to the context of Sasakian manifolds. Branched holomorphic Cartan geometries on Sasakian Calabi–Yau manifolds are investigated in particular.

We consider a problem of stability of a membrane of an infinite span and a finite chord length that is submerged in a uniform flow of finite depth with free surface. In the shallow water approximation, Nemtsov (1985) has shown that an infinite-chord membrane is susceptible to flutter instability due to excitation of long gravity waves on the free surface if the velocity of the flow exceeds the phase velocity of the waves and placed this phenomenon into the general physical context of the anomalous Doppler effect. In the present work we derive a full nonlinear eigenvalue problem for an integro-differential equation in the case of the finite-chord Nemtsov membrane in the finite-depth flow. In the shallow- and deep water limits we develop a perturbation theory in the small added mass ratio parameter acting as an effective dissipation parameter in the system, to find explicit analytical expressions for the frequencies and the growth rates of the membrane modes coupled to the surface waves. This result reveals a new intricate pattern of instability pockets in the parameter space and allows for its analytical description. The case of an arbitrary depth flow with free surface requires numerical solution of a new non-polynomial nonlinear eigenvalue problem. We propose an original approach combining methods of complex analysis and residue calculus, Galerkin discretization, Newton method and parallelization techniques implemented in MATLAB to produce high-accuracy stability diagrams within an unprecedentedly wide range of system's parameters. We believe that the Nemtsov membrane appears to play the same paradigmatic role for understanding radiation-induced instabilities as the famous Lamb oscillator coupled to a string has played for understanding radiation damping.

We report anomalous heating in a colloidal system, the first observation of the inverse Mpemba effect, where an initially cold system heats up faster than an identical warm system coupled to the same thermal bath. For an overdamped, Brownian colloidal particle moving in a tilted double-well potential, we find a non-monotonic dependence of the heating times on the initial temperature of the system, as predicted by an eigenfunction expansion of the associated Fokker-Planck equation. By carefully tuning parameters, we also observe a "strong" version of anomalous heating, where a cold system heats up exponentially faster than systems prepared under slightly different conditions, Comment: 8 pages, 7 figures

We consider a time-dependent small quantum system weakly coupled to an environnement, whose effective dynamics we address by means of a Lindblad equation. We assume the Hamiltonian part of the Lindbladian is slowly varying in time and the dissipator part has small amplitude. We study the properties of the evolved state of the small system as the adiabatic parameter and coupling constant both go to zero, in various asymptotic regimes. In particular, we analyse the deviations of the transition probabilities of the small system between the instantaneous eigenspaces of the Hamiltonian with respect to their values in the purely Hamiltonian adiabatic setup, as a function of both parameters., Comment: Some arguments slightly extended, comments and references added, typos corrected. To appear in Commun. Math. Phys

The zeroth line bundle cohomology on Calabi-Yau three-folds encodes information about the existence of flop transitions and the genus zero Gromov-Witten invariants. We illustrate this claim by studying several Picard number 2 Calabi-Yau three-folds realised as complete intersections in products of projective spaces. Many of these manifolds exhibit certain symmetries on the Picard lattice which preserve the zeroth cohomology., 7 pages, 4 figures

Ocean eddies play an important role in the transport of heat, salt, nutrients, or pollutants. During a finite-time advection, the gradients of these tracers can increase or decrease, depending on a growth rate and the angle between flow gradients and initial tracer gradients. The growth rate is directly related to finite-time Lyapunov exponents. Numerous studies on mixing and/or tracer downscaling methods rely on satellite altimeter-derived ocean velocities. Filtering most oceanic small-scale eddies, the resulting smooth Eulerian velocities are often stationary during the characteristic time of tracer gradient growth. While smooth, these velocity fields are still locally misaligned, and thus uncorrelated, to many coarse-scale tracer observations amendable to downscaling [e.g., sea surface temperature (SST), sea surface salinity (SSS)]. Using finite-time advections, the averaged squared norm of tracer gradients can then only increase, with local growth rate independent of the initial coarse-scale tracer distribution. The key mixing processes are then only governed by locally uniform shears and foldings around stationary convective cells. To predict the tracer deformations and the evolution of their second-order statistics, an efficient proxy is proposed. Applied to a single velocity snapshot, this proxy extends the Okubo–Weiss criterion. For the Lagrangian-advection-based downscaling methods, it further successfully predicts the evolution of tracer spectral energy density after a finite time, and the optimal time to stop the downscaling operation. A practical estimation can then be proposed to define an effective parameterization of the horizontal eddy diffusivity. Significance Statement An analytical formalism is adopted to derive new exact and approximate relations that express the clustering of tracers transported by upper-ocean flows. This formalism bridges previous Eulerian and Lagrangian approaches. Accordingly, for slow and smooth upper-ocean flows, a rapid prognosis estimate can solely be performed using single-time velocity field observations. Well suited to satellite-altimeter measurements, it will help rapidly identify and monitor mixing regions occurring in the vicinity of ocean eddy boundaries.

