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Mathematical Physics papers — page 243

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Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Three
Quasi-periodic solutions of the Gross-Pitaevskii equation with a periodic potential in dimension three are studied. It is proven that there is an extensive "non-resonant" set $ G…
Yulia Karpeshina, Seonguk Kim, Roman ShterenbergFeb 14, 2022
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Continuum limit of the lattice quantum graph Hamiltonian
We consider the quantum graph Hamiltonian on the square lattice in Euclidean space, and we show that the spectrum of the Hamiltonian converges to the corresponding Schrödinger operator on the…
Pavel Exner, Shu Nakamura, Yukihide TadanoFeb 14, 2022
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Invariant KAM tori: from theory to applications to exoplanetary systems
We consider the classical problem of the construction of invariant tori exploiting suitable Hamiltonian normal forms. This kind of approach can be translated by means of the Lie series method into…
Ugo Locatelli, Chiara Caracciolo, Marco Sansottera et al.Feb 14, 2022
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On the generators of quantum dynamical semigroups with invariant subalgebras
The problem of characterizing GKLS-generators and CP-maps with an invariant appeared in different guises in the literature. We prove two unifying results which hold even for weakly closed *-algebras:…
Markus Hasenöhrl, Matthias C. CaroFeb 11, 2022
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Universality of replica-symmetry breaking in the transverse field Sherrington-Kirkpatrick model
The existence theorem for replica-symmetry breaking (RSB) in the transverse field Sherrington-Kirkpatrick (SK) model is extended to the model with a general random exchange interactions. The relation…
C. Itoi, H. Ishimori, K. Sato et al.Feb 11, 2022
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Thermodynamic limit of the Pieces' Model V2
We study the ground states of the pieces' model in the Fermi-Dirac statistics in the thermodynamic limit. In other words, we consider the minimizing configurations of n interacting fermions…
Vadim OgnovFeb 11, 2022
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Markovian Repeated Interaction Quantum Systems
We study a class of dynamical semigroups (Ln)n∈N that emerge, by a Feynman--Kac type formalism, from a random quantum dynