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This paper deals with the numerical modeling of immiscible three-phase flows. The main focus here is on the numerical treatment of the source terms of the model. A new scheme based on a more coupled approach than the preexisting fractional step strategy is presented. Properties of this scheme are given. Numerical applications highlight the benefits of this scheme in terms of both accuracy and stability.

We provide an intersection-theoretic formula for the Euler characteristic of the moduli space of smooth curves. This formula reads purely in terms of Hodge integrals and, as a corollary, the standard calculus of tautological classes gives a new short proof of the Harer-Zagier formula. Our result is based on the Gauss-Bonnet formula, and on the observation that a certain parametrisation of the $\Omega$-class - the Chern class of the universal $r$-th root of the twisted log canonical bundle - provides the Chern class of the log tangent bundle to the moduli space of smooth curves. Being $\Omega$-classes by now employed in many enumerative problems, mostly recently found and at times surprisingly different from each other, we dedicate some work to produce an extensive list of their general properties: extending existing ones, finding new ones, and writing down some only known to the experts., Comment: 13 pages

International audience

In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure on the stable $\infty$-category $\mathsf{Coh}^{\mathsf{b}}(\mathbb{R}\mathsf{M})$ of complexes of sheaves with bounded coherent cohomology on a derived moduli stack $\mathbb{R}\mathsf{M}$. In the surface case, $\mathbb{R}\mathsf{M}$ is a suitable derived enhancement of the moduli stack $\mathsf{M}$ of coherent sheaves on the surface. This construction categorifies the K-theoretical and cohomological Hall algebras of coherent sheaves on a surface of Zhao and Kapranov-Vasserot. In the curve case, we define three categorified Hall algebras associated with suitable derived enhancements of the moduli stack of Higgs sheaves on a curve $X$, the moduli stack of vector bundles with flat connections on $X$, and the moduli stack of finite-dimensional local systems on $X$, respectively. In the Higgs sheaves case we obtain a categorification of the K-theoretical and cohomological Hall algebras of Higgs sheaves on a curve of Minets and Sala-Schiffmann, while in the other two cases our construction yields, by passing to $\mathsf K_0$, new K-theoretical Hall algebras, and by passing to $\mathsf H_\ast^{\mathsf{BM}}$, new cohomological Hall algebras. Finally, we show that the Riemann-Hilbert and the non-abelian Hodge correspondences can be lifted to the level of our categorified Hall algebras of a curve., Comment: v4: 71 pages; Final version. v3: 69 pages; introduction expanded; proofs in Sections 2 and 3 strengthened; new appendix about ind quasi-compact stacks and their correspondences included. The main results are unchanged

We revisit the classical zero-thickness Generalized Sheet Transition Conditions (GSTCs) which are a key tool for efficiently designing metafilms able to control the flow of light in a desired way. It is shown that it is more convenient to use an enlarged formulation of the GSTC in which the original metafilm is replaced by GSTCs that exclude the layer from the physical or computational domain. These new "layer" transition conditions have the same form as their "sheet" analogues hence they do not necessitate additional complications in their use; their advantage is that they provide a well-posed problem hence guaranty the stability of numerical schemes in the timedomain. These assessments are demonstrated for an all-dielectric structure; the effective susceptibility tensors are derived thanks to asymptotic analysis combined with homogenization technique and bounds for the susceptibilities entering the balance of energy are provided. While negative constant susceptibilities appear in the classical zero-thickness GSTCs, their values in the enlarged formulation are always positive which ensure the stability of the effective problem. Validation of the effective model is provided by means of comparison with direct numerics in two and three dimensions.

We present two new quantum-integrable models with long-range spin interactions. First, a partially isotropic (xxz-type) spin chain that unifies the Inozemtsev and partially isotropic Haldane-Shastry chains. It has important implications even for the isotropic Inozemtsev chain. Its short-range limit is a twisted Heisenberg xxz chain. Second, a quantum many-body system with spins that generalises the elliptic Ruijsenaars model using dynamical R-matrices. It unifies the elliptic spin-Calogero-Sutherland and trigonometric spin-Ruijsenaars-Macdonald models, and gives our spin chain by 'freezing'., v1: 8 pages, 1 figure; v2-3: minor changes

