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Discrete, Continuous and Asymptotic for a Modified Singularly Gaussian Unitary Ensemble and the Smallest Eigenvalue of Its Large Hankel Matrices Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2024-03-02 Dan Wang, Mengkun Zhu
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On the KPZ Scaling and the KPZ Fixed Point for TASEP Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2024-01-29 Yuta Arai
We consider all totally asymmetric simple exclusion processes (TASEPs) whose transition probabilities are given by the Schütz-type formulas and which jump with homogeneous rates. We show that the multi-point distribution of particle positions and the KPZ scaling are described using the probability generating function of the rightmost particle’s jump. For all TASEPs satisfying certain assumptions, we
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On the Integrable Structure of Deformed Sine Kernel Determinants Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2024-01-27
Abstract We study a family of Fredholm determinants associated to deformations of the sine kernel, parametrized by a weight function w. For a specific choice of w, this kernel describes bulk statistics of finite temperature free fermions. We establish a connection between these determinants and a system of integro-differential equations generalizing the fifth Painlevé equation, and we show that they
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Multicritical Schur Measures and Higher-Order Analogues of the Tracy–Widom Distribution Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2024-01-25
Abstract We introduce multicritical Schur measures, which are probability laws on integer partitions which give rise to non-generic fluctuations at their edge. They are in the same universality classes as one-dimensional momentum-space models of free fermions in flat confining potentials, studied by Le Doussal, Majumdar and Schehr. These universality classes involve critical exponents of the form \(1/(2m+1)\)
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Tau-Function of the Multi-component CKP Hierarchy Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2024-01-02 A. Zabrodin
We consider multi-component Kadomtsev-Petviashvili hierarchy of type C (the multi-component CKP hierarchy) originally defined with the help of matrix pseudo-differential operators via the Lax-Sato formalism. Starting from the bilinear relation for the wave functions, we prove existence of the tau-function for the multi-component CKP hierarchy and provide a formula which expresses the wave functions
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Complex Creation Operator and Planar Automorphic Functions Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-11-01 Ghanmi Allal, Imlal Lahcen
We provide a concrete characterization of the poly-analytic planar automorphic functions, a special class of non analytic planar automorphic functions with respect to the Appell–Humbert automorphy factor, arising as images of the holomorphic ones by means of the creation differential operator. This is closely connected to the spectral theory of the magnetic Laplacian on the complex plane.
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Surgery Transformations and Spectral Estimates of $$\delta $$ Beam Operators Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-10-17 Aftab Ali, Muhammad Usman
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Cohomology of Lie Algebra Morphism Triples and Some Applications Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-09-25 Apurba Das
A Lie algebra morphism triple is a triple \((\mathfrak {g}, \mathfrak {h}, \phi )\) consisting of two Lie algebras \(\mathfrak {g}, \mathfrak {h}\) and a Lie algebra homomorphism \(\phi : \mathfrak {g} \rightarrow \mathfrak {h}\). We define representations and cohomology of Lie algebra morphism triples. As applications of our cohomology, we study some aspects of deformations, abelian extensions of
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The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve $$y=x^{n}$$ Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-09-19 Jaume Llibre, Claudia Valls
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The Inverse Spectral Map for Dimers Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-09-12 T. George, A. B. Goncharov, R. Kenyon
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Integrable Systems of Finite Type from F-Cohomological Field Theories Without Unit Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-09-09 Alexandr Buryak, Danil Gubarevich
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Some Non-periodic p-Adic Generalized Gibbs Measures for the Ising Model on a Cayley Tree of Order k Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-08-31 Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev
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Relative Entropy of Fermion Excitation States on the CAR Algebra Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-08-30 Stefano Galanda, Albert Much, Rainer Verch
The relative entropy of certain states on the algebra of canonical anticommutation relations (CAR) is studied in the present work. The CAR algebra is used to describe fermionic degrees of freedom in quantum mechanics and quantum field theory. The states for which the relative entropy is investigated are multi-excitation states (similar to multi-particle states) with respect to KMS states defined with
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Elliptic Solutions of the Toda Lattice with Constraint of Type B and Deformed Ruijsenaars–Schneider System Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-08-03 V. Prokofev, A. Zabrodin
We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars–Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By studying more general elliptic solutions (elliptic families)
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Discrete Field Theory: Symmetries and Conservation Laws Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-08-03 M. Skopenkov
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Extensions and Generalizations of Lattice Gelfand–Dickey Hierarchy Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-07-29 Lixiang Zhang, Chuanzhong Li
In this paper, for the extended lattice Gelfand–Dickey hierarchy, we construct its n-fold Darboux transformation and additional flows. And we prove that these flows are actually symmetries of the extended lattice Gelfand–Dickey hierarchy. Further, we show how the additional flows act on the tau function. On this basis, we generalize the extended lattice Gelfand–Dickey hierarchy to the multicomponent
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On the Global Minimum of the Energy–Momentum Relation for the Polaron Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-07-26 Jonas Lampart, David Mitrouskas, Krzysztof Myśliwy
For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling.