Tensor network states are used extensively as a mathematically convenient description of physically relevant states of many-body quantum systems. Those built on regular lattices, i.e. matrix product states (MPS) in dimension 1 and projected entangled pair states (PEPS) in dimension 2 or higher, are of particular interest in condensed matter physics. The general goal of this work is to characterize which features of MPS and PEPS are generic and which are, on the contrary, exceptional. This problem can be rephrased as follows: given an MPS or PEPS sampled at random, what are the features that it displays with either high or low probability? One property which we are particularly interested in is that of having either rapidly decaying or long-range correlations. In a nutshell, our main result is that translation-invariant MPS and PEPS typically exhibit exponential decay of correlations at a high rate. We have two distinct ways of getting to this conclusion, depending on the dimensional regime under consideration. Both yield intermediate results which are of independent interest, namely: the parent Hamiltonian and the transfer operator of such MPS and PEPS typically have a large spectral gap. In all these statements, our aim is to get a quantitative estimate of the considered quantity (generic correlation length or spectral gap), which has the best possible dependency on the physical and bond dimensions of the random MPS or PEPS., 53 pages, 7 figures. v2: a bug in Section 4 has been fixed and a few changes have been made to the presentation. v3: published version

The second author constructed a topological ribbon Hopf algebra from the unrolled quantum group associated with the super Lie algebra $\mathfrak{sl}(2|1)$. We generalize this fact to the context of unrolled quantum groups and construct the associated topological ribbon Hopf algebras. Then we use such an algebra, the discrete Fourier transforms, a symmetrized graded integral and a modified trace to define a modified graded Hennings invariant. Finally, we use the notion of a modified integral to extend this invariant to empty manifolds and show that it recovers the CGP-invariant., 54 pages, 42 figures

International audience; We report an original and straightforward method for both optical and electrical characterization of vertical GaN nanowire arrays epitaxially grown on silicon through visible-infrared spectroscopic ellipsometry methods. For the initial purpose of adding new inputs to the ellipsometry model, focused ion-beam tomography experiments were conducted to extract porosity/depth profiles of these systems. To reproduce the optical free-carrier behavior in the infrared, the ellipsometric data acquired were fitted to an anisotropic Bruggeman model including Tauc-Lorentz and Drude oscillators, which enabled the determination of carrier density and in-grain mobility. The nice agreement of these results with those obtained by combining Hall effect measurements, X-ray diffraction, and transmission electron microscopy studies supported the validity of the proposed method, opening new horizons in the characterization of nanowire-based semiconducting layers.

International audience; The dynamics of ignition of premixed hydrogen–air from a hot glow plug were investigated in a combined experimental and numerical study. Surface temperatures during heating and at ignition were obtained from 2-color pyrometry, gas temperatures were measured by high-speed Mach–Zehnder interferometry, and far-field effects were captured by high-speed schlieren imaging. Numerical simulations considered detailed chemical kinetics and differential diffusion effects. In addition to the known cyclic (puffing) combustion phenomenon, singular ignition events (single puff) were observed near the lean flammability limit. Detailed analysis of the results of our numerical simulations reveal the existence of multiple combustion transients within the thermal boundary layer following the initial ignition event and, at late times, sustained chemical reaction within a thermal plume above the glow plug. The results have significant implications for ignition from hot surfaces within near-flammability limit mixtures, at the edge of plumes resulting from accidental release of hydrogen, or within the containments of nuclear power plants during severe accidents.

We construct quantum invariants of balanced sutured 3-manifolds with a $Spin^{c}$ structure out of an involutive (possibly non-unimodular) Hopf superalgebra $H$. If $H$ is the Borel subalgebra of $U_{q}(\mathfrak{gl}(1|1))$, we show that our invariant is computed via Fox calculus and it is a normalization of Reidemeister torsion. The invariant is defined via a modification of a construction of G. Kuperberg, where we use the $Spin^{c}$ structure to take care of the non-unimodularity of $H$ or $H^{*}$., Comment: 41 pages. Several changes: all Hopf algebra expressions are now written in tensor network notation, previous Sect. 3 is now part of Sect. 2, previous Subsections 5.1, 5.2 are now part of Sect. 3, arguments of Sect. 6 (previous Sect. 7) have been streamlined. To be published in Canadian Journal of Mathematics