We present a covariant quantization scheme for the so-called ``partially massless" graviton field in de Sitter spacetime. Our approach is founded on the principles of the de Sitter group representation theory (in the sense given by Wigner), the Wightman-G\"{a}rding axioms for gauge-invariant fields (Gupta-Bleuler scheme), and the essential analyticity prerequisites in the complexified pseudo-Riemannian manifold. To implement the quantization process effectively, we adopt coordinate-independent (global) de Sitter plane waves. These plane waves, defined in the appropriate tube domains of complex de Sitter spacetime, serve as the de Sitter counterparts to the standard Minkowskian plane waves. By employing these analytical plane waves, we enable a spectral analysis of the corresponding two-point function that closely resembles the Fourier analysis typically employed in the flat Minkowskian case. Within this framework, we present the Wightman two-point function for the partially massless graviton field, which satisfies the essential criteria of locality, covariance, and normal analyticity. Furthermore, we provide insights into the underlying Hilbert space structure and the corresponding unsmeared field operator. A direct consequence of this quantization construction confirms the widely accepted notion of light-cone propagation for the de Sitter partially massless graviton field., Comment: 22 pages, no figure

Internal intervals spanned by finite ranges of a conformal coordinate $z$ and terminating at a pair of singularities are a common feature of many string compactifications with broken supersymmetry. The squared masses emerging in lower-dimensional Minkowski spaces are then eigenvalues of Schr\"odinger-like operators, whose potentials have double poles at the ends of the intervals. For one-component systems, the possible self-adjoint extensions of Schr\"odinger operators are described by points in $AdS_3 \times S^1$, and those corresponding to independent boundary conditions at the ends of the intervals by points on the boundary of $AdS_3$. The perturbative stability of compactifications to Minkowski space time depends, in general, on these choices of self-adjoint extensions. We apply this setup to the orientifold vacua driven by the ``tadpole potential'' $V=T \ e^{\,\frac{3}{2}\,\phi}$ and find, in nine dimensions, a massive scalar spectrum, a unique choice of boundary conditions with stable tensor modes and a massless graviton, and a wide range of choices leading to massless and/or massive vector modes., Comment: 49 pages, LaTeX, 13 figures. References added, misprints corrected in eqs. (3.71) and (3.72). Final version to appear in JHEP

International audience; We investigate the inverse problem of retrieving the magnetic potential of an Iwatsuka Hamiltonian by knowledge of the second component of the quantum velocity. We show that knowledge of the quantum currents carried by a suitable set of states with energy concentration within the first spectral band of the Schrödinger operator, uniquely determines the magnetic field.

We determine the spaces of states of the two-dimensional $O(n)$ and $Q$-state Potts models with generic parameters $n,Q\in \mathbb{C}$ as representations of their known symmetry algebras. While the relevant representations of the conformal algebra were recently worked out, it remained to determine the action of the global symmetry groups: the orthogonal group for the $O(n)$ model, and the symmetric group $S_Q$ for the $Q$-state Potts model. We do this by two independent methods. First we compute the twisted torus partition functions of the models at criticality. The twist in question is the insertion of a group element along one cycle of the torus: this breaks modular invariance, but allows the partition function to have a unique decomposition into characters of irreducible representations of the global symmetry group. Our second method reduces the problem to determining branching rules of certain diagram algebras. For the $O(n)$ model, we decompose representations of the Brauer algebra into representations of its unoriented Jones--Temperley--Lieb subalgebra. For the $Q$-state Potts model, we decompose representations of the partition algebra into representations of the appropriate subalgebra. We find explicit expressions for these decompositions as sums over certain sets of diagrams, and over standard Young tableaux. We check that both methods agree in many cases. Moreover, our spaces of states are consistent with recent bootstrap results on four-point functions of the corresponding CFTs., 60 pages, v2: minor clarifications

Phase transitions with spontaneous symmetry breaking are expected for group field theories as a basic feature of the geometogenesis scenario. The following paper aims to investigate the equilibrium phase for group field theory by using the ergodic hypothesis on which the Gibbs-Boltzmann distributions must break down. The breaking of the ergodicity can be considered dynamically, by introducing a fictitious time inducing a stochastic process described through a Langevin equation, from which the randomness of the tensor field will be a consequence. This type of equation is considered particularly for complex just-renormalizable Abelian model of rank $d=5$, and we study some of their properties by using a renormalization group considering a coarse-graining both in time and space., Comment: 76 pages, 18 figures

We compute all worldsheet three-point functions involving spectrally-flowed operators in chiral multiplets of the space-time theory for strings in AdS$_3\times$S$^3\times$T$^4$, thus completing the analysis of the full AdS$_3$/CFT$_2$ chiral ring. We make use of techniques recently developed for the bosonic sector, based on holomorphic covering maps from the worldsheet to the AdS$_3$ boundary. We highlight the role of the so-called series identifications when dealing with the complications originated by picture-changing spectrally-flowed states. We find an exact agreement with the predictions from the holographic CFT at the symmetric orbifold point, including both extremal and non-extremal correlators., 27 pages

International audience; We propose a new framework for tensor decomposition based on trace invariants, which are particular cases of tensor networks. In general, tensor networks are diagrams/graphs that specify a way to "multiply" a collection of tensors together to produce another tensor, matrix or scalar. The particularity of trace invariants is that the operation of multiplying copies of a certain input tensor that produces a scalar obeys specific symmetry constraints. In other words, the scalar resulting from this multiplication is invariant under some specific transformations of the involved tensor. We focus our study on the O(N)-invariant graphs, i.e. invariant under orthogonal transformations of the input tensor. The proposed approach is novel and versatile since it allows to address different theoretical and practical aspects of both CANDECOMP/PARAFAC (CP) and Tucker decomposition models. In particular we obtain several results: (i) we generalize the computational limit of Tensor PCA (a rank-one tensor decomposition) to the case of a tensor with axes of different dimensions (ii) we introduce new algorithms for both decomposition models (iii) we obtain theoretical guarantees for these algorithms and (iv) we show improvements with respect to state of the art on synthetic and real data which also highlights a promising potential for practical applications.

International audience; Underground nuclear explosions generate non-isothermal two-phase flow, heat and mass transfer, and tracer transport through fractured porous media. The governing equations of these coupled phenomena on the Darcy scale are presented and the corresponding numerical code is briefly described. Two configurations are considered. In the first one, the damaged zone generated by the explosion is replaced by equivalent macroscopic boundary conditions at the bottom of the medium. Vapor condensation at distance from this zone plays a crucial role and slows down the tracer transport to the ground surface, while the presence of hot liquid water and of hot rubble particles in it accelerates it. In the second configuration, the damaged zone itself is treated as a porous medium with specific properties and is integrated in the simulation domain. Several regions can be distinguished with different properties, such as the chimney, the cavity, the solidified magma, the fractured porous medium, and the intact porous medium. Phase change, heat transfer and tracer transport can be detailed in these regions and at the boundaries between them. Among the most important conclusions, the role of phase change, of the thermal properties and therefore of the temperature, is pointed out.

Generalizing our recent joint paper with Vasily Pestun (arXiv:2001.04929), we construct a family of $SO(2r),Sp(2r),SO(2r+1)$ rational Lax matrices, polynomial in the spectral parameter, parametrized by the divisors on the projective line with coefficients being dominant integral coweights of associated Lie algebras. To this end, we provide the RTT realization of the antidominantly shifted extended Drinfeld Yangians of $\mathfrak{so}_{2r}, \mathfrak{sp}_{2r}, \mathfrak{so}_{2r+1}$, and of their coproduct homomorphisms. This establishes some of the recent conjectures in the physics literature by Costello-Gaiotto-Yagi (arXiv:2103.01835) in the classical types., Comment: v3: 67 pages, minor corrections, details added. v2: 65 pages, minor corrections, some details added, Remark 4.37 added. v1: 64 pages, comments are welcome!

International audience; The zero locus of a bivariate polynomial P(x,y)=0P(x,y)=0P(x,y)=0 defines a compact Riemann surface Σ\SigmaΣ. The fundamental second kind differential is a symmetric 1⊗11\otimes 11⊗1-form on Σ×Σ\Sigma\times\SigmaΣ×Σ that has a double pole at coinciding points and no other pole. As its name indicates, this is one of the most important geometric objects on a Riemann surface. Here we give a rational expression in terms of combinatorics of the Newton's polygon of PPP, involving only integer combinations of products of coefficients of PPP. Since the expression uses only combinatorics, the coefficients are in the same field as the coefficients of PPP.