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Existence and Uniqueness of Solutions to Backward 2D and 3D Stochastic Convective Brinkman–Forchheimer Equations Forced by Lévy Noise Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-07-03 Manil T. Mohan
The two- and three-dimensional incompressible backward stochastic convective Brinkman–Forchheimer (BSCBF) equations on a torus driven by Lévy noise are considered in this paper. A-priori estimates for adapted solutions of the finite-dimensional approximation of 2D and 3D BSCBF equations are obtained. For a given terminal data, the existence and uniqueness of pathwise adapted strong solutions is proved
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Self-Adjointness of a Class of Multi-Spin–Boson Models with Ultraviolet Divergences Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-06-12 Davide Lonigro
We study a class of quantum Hamiltonian models describing a family of N two-level systems (spins) coupled with a structured boson field of positive mass, with a rotating-wave coupling mediated by form factors possibly exhibiting ultraviolet divergences. Spin–spin interactions which do not modify the total number of excitations are also included. Generalizing previous results in the single-spin case
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On Quantum Optimal Transport Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-06-06 Sam Cole, Michał Eckstein, Shmuel Friedland, Karol Życzkowski
We analyze a quantum version of the Monge–Kantorovich optimal transport problem. The quantum transport cost related to a Hermitian cost matrix C is minimized over the set of all bipartite coupling states \(\rho ^{AB}\) with fixed reduced density matrices \(\rho ^A\) and \(\rho ^B\) of size m and n. The minimum quantum optimal transport cost \(\textrm{T}^Q_{C}(\rho ^A,\rho ^B)\) can be efficiently computed
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Braided Hopf Algebras and Gauge Transformations II: $$*$$ -Structures and Examples Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-05-11 Paolo Aschieri, Giovanni Landi, Chiara Pagani
We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge transformations of bundles on noncommutative spheres. The braiding of these algebras is implemented by the triangular structure of the symmetry Hopf algebra. We present a systematic analysis of compatible
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Hydrodynamical Behavior for the Symmetric Simple Partial Exclusion with Open Boundary Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-05-08 C. Franceschini, P. Gonçalves, B. Salvador
We analyze the symmetric simple partial exclusion process, which allows at most \(\alpha \) particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter \(\theta \in {\mathbb {R}}\). We prove that the hydrodynamic behavior is given by the heat equation and depending on the value of \(\theta \), the equation is supplemented with different boundary
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Consistency of the Bäcklund Transformation for the Spin Calogero–Moser System Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-05-08 Bjorn K. Berntson
We prove the consistency of the Bäcklund transformation (BT) for the spin Calogero–Moser (sCM) system in the rational, trigonometric, and hyperbolic cases. The BT for the sCM system consists of an overdetermined system of ordinary differential equations; to establish our result, we construct and analyze certain functions that measure the departure of this overdetermined system from consistency. We
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A Riemann Hilbert Approach to the Study of the Generating Function Associated to the Pearcey Process Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-04-25 Thomas Chouteau
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Gibbs Measures for HC-Model with a Cuountable Set of Spin Values on a Cayley Tree Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-03-28 R. M. Khakimov, M. T. Makhammadaliev, U. A. Rozikov
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A Comparison of Two Quantum Distances Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-03-13 Jens Kaad, David Kyed
We show that Rieffel’s quantum Gromov–Hausdorff distance between two compact quantum metric spaces is not equivalent to the ordinary Gromov–Hausdorff distance applied to the associated state spaces.