International audience; We present a general formalism to model and calculate linear and nonlinear optical processes in composite systems,based on a graphical representation of light-matter interactions by loop diagrams associated with Feynmanrules. Through this formalism, we recover the usual second-order response of a simple system by drawing fourtimes fewer loop diagrams than doubled-sided ones. For composite systems, we introduce coupling Hamiltoniansbetween subsystems (for example, a molecule and a substrate), graphically represented by virtual bosons. In thisway, we enumerate all the diagrams describing the second-order response of the system and show how to selectthose relevant for the calculation of the molecular second-order hyperpolarizabilities under the influence of thesubstrate, including effective second-order contributions from the molecular third-order response. As it appliesto all nonlinear processes and an arbitrary number of interacting partners, this representation provides a generalframe for the calculation of the nonlinear response of arbitrarily complex systems.

We present a multi-scale topological analysis of the temperature fluctuation maps from the NPIPE and FFP10 datasets, invoking relative homology to account for the analysis in the presence of masks. For the topological components, we detect a $2.96\sigma$ deviation between the observations and simulations at $N = 128, FWHM = 80'$, for the FFP10 dataset. For the topological loops, we observe a high deviation between the observation and simulations in the number of loops at $FWHM = 320'$, at a low dimensionless threshold $\nu = -2.5$, for the NPIPE dataset. Under a Gaussian assumption, this would amount to a deviation of $\sim 4\sigma$ . However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by $600$ simulations. The FFP10 dataset, indicates a $2.77\sigma$ deviation at this resolution and threshold. The Euler characteristic reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the $\chi^2$ test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the $\chi^2$ test in the final interpretation, as it indicates the most conservative differences. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within $2\sigma$., Comment: 16 figures, 2 tables. Matches accepted version in A&A. arXiv admin note: substantial text overlap with arXiv:2101.02237

Isochrone potentials, as defined by Michel H\'enon in the fifties, are spherically symmetric potentials within which a particle orbits with a radial period that is independent of its angular momentum. Isochrone potentials encompass the Kepler and harmonic potential, along with many other. In this article, we revisit the classical problem of motion in isochrone potentials, from the point of view of Hamiltonian mechanics. First, we use a particularly well-suited set of action-angle coordinates to solve the dynamics, showing that the well-known Kepler equation and eccentric anomaly parametrisation are valid for any isochrone orbit (and not just Keplerian ellipses). Second, by using the powerful machinery of Birkhoff normal forms, we provide a self-consistent proof of the isochrone theorem, that relates isochrone potentials to parabolae in the plane, which is the basis of all literature on the subject. Along the way, we show how some fundamental results of celestial mechanics such as the Bertrand theorem and Kepler's third law are naturally encoded in the formalism., Comment: 36 pages, 5 figures, 1 table

We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized $T\bar T$ deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number $k$ of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As $k\to\infty$ the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S-matrices describing the $\Phi_{1,3}$ integrable deformation of non-unitary minimal models $\mathcal M_{2,2n+3}$., Comment: 37 pages, 11 figures

Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational spectroscopy, so it is critical to understand if the quasinormal mode spectrum is stable against perturbations. It was recently shown that the pseudospectrum can shed light on the spectral stability of black hole quasinormal modes. We study the pseudospectrum of Reissner-Nordstr\"om spacetimes and we find a spectral instability of scalar and gravitoelectric quasinormal modes in subextremal and extremal black holes, extending similar findings for the Schwarzschild spacetime. The asymptotic structure of pseudospectral contour levels is the same for scalar and gravitoelectric perturbations. By making different gauge choices in the hyperboloidal slicing of the spacetime, we find that the broad features of the pseudospectra are remarkably gauge-independent. The gravitational-led and electromagnetic-led quasinormal modes of extremal Reissner-Nordstr\"om black holes exhibit "strong" isospectrality: not only their spectrum coincides, but the whole pseudospectrum is the same for both classes of perturbations. We observe that a conformal duality between the extremal horizon and spacetime boundaries at infinity is responsible for such "strong" isospectrality property., Comment: 17 pages, 10 figures, matches published version