International audience; The goal of this article is to develop local discontinuous Galerkin (LDG) schemes for solving a time fractional equation describing the ultrasonic wave in a homogeneous isotropic porous material. Two novel semi-discrete LDG schemes are designed for the considered model. The semi-discrete LDG schemes are constructed by splitting the original model into a coupled system. The first semi-discrete scheme follows the traditional LDG method by splitting second-order space derivative. The second one splits the original model for both time and space derivatives. The discontinuous Galerkin is used for the spatial discretization. Two kinds of fully discrete LDG schemes are presented by using the Grünwald-Letnikov and L1 approximation formulas for the time fractional derivatives. The L 2 norm stability and convergence analysis are carried out for both semi-discrete and fully discrete LDG schemes. The stability analysis reveals that the numerical schemes are unconditionally stable in L 2 norm and convergence with optimal convergence rate. Finally, numerical examples are presented to test the effectiveness of the proposed schemes and the correctness of the theoretical analysis.

We show that conditional expectations, optimal hypotheses, disintegrations and adjoints of unital completely positive maps are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita–Takesaki modular group and we provide extensions of a theorem of Takesaki as well as a theorem of Accardi and Cecchini to the setting of not necessarily faithful states on finite-dimensional $C^{\ast}$-algebras.

We present two finite volume approaches for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with cross-diffusion and volume filling. Both methods utilize a two-point flux approximation and are part of the exponentially fitted scheme framework. The only difference between the two is the selection of a Stolarsky mean for the drift term originating from a self-consistent electric potential. The first version of the scheme, referred to as (SQRA), uses a geometric mean and is an extension of the squareroot approximation scheme. The second scheme, (SG), utilizes an inverse logarithmic mean to create a generalized version of the Scharfetter-Gummel scheme. Both approaches ensure the decay of some discrete free energy. Classical numerical analysis results-existence of discrete solution, convergence of the scheme as the grid size and the time step go to 0-follow. Numerical simulations show that both schemes are effective for moderately small Debye lengths, with the (SG) scheme demonstrating greater robustness in the small Debye length regime.

We consider an $XYZ$ spin chain within the framework of the generalized algebraic Bethe ansatz. We calculate the actions of monodromy matrix elements on Bethe vectors as a linear combination of new Bethe vectors. We also compute the multiple action of the gauge transformed monodromy matrix elements on the pre-Bethe vector and conceive the result in terms of a partition function of the 8-vertex model., 21 pahes, no figures, typos are corrected

In its traditional form, the string field in closed string field theory is constrained by the level-matching condition, which is imposed beside the action. By analogy with the similar problem for the Ramond sector, it was understood by Okawa and Sakaguchi how to lift this condition and work with unconstrained field by introducing spurious free fields. These authors also pointed out that new backgrounds may exist thanks to a new gauge field which is trivial on flat space, but can generate fluxes on a toroidal background. In this paper, we perform a complete study of the free theory at the tachyonic and massless levels with the aim of setting the stage for studying backgrounds without level-matching., 31 pages; v2: minor updates, published version

International audience; The local navigation of pedestrians amid a crowd is generally believed to involve no anticipation beyond (at best) the avoidance of the most imminent collisions. We show that current models rooted in this belief fail to reproduce some key features experimentally evidenced when a dense static crowd is crossed by an intruder. We identify the missing ingredient as the pedestrians' ability to plan their motion well beyond the next interaction, whence they may accept to move towards denser regions for a short time. To account for this effect, we introduce a minimal model based on mean-field game theory, which proves remarkably successful in replicating the aforementioned observations as well as other daily-life situations involving collective behaviour in dense crowds, such as partial metro boarding. This demonstrates the ability of game approaches to capture the anticipatory effects at play in operational crowd dynamics.

From the Bretton Woods agreement in 1944 till the present day, the US dollar has been the dominant currency in the world trade. However, the rise of the Chinese economy led recently to the emergence of trade transactions in Chinese yuan. Here, we analyze mathematically how the structure of the international trade flows would favor a country to trade whether in US dollar or in Chinese yuan. The computation of the trade currency preference is based on the world trade network built from the 2010-2020 UN Comtrade data. The preference of a country to trade in US dollar or Chinese yuan is determined by two multiplicative factors: the relative weight of trade volume exchanged by the country with its direct trade partners, and the relative weight of its trade partners in the global international trade. The performed analysis, based on Ising spin interactions on the world trade network, shows that, from 2010 to present, a transition took place, and the majority of the world countries would have now a preference to trade in Chinese yuan if one only consider the world trade network structure., The preprint contains 19 pages including 13 pages of supplementary materials, 12 figures (including 7 supplementary figs) and 6 tables

This paper presents $\Psi$-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems with mixed boundary conditions. By leveraging the Implicit Layer Theory, $\Psi$-GNN models an ''infinitely'' deep network, thus avoiding the empirical tuning of the number of required Message Passing layers to attain the solution. Its original architecture explicitly takes into account the boundary conditions, a critical prerequisite for physical applications, and is able to adapt to any initially provided solution. $\Psi$-GNN is trained using a ''physics-informed'' loss, and the training process is stable by design, and insensitive to its initialization. Furthermore, the consistency of the approach is theoretically proven, and its flexibility and generalization efficiency are experimentally demonstrated: the same learned model can accurately handle unstructured meshes of various sizes, as well as different boundary conditions. To the best of our knowledge, $\Psi$-GNN is the first physics-informed GNN-based method that can handle various unstructured domains, boundary conditions and initial solutions while also providing convergence guarantees.

We study the relation between supersymmetry and geometric flows driven by the Bianchi identity for the three-form flux $H$ in heterotic supergravity. We describe how the flow equations can be derived from a functional that appears in a rewriting of the bosonic action in terms of squares of supersymmetry operators. On a complex threefold, the resulting equations match what is known in the mathematics literature as "anomaly flow". We generalise this to seven- and eight-manifolds with G$_2$ or Spin(7) structures and discuss examples where the manifold is a torus fibration over a K3 surface. In the latter cases, the flow simplifies to a single scalar equation, with the existence of the supergravity solution implied by the long-time existence and convergence of the flow. We also comment on the $\alpha'$ expansion and highlight the importance of using the proper connection in the Bianchi identity to ensure that the flow's fixed points satisfy the supergravity equations of motion., Comment: 47 pages plus appendices

We develop a mathematical formalism that allows to study decoherence with a great level generality, so as to make it appear as a geometrical phenomenon between reservoirs of dimensions. It enables us to give quantitative estimates of the level of decoherence induced by a purely random environment on a system according to their respectives sizes, and to exhibit some links with entanglement entropy.

The Parisi scheme for equilibrium and the corresponding slow dynamics with multithermalization - same temperature common to all observables, different temperatures only possible at widely separated timescales - imply one another. Consistency requires that two systems brought into infinitesimal coupling be able to rearrange their timescales in order that all their temperatures match: this time reorganisation is only possible because the systems have a set of time-reparametrization invariances, that are thus seen to be an essential component of the scenario.

In his seminal paper [1], Araki introduced an elegant extension of the Jordan-Wigner transformation which establishes a precise connection between quantum spin systems and Fermi lattice gases in one dimension in the so-called infinite system idealization of quantum statistical mechanics. His extension allows in particular for the rigorous study of numerous aspects of the prominent XY chain over the two sided infinite discrete line without having to resort to a thermodynamic limit procedure at an intermediate or at the final stage. We rigorously review and elaborate this extension from scratch which makes the paper rather self-contained. In the course of the construction, we also present a simple and concrete realization of Araki's crossed product extension., 54 pages, 8 figures

International audience; We consider the Abdesselam-Rivasseau (AR) model turning the Jacobian Conjecture (JC) into a problem of the perturbative quantum field theory. Within the AR model, the JC inverse map is represented by a formal integral generating the tree's expansion for this map. By assigning a color to the one out-coming edge in the vertex of the AR model, we perform selective Gaussian integration and show the termination of the tree's series for the inverse map. The latter implies the correctness of JC.

Correlation functions of the $\text{SL}(2,\mathbb{R})$-WZW model involving spectrally flowed vertex operators are notoriously difficult to compute. An explicit integral expression for the corresponding three-point functions was recently conjectured in [arXiv:2105.12130v2]. In this paper, we provide a proof for this conjecture. For this, we extend the methods of [arXiv:2208.00978] based on the so-called $\text{SL}(2,\mathbb{R})$ series identifications, which relate vertex operators belonging to different spectral flow sectors. We also highlight the role of holomorphic covering maps in this context. Our results constitute an important milestone for proving this instance of the AdS$_3$/CFT$_2$ holographic duality at finite 't Hooft coupling., 22 pages

International audience; A two-step up-scaling methodology is established to determine a temporal Electric Equivalent Circuit (EEC) model of aged graphite electrodes. The methodology is fed with original experimental results of graphite impedance spectra obtained upon aging on graphite-NMC pouches instrumented with reference electrodes. An analytical expression is first derived which includes the impedance contributions from interfacial kinetics, double-layer adsorption, solid-phase diffusion processes in the graphite particles as well as lithium diffusion through the SEI layer. The derivation of the temporal EEC model from this analytical expression using Foster series allows to link the EEC model parameters to materials properties and to tune the accuracy of the model by choosing the number of RC elements in the series. The validity of the model is ascertained by comparison with the experimental data obtained at different aging time and for two cycling temperature conditions. In particular, accounting for lithium diffusion through the SEI is necessary to capture the evolution of the impedance spectra of significantly aged graphite electrodes.

In this work, we derive the global sharp decay, as both a lower and an upper bounds, for the spin $\pm \mathfrak{s}$ components, which are solutions to the Teukolsky equation, in the black hole exterior and on the event horizon of a slowly rotating Kerr spacetime. These estimates are generalized to any subextreme Kerr background under an integrated local energy decay estimate. Our results apply to the scalar field $(\mathfrak{s}=0)$, the Maxwell field $(\mathfrak{s}=1)$ and the linearized gravity $(\mathfrak{s}=2)$ and confirm the Price's law decay that is conjectured to be sharp. Our analyses rely on a novel global conservation law for the Teukolsky equation, and this new approach can be applied to derive the precise asymptotics for solutions to semilinear wave equations., The published version

Submitted to SciPost Physics Proceedings. Proceedings of the 34th International Colloquium on Group Theoretical Methods in Physics Strasbourg, 18-22 July 2022; The ΛCDM standard model of cosmology involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the (positive) cosmological constant Λ associated with a de Sitter geometry, we propose to explain dark matter as a pure QCD effect, namely a gluonic Bose Einstein condensate with the status of a Cosmic Gluonic Background (CGB). This effect is due to the trace anomaly viewed as an effective negative cosmological constant determining an Anti de Sitter geometry and accompanying baryonic matter at the hadronization transition from the quark gluon plasma phase to the colorless hadronic phase. Our approach also allows to assume a ratio Dark/Visible equal to 11/2.

International audience; Simulated free surface transients in periodic urban layouts have been reported to be self-similar in the space-time domain when averaged on the scale of the building period. Such self-similarity is incompatible with the head loss model formulae used in most porosity-based shallow water models. Verifying it experimentally is thus of salient importance. New dam-break flow laboratory experiments are reported, where two different configurations of idealized periodic buildings layouts are explored. A space-time analysis of the experimental water level fields validates the self-similar character of the flow. Simulating the experiment using the two-dimensional shallow water model also yields self-similar period-averaged flow solutions. Then, the Single Porosity (SP), Integral Porosity (IP) and Dual Integral Porosity (DIP) models are applied. Although all three models behave in a similar fashion when the storage and connectivity porosities are close to each other, the DIP model is the one that upscales best the refined 2D solution.

Jackiw-Teitelboim dilaton-quantum-gravity localizes on a double-scaled random-matrix model, whose perturbative free energy is an asymptotic series. Understanding the resurgent properties of this asymptotic series, including its completion into a full transseries, requires understanding the nonperturbative instanton sectors of the matrix model for Jackiw-Teitelboim gravity. The present work addresses this question by setting-up instanton calculus associated to eigenvalue tunneling (or ZZ-brane contributions), directly in the matrix model. In order to systematize such calculations, a nonperturbative extension of the topological recursion formalism is required -- which is herein both constructed and applied to the present problem. Large-order tests of the perturbative genus expansion validate the resurgent nature of Jackiw-Teitelboim gravity, both for its free energy and for its (multi-resolvent) correlation functions. Both ZZ and FZZT nonperturbative effects are required by resurgence, and they further display resonance upon the Borel plane. Finally, the resurgence properties of the multi-resolvent correlation functions yield new and improved resurgence formulae for the large-genus growth of Weil-Petersson volumes., Comment: 63 pages, 52 plots in 16 figures, jheppub-nosort.sty

International audience; Given a crossed module $\chi$, we introduce $\chi$-graded monoidal categories and $\chi$-fusion categories. We use spherical $\chi$-fusion categories to construct (via the state sum method) 3-dimensional Homotopy Quantum Field Theories with target the classifying space $B\chi$ of the crossed module $\chi$ (which is a homotopy 2-type).