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Gibbs Measures of the Blume–Emery–Griffiths Model on the Cayley Tree Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-03-03 G. Botirov, F. Haydarov, U. Qayumov
In this paper we consider the Blume–Emery–Griffiths model on Cayley trees. We reduce the problem of describing the splitting Gibbs measures of the Blume–Emery–Griffiths model to the description of the solutions of some algebraic equation. Also, we analyse the set of translation-invariant splitting Gibbs measures for a two parametric BEG model on Cayley trees.
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The Near-Critical Two-Point Function and the Torus Plateau for Weakly Self-avoiding Walk in High Dimensions Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-02-17 Gordon Slade
We use the lace expansion to study the long-distance decay of the two-point function of weakly self-avoiding walk on the integer lattice \(\mathbb {Z}^d\) in dimensions \(d>4\), in the vicinity of the critical point, and prove an upper bound \(|x|^{-(d-2)}\exp [-c|x|/\xi ]\), where the correlation length \(\xi \) has a square root divergence at the critical point. As an application, we prove that the
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On the Integrability of a Four-Prototype Rössler System Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-02-16 Jaume Llibre, Claudia Valls
We consider a four-prototype Rossler system introduced by Otto Rössler among others as prototypes of the simplest autonomous differential equations (in the sense of minimal dimension, minimal number of parameters, minimal number of nonlinear terms) having chaotic behavior. We contribute towards the understanding of its chaotic behavior by studying its integrability from different points of view. We
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Mean-field behavior of Nearest-Neighbor Oriented Percolation on the BCC Lattice Above 8 + 1 Dimensions Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-02-14 Lung-Chi Chen, Satoshi Handa, Yoshinori Kamijima
In this paper, we consider nearest-neighbor oriented percolation with independent Bernoulli bond-occupation probability on the d-dimensional body-centered cubic (BCC) lattice \({\mathbb {L}^d}\) and the set of non-negative integers \({{\mathbb {Z}}_+}\). Thanks to the orderly structure of the BCC lattice, we prove that the infrared bound holds on \({\mathbb {L}^d} \times {{\mathbb {Z}}_+}\) in all
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Long Time Asymptotic Behavior for the Nonlocal mKdV Equation in Solitonic Space–Time Regions Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-01-28 Xuan Zhou, Engui Fan
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Lusztig Factorization Dynamics of the Full Kostant–Toda Lattices Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2023-01-17 Nicholas M. Ercolani, Jonathan Ramalheira-Tsu
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Heisenberg Dynamics for Non Self-Adjoint Hamiltonians: Symmetries and Derivations Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-12-19 F. Bagarello
In some recent literature the role of non self-adjoint Hamiltonians, \(H\ne H^\dagger \), is often considered in connection with gain-loss systems. The dynamics for these systems is, most of the times, given in terms of a Schrödinger equation. In this paper we rather focus on the Heisenberg-like picture of quantum mechanics, stressing the (few) similarities and the (many) differences with respected
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Slit-Strip Ising Boundary Conformal Field Theory 1: Discrete and Continuous Function Spaces Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-12-05 Taha Ameen, Kalle Kytölä, S. C. Park, David Radnell
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Bispectrality of $$AG_2$$ Calogero–Moser–Sutherland System Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-11-28 Misha Feigin, Martin Vrabec
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Stability of the Classical Catenoid and Darboux–Pöschl–Teller Potentials Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-10-29 Jens Hoppe, Per Moosavi
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Bi-infinite Solutions for KdV- and Toda-Type Discrete Integrable Systems Based on Path Encodings Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-10-22 David A. Croydon, Makiko Sasada, Satoshi Tsujimoto
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On Bose–Einstein condensates in the Thomas–Fermi regime Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-10-14 Daniele Dimonte, Emanuela L. Giacomelli
We study a system of N trapped bosons in the Thomas–Fermi regime with an interacting pair potential of the form \( g_N N^{3\beta -1} V(N^\beta x) \), for some \( \beta \in (0,1/3) \) and \( g_N \) diverging as \( N \rightarrow \infty \). We prove that there is complete Bose–Einstein condensation at the level of the ground state and, furthermore, that, if \( \beta \in (0,1/6) \), condensation is preserved
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Quasilinear Systems of First Order PDEs with Nonlocal Hamiltonian Structures Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-10-15 Pierandrea Vergallo
In this paper we investigate whether a quasilinear system of PDEs of first order admits Hamiltonian formulation with local and nonlocal operators. By using the theory of differential coverings, we find differential-geometric conditions necessary to write a given system with one of the three Hamiltonian operators investigated.
