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Mathematical Physics papers — page 221

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Fine structure of flat bands in a chiral model of magic angles
We analyze symmetries of Bloch eigenfunctions at magic angles for the Tarnopolsky--Kruchkov--Vishwanath chiral model of the twisted bilayer graphene (TBG) following the framework introduced by…
Simon Becker, Tristan Humbert, Maciej ZworskiAug 2, 2022
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Integrability in the chiral model of magic angles
Magic angles in the chiral model of twisted bilayer graphene are parameters for which the chiral version of the Bistritzer--MacDonald Hamiltonian exhibits a flat band at energy zero. We compute the…
Simon Becker, Tristan Humbert, Maciej ZworskiAug 2, 2022
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Perturbative connection formulas for Heun equations
Connection formulas relating Frobenius solutions of linear ODEs at different Fuchsian singular points can be expressed in terms of the large order asymptotics of the corresponding power series. We…
O. Lisovyy, A. NaidiukAug 2, 2022
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The Gell-Mann-Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime
We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in…
Martin Ravn Christiansen, Christian Hainzl, Phan Thành NamAug 2, 2022
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On asymptotic expansions of resolvents for Poisson distributed random Schrödinger operators
We study expectation values of matrix elements of the resolvent for a random Schrödinger operator with potential distributed according to a Poisson process. Asymptotic expansions for these matrix…
David Hasler, Jannis KobersteinAug 2, 2022
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Large-time asymptotics to the focusing nonlocal modified Kortweg-de Vries equation with step-like boundary conditions
We investigate the large-time asymptotics of solution for the Cauchy problem of the nonlocal focusing modified Kortweg-de Vries (MKdV) equation with step-like initial data, i.e., $u0(x)→…
Taiyang Xu, Engui FanAug 2, 2022
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ε-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
We present a new methodology, suitable for implementation on computer, to perform the ε-expansion of hypergeometric functions with linear ε dependent Pochhammer parameters in any…
Souvik BeraAug 1, 2022
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Motion of Lee-Yang zeros
We consider the zeros of the partition function of the Ising model with ferromagnetic pair interactions and complex external field. Under the assumption that the graph with strictly positive…
Qi Hou, Jianping Jiang, Charles M. NewmanAug 1, 2022
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A continuous analog of the binary Darboux transformation for the Korteweg-de Vries equation
In the KdV context we put forward a continuous version of the binary Darboux transformation (aka the double commutation method). Our approach is based on the Riemann-Hilbert problem and yields a new…
Alexei RybkinAug 1, 2022
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Tensor types and their use in physics
The content of this paper can be roughly organized into a three-level hierarchy of generality. At the first, most general level, we introduce a new language which allows us to express various…
Andreas Bauer, Alexander NietnerAug 1, 2022
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Reduction of Lagrangian Equations of Motion of Modified Newtonian Theory of Gravity with respect to the Similarity Group
The equivalence class of absolute configurations of a system under the group of similarity transformations Sim(3) is called the shape of the system. The Sim(3) invariant Lagrangian of the…
Sahand TokasiJul 30, 2022
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Weak Edgeworth expansion for the mean-field interacting Bose gas
We consider the ground state and the low-energy excited states of a system of N identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive an Edgeworth…
Lea Boßmann, Sören PetratJul 30, 2022
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Stability of determination of Riemann surface from its DN-map in terms of Teichmüller distance
As is known, the Dirichlet-to-Neumann operator Λ of a Riemannian surface (M,g) determines the surface up to conformal equivalence class [(M,g)]. Such classes constitute the Teichmüller space…
M. I. Belishev, D. V. KorikovJul 30, 2022
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Beyond mean field: condensate coupled with pair excitations
We prove existence results for a system of partial differential equations describing the approximate condensate wavefunction and pair-excitation kernel of a dilute (T=0) Bose gas in the stationary…
Stephen SorokanichJul 29, 2022
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Ensemble forecasts in reproducing kernel Hilbert space family
A methodological framework for ensemble-based estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system…
Benjamin Dufée, Bérenger Hug, Etienne Mémin et al.Jul 29, 2022
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Universal Chern number statistics in random matrix fields
We investigate the probability distribution of Chern numbers (quantum Hall effect integers) for a parametric version of the GUE random matrix ensemble, which is a model for a chaotic or disordered…
Or Swartzberg, Michael Wilkinson, Omri GatJul 28, 2022
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From Euler elements and 3-gradings to non-compactly causal symmetric spaces
In this article we discuss the interplay between causal structures of symmetric spaces and geometric aspects of Algebraic Quantum Field Theory (AQFT). The central focus is the set of Euler elements…
Vincenzo Morinelli, Karl-Hermann Neeb, Gestur OlafssonJul 28, 2022
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p-Adic Statistical Field Theory and Deep Belief Networks
In this work we initiate the study of the correspondence between p-adic statistical field theories (SFTs) and neural networks (NNs). In general quantum field theories over a p-adic spacetime can be…
W. A. Zúñiga-GalindoJul 28, 2022
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Scaling asymptotics of spectral Wigner functions
We prove that smooth Wigner-Weyl spectral sums at an energy level E exhibit Airy scaling asymptotics across the classical energy surface E. This was proved earlier by the authors for the…
Boris Hanin, Steve ZelditchJul 27, 2022
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Bogoliubov theory for the dilute Fermi gas in three dimensions
In a dilute system of N fermions with spin 1/2 in three dimensions, we study the correlation energy which is given by the difference between the ground state energy and the energy of the…
Emanuela L. GiacomelliJul 27, 2022
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D-dimensional cellular automata provide Salem's singular function Lα with α=1/(2D+1) and 1/(2D+1)
Salem's singular function is strictly increasing, continuous, and has a derivative equal to zero almost everywhere in [0,1]; it is also known as de Rham's singular function or…
Akane KawaharadaJul 27, 2022
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Robustness of Excitations in the Random Dimer Model
The ground state solution of the random dimer model is at a critical point after, which has been shown with random link excitations. In this paper we test the robustness of the random dimer model to…
Daniel RetiJul 26, 2022
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Entangled Quantum States of Causal Fermion Systems and Unitary Group Integrals
This paper is dedicated to a detailed analysis and computation of quantum states of causal fermion systems. The mathematical core is to compute integrals over the unitary group asymptotically for a…
Felix Finster, Niky Kamran, Moritz ReintjesJul 26, 2022
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The Geometry of Supersymmetry / A concise introduction
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states…
Norbert Poncin, Sarah SchoutenJul 26, 2022
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On constant solutions of SU(2) Yang-Mills-Dirac equations
For the first time, a complete classification of all constant solutions of the Yang-Mills-Dirac equations with SU(2) gauge symmetry in Minkowski space R1,3 is given. The explicit form…
D. S. ShirokovJul 25, 2022
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