These notes contain essentially a rewriting of several properties of two well-known quantities, the so-called theta symbol (or triangular symbol), which is rational, and the 6j symbol, which is usually irrational, in terms of two related integer-valued functions called gon and tet. Existence of these related integer-valued avatars, sharing most essential properties with their more popular partners, although a known fact, is often overlooked. The properties of gon and tet are easier to obtain, or to formulate, than those of the corresponding theta and 6j symbols, both in the classical and quantum situations. Their evaluation is also simpler (the paper displays a number of explicit formulae and evaluation procedures that may speed up some computer programs). These two integer-valued functions are unusual, in that their properties do not appear to be often discussed in the literature, but their features reflect those of related real-valued functions discussed in many places. Some of the properties that we shall discuss seem however to be new, in particular several relations between the function gon and the inverse Hilbert matrices., 34 pages, 10 figures. Extended revised version: comments added, new references, new appendix, corrected typos

The Asymptotic Equipartition Property (AEP) in information theory establishes that independent and identically distributed (i.i.d.) states behave in a way that is similar to uniform states. In particular, with appropriate smoothing, for such states both the min and the max relative entropy asymptotically coincide with the relative entropy. In this paper, we generalize several such equipartition properties to states on general von Neumann algebras. First, we show that the smooth max relative entropy of i.i.d. states on a von Neumann algebra has an asymptotic rate given by the quantum relative entropy. In fact, our AEP not only applies to states, but also to quantum channels with appropriate restrictions. In addition, going beyond the i.i.d. assumption, we show that for states that are produced by a sequential process of quantum channels, the smooth max relative entropy can be upper bounded by the sum of appropriate channel relative entropies. Our main technical contributions are to extend to the context of general von Neumann algebras a chain rule for quantum channels, as well as an additivity result for the channel relative entropy with a replacer channel., updated version with a new section on application

Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the stable aggregate of flexible element (SAFE) method and include only the first non-zero wave-related correction to the familiar semi-classical approximation. Application to a couple of widely studied potentials that do not permit closed-form solutions is used to demonstrate surprising accuracy even in cases that are far from any asymptotic limit. We explore the absence of alternate terms in the asymptotic expansions as a way to explain the accuracy of the end results. Those results are expressed as definite integrals with integrands involving the parameter used in the SAFE method to control the extent of the associated elemental field contributions. Importantly, the integrals themselves are shown to be precisely independent of that parameter. Further, although the derivation proceeds by way of an asymptotic expansion for the wavefield that involves the associated classical motion, those entities do not appear in the end results which are expressed in terms of just the potential function and its first four derivatives.

In S. Giombi, I. Klebanov, F. Popov, S. Prakash and G. Tarnopolsky, {\it Phys. Rev.} {\bf D} 98 (2018) 10, 105005, a prismatic tensor model was introduced. We study here the diagrammatics and the double scaling limit of this model, using the intermediate field method. We explicitly exhibit the next-to-leading order Feynman graphs in the $1/N$ expansion. Using appropriate combinatorial tools, we further study the general term of the $1/N$ expansion and we compute the $2-$point function in the double scaling limit., Comment: 40 pages, many figures

Usual approaches to quantisation of a 3-Toda lead to numerical calculations requiring many steps that can be time consuming to insure their reliability. In order to reduce as much as possible the numerical part of the EKB quantisation procedure, and then to ease numerical calculations, we propose a reformulation of the mathematical framework with more adapted variables. The resulting equations and procedure might be easily implemented in a short Mathematica code. This more explicit framework will be useful for studying quantum Toda-Bianchi IX models in quantum cosmology where the true Bianchi IX anisotropy Hamiltonian can be approximated by a 3-particle Toda system., submitted Eur. Phys. J. C