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Limit Theorems for Multi-group Curie–Weiss Models via the Method of Moments Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-09-24 Werner Kirsch, Gabor Toth
We study a multi-group version of the mean-field or Curie–Weiss spin model. For this model, we show how, analogously to the classical (single-group) model, the three temperature regimes are defined. Then we use the method of moments to determine for each regime how the vector of the group magnetisations behaves asymptotically. Some possible applications to social or political sciences are discussed
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Conjugate Frobenius Manifold and Inversion Symmetry Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-09-12 Zainab Al-Maamari, Yassir Dinar
We give a conjugacy relation on certain type of Frobenius manifold structures using the theory of flat pencils of metrics. It leads to a geometric interpretation for the inversion symmetry of solutions to Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations.
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Frobenius Manifolds on Orbits Spaces Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-08-25 Zainab Al-Maamari, Yassir Dinar
The orbits space of an irreducible linear representation of a finite group is a variety whose coordinate ring is the ring of invariant polynomials. Boris Dubrovin proved that the orbits space of the standard reflection representation of an irreducible finite Coxeter group \({\mathcal {W}}\) acquires a natural polynomial Frobenius manifold structure. We apply Dubrovin’s method on various orbits spaces
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Equivariant Spectral Triples for Homogeneous Spaces of the Compact Quantum Group $$U_q(2)$$ U q ( 2 ) Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-08-08 Satyajit Guin, Bipul Saurabh
In this article, we study homogeneous spaces \(U_q(2)/_\phi \mathbb {T}\) and \(U_q(2)/_\psi \mathbb {T}\) of the compact quantum group \(U_q(2),\,q\in {\mathbb {C}}\setminus \{0\}\). The homogeneous space \(U_q(2)/_\phi \mathbb {T}\) is shown to be the braided quantum group \(SU_q(2)\). The homogeneous space \(U_q(2)/_\psi \mathbb {T}\) is established as a universal \(C^*\)-algebra given by a finite
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Gauge Symmetries and Renormalization Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-08-06 David Prinz
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Levi–Civita Connections on Quantum Spheres Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-07-06 Joakim Arnlind, Kwalombota Ilwale, Giovanni Landi
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Lattice Gauge Theory and a Random-Medium Ising Model Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-07-06 Mikhail Skopenkov
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Prolongations of Convenient Lie Algebroids Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-06-21 Patrick Cabau, Fernand Pelletier
We first define the concept of Lie algebroid in the convenient setting. In reference to the finite dimensional context, we adapt the notion of prolongation of a Lie algebroid over a fibred manifold to a convenient Lie algebroid over a fibred manifold. Then we show that this construction is stable under projective and direct limits under adequate assumptions.
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The Zeros of the Partition Function of the Pinning Model Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-06-09 Giambattista Giacomin, Rafael L. Greenblatt
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Convergence and an Explicit Formula for the Joint Moments of the Circular Jacobi $$\beta $$ β -Ensemble Characteristic Polynomial Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-05-14 Theodoros Assiotis, Mustafa Alper Gunes, Arun Soor
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A Remark on the Spherical Bipartite Spin Glass Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-05-03 Giuseppe Genovese
Auffinger and Chen (J Stat Phys 157:40–59, 2014) proved a variational formula for the free energy of the spherical bipartite spin glass in terms of a global minimum over the overlaps. We show that a different optimisation procedure leads to a saddle point, similar to the one achieved for models on the vertices of the hypercube.