We perform the analysis of the focusing nonlinear Schr\"odinger equation on the half-line with time-dependent boundary conditions along the lines of the nonlinear method of images with the help of B\"acklund transformations. The difficulty arising from having such time-dependent boundary conditions at $x=0$ is overcome by changing the viewpoint of the method and fixing the B\"acklund transformation at infinity as well as relating its value at $x=0$ to a time-dependent reflection matrix. The interplay between the various aspects of integrable boundary conditions is reviewed in detail to brush a picture of the area. We find two possible classes of solutions. One is very similar to the case of Robin boundary conditions whereby solitons are reflected at the boundary, as a result of an effective interaction with their images on the other half-line. The new regime of solutions supports the existence of one soliton that is not reflected at the boundary but can be either absorbed or emitted by it. We demonstrate that this is a unique feature of time-dependent integrable boundary conditions., Comment: 38 pages. 5 figures. Authors' version of the published article. Accessiblefrom https://onlinelibrary.wiley.com/doi/10.1111/sapm.12456

International audience; Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It is known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). These are revealed when the path-integral action is written as a function not only of the physical fields, but also of Grassmann fields representing a Jacobian arising from the noise distribution. SUSYs leave the action invariant upon a transformation of the fields that mixes the physical and the Grassmann ones. We show that, contrarily to the common belief, it is possible to extend the known reversible construction to the case of arbitrary irreversible dynamics, for overdamped Langevin equations with additive white noise - provided their steady state is known. The construction is based on the fact that the Grassmann representation of the functional determinant is not unique, and can be chosen so as to present a generalization of the Parisi-Sourlas SUSY. Our approach is valid both for Martin-Siggia-Rose-Janssen-de Dominicis and for Onsager-Machlup actions. We show how such SUSYs are related to time-reversal symmetries and allow one to derive modified fluctuation-dissipation relations valid in non-equilibrium. We give as a concrete example the results for the Kardar-Parisi-Zhang equation.

We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a relation with the Ramanujan continued fraction identity and appropriate generalizations., Comment: 20 pages

In this paper, we start the investigation of a new natural approach to "unifying" noncommutative gauge field theories (NCGFT) based on approximately finite-dimensional ($AF$) $C^*$-algebras. The defining inductive sequence of an $AF$ $C^*$-algebra is lifted to enable the construction of a sequence of NCGFT of Yang-Mills-Higgs types. The present paper focus on derivation-based noncommutative field theories. A mathematical study of the ingredients involved in the construction of a NCGFT is given in the framework of $AF$ $C^*$-algebras: derivation-based differential calculus, modules, connections, metrics and Hodge $\star$-operators, Lagrangians... Some physical applications concerning mass spectra generated by Spontaneous Symmetry Breaking Mechanisms (SSBM) are proposed using numerical computations for specific situations., Comment: 42 pages, 20 figures

We present an English translation of Erwin Schr\"odinger's paper on "On the Reversal of the Laws of Nature". In this paper Schr\"odinger analyses the idea of time reversal of a diffusion process. Schr\"odinger's paper acted as a prominent source of inspiration for the works of Bernstein on reciprocal processes and of Kolmogorov on time reversal properties of Markov processes and detailed balance. The ideas outlined by Schr\"odinger also inspired the development of probabilistic interpretations of quantum mechanics by F\'enyes, Nelson and others as well as the notion of "Euclidean Quantum Mechanics" as probabilistic analogue of quantization. In the second part of the paper Schr\"odinger discusses the relation between time reversal and statistical laws of physics. We emphasize in our commentary the relevance of Schr\"odinger's intuitions for contemporary developments in statistical nano-physics., Comment: Revised version. 24 pages, 2 figures. Introduction 2 pages, Translation of the german original pag. 3-10, Commentary pag 10-22

We consider the problem of determining the achievable region of the universal $$1 \rightarrow 2$$ asymmetric quantum cloning problem. This concerns the quantum cloning of any quantum state to two approximate clones of different qualities. Measuring the cloning performance with the probabilities of the mixed clone states as the figure of merit, we show that the physical region is a union of ellipses in the plane. The study of these regions has consequences for the eavesdropping on quantum cryptography, and a wide variety of tasks. Equivalently, we characterize the region of quantum-state compatibility of two possibly different isotropic states, considering, for the first time, negative figures of merit.

We obtain a simple formula for the stationary measure of the height field evolving according to the Kardar-Parisi-Zhang equation on the interval $[0,L]$ with general Neumann type boundary conditions and any interval size. This is achieved using the recent results of Corwin and Knizel (arXiv:2103.12253) together with Liouville quantum mechanics. Our formula allows to easily determine the stationary measure in various limits: KPZ fixed point on an interval, half-line KPZ equation, KPZ fixed point on a half-line, as well as the Edwards-Wilkinson equation on an interval., Letter + supplementary material. v4: typos corrected, final version