We explore the main issues that appear in (relativistic) quantum mechanics relative to the implementation of measurements. This approach reveals how fruitful these topics are for theoretical physics. Endeavoring to formulate an exhaustive solution to the measurement problem leads us to a better understanding of the status of the collapse and of the emergence of classicality, thanks to a precise definition of the measurement and some new vocabulary to speak of quantum mechanics and decoherence. The result may be seen as a step beyond the many-worlds interpretation of quantum mechanics. When the relativistic constraints are added, a consistency condition constraining any relativistic quantum theory is formulated, from which can be deduced the locality of physics as well as, in the context of quantum field theory, the microcausality hypothesis. Moreover, it also implies the non-measurability of fermionic fields. On the way, two different arguments are given to show that a deterministic theory superseding quantum mechanics can not be formulated.

We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The technical difficulties due to the breaking of $\mathsf{U}(1)$ symmetry and the absence of a reference state are overcome by an algebraic construction where the two-boundary Temperley-Lieb Hamiltonian is realised in a new $U_{\mathfrak{q}}\mathfrak{sl}_2$-invariant spin chain involving infinite-dimensional Verma modules on the edges [J. High Energy Phys. 2022 (2022), no. 11, 016, 64 pages, arXiv:2207.12772]. The equivalence of the two Hamiltonians is established by proving Schur-Weyl duality between $U_{\mathfrak{q}}\mathfrak{sl}_2$ and the two-boundary Temperley-Lieb algebra. In this framework, the Nepomechie condition turns out to have a simple algebraic interpretation in terms of quantum group fusion rules.

We survey sum rules for spectral zeta functions of homogeneous 1D Schr\"odinger operators, that mainly result from the exact WKB method., Comment: 14 pages, 1 figure, 4 tables. In honour of Prof. M.V. BERRY's 80-th birthday. V2: new eqs.(32), (33), (35) added. V3: added text in Secs.1.2 and 3.3, new eq.(30), numerical Appendix

Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete positivity is replaced by positivity is known to be false. A natural question is whether extendibility could still hold for positive maps satisfying stronger conditions, such as being unital and norm 1. Here we provide three counterexamples showing that positive norm-one unital maps defined on an operator subsystem of a matrix algebra cannot be extended to a positive map on the full matrix algebra. The first counterexample is an unextendible positive unital map with unit norm, the second counterexample is an unextendible positive unital isometry on a real operator space, and the third counterexample is an unextendible positive unital isometry on a complex operator space., Comments are welcome

International audience; During intercalation, some layered intercalation compounds undergo phase separation between several stable phases, known as stages. Of particular interest is the case of graphite, widely used in negative electrodes of batteries. Here, thermodynamics and kinetics of stage formation are studied using a multilayer free energy framework based on mean-field theory, accounting for both intralayer and interlayer interactions. More specifically, an order parameter is introduced to describe the local evolution of the stacking sequence of graphene sheets around lithium islands, enabling the distinction between the liquid-like stage 2L and the stage 2. In particular, we show that an interlayer interaction between the lithium ions and the host structure is necessary to counterbalance the enthalpic term of the lithium intralayer energy and allow the formation of islands with intermediate concentrations, characteristics of the liquid-like phases. Introducing the developed free energy model in Cahn-Hilliard's and Allen-Cahn's equations, we study the stages emergence during spinodal decompositions. Staggered domains of lithium surrounded by different graphene stacking arise naturally with characteristics typical of stages 1′, 3L, 2L, 2, and 1.

We show that partial mass concentration can happen for stationary solutions of aggregation–diffusion equations with homogeneous attractive kernels in the fast diffusion range. More precisely, we prove that the free energy admits a radial global minimizer in the set of probability measures which may have part of its mass concentrated in a Dirac delta at a given point. In the case of the quartic interaction potential, we find the exact range of the diffusion exponent where concentration occurs in space dimensions [Formula: see text]. We then provide numerical computations which suggest the occurrence of mass concentration in all dimensions [Formula: see text], for homogeneous interaction potentials with higher power.

We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the problem in the CNOT+rotation gate set from a mathematical programming standpoint, offering contributions both in terms of understanding the mathematics of the problem and its efficient solution. Among the results that we present, we are able to derive a 14-CNOT 4-qubit Toffoli decomposition from scratch, and show that the Quantum Shannon Decomposition can be compressed by a factor of two without practical loss of fidelity., Comment: 25 pages, 9 figures, 3 tables

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