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Box and Ball System with Numbered Boxes Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-04-24 Yusaku Yamamoto, Akiko Fukuda, Sonomi Kakizaki, Emiko Ishiwata, Masashi Iwasaki, Yoshimasa Nakamura
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Bose–Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross–Pitaevskii Regime Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-04-12 Christian Brennecke, Benjamin Schlein, Severin Schraven
We consider a Bose gas consisting of N particles in \({\mathbb {R}}^3\), trapped by an external field and interacting through a two-body potential with scattering length of order \(N^{-1}\). We prove that low energy states exhibit complete Bose–Einstein condensation with optimal rate, generalizing previous work in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018; 376:1311–1395, 2020), restricted
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A $${\mathbb {Z}}_{2}$$ Z 2 -Topological Index for Quasi-Free Fermions Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-03-14 N. J. B. Aza, A. F. Reyes-Lega, L. A. M. Sequera
We use infinite dimensional self-dual \(\mathrm {CAR}\) \(C^{*}\)-algebras to study a \({\mathbb {Z}}_{2}\)-index, which classifies free-fermion systems embedded on \({\mathbb {Z}}^{d}\) disordered lattices. Combes–Thomas estimates are pivotal to show that the \({\mathbb {Z}}_{2}\)-index is uniform with respect to the size of the system. We additionally deal with the set of ground states to completely
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Weyl’s Laws and Connes’ Integration Formulas for Matrix-Valued $$L\!\log \!L$$ L log L -Orlicz Potentials Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-03-12 Raphaël Ponge
Thanks to the Birman-Schwinger principle, Weyl’s laws for Birman-Schwinger operators yields semiclassical Weyl’s laws for the corresponding Schrödinger operators. In a recent preprint Rozenblum established quite general Weyl’s laws for Birman-Schwinger operators associated with pseudodifferential operators of critical order and potentials that are product of \(L\!\log \!L\)-Orlicz functions and Alfhors-regular
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J-Trajectories in 4-Dimensional Solvable Lie Group $$\mathrm {Sol}_0^4$$ Sol 0 4 Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-03-06 Zlatko Erjavec, Jun-ichi Inoguchi
J-trajectories are arc length parameterized curves in almost Hermitian manifold which satisfy the equation \(\nabla _{{\dot{\gamma }}}{\dot{\gamma }}=q J {\dot{\gamma }}\). In this paper J-trajectories in the solvable Lie group \(\mathrm {Sol}_0^4\) are investigated. The first and the second curvature of a non-geodesic J-trajectory in an arbitrary LCK manifold whose anti Lee field has constant length
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Regularising Transformations for Complex Differential Equations with Movable Algebraic Singularities Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-03-06 Thomas Kecker, Galina Filipuk
In a 1979 paper, Okamoto introduced the space of initial values for the six Painlevé equations and their associated Hamiltonian systems, showing that these define regular initial value problems at every point of an augmented phase space, a rational surface with certain exceptional divisors removed. We show that the construction of the space of initial values remains meaningful for certain classes of
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On Tsallis and Kaniadakis Divergences Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-02-24 Răzvan-Cornel Sfetcu, Sorina-Cezarina Sfetcu, Vasile Preda
We study some properties concerning Tsallis and Kaniadakis divergences between two probability measures. More exactly, we prove the pseudo-additivity, non-negativity, monotonicity and find some bounds for the divergences mentioned above.
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Factorization Problems on Rational Loop Groups, and the Poisson Geometry of Yang-Baxter Maps Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-02-19 Luen-Chau Li
The study of set-theoretic solutions of the Yang-Baxter equation, also known as Yang-Baxter maps, is historically a meeting ground for various areas of mathematics and mathematical physics. In this work, we study factorization problems on rational loop groups, which give rise to Yang-Baxter maps on various geometrical objects. We also study the symplectic and Poisson geometry of these Yang-Baxter maps
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Involutions of Halphen Pencils of Index 2 and Discrete Integrable Systems Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-02-05 Kangning Wei
We constructed involutions for a Halphen pencil of index 2, and proved that the birational mapping corresponding to the autonomous reduction of the elliptic Painlevé equation for the same pencil can be obtained as the composition of two such involutions.
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Phase Transitions and Percolation at Criticality in Enhanced Random Connection Models Math. Phys. Anal. Geom. (IF 1.0) Pub Date : 2022-01-13 Iyer, Srikanth K., Jhawar, Sanjoy Kr.
We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a homogeneous Poisson point process \(\mathcal {P}_{\lambda }\) in \(\mathbb {R}^{2}\) of intensity λ. In the homogeneous RCM, the vertices at x,y are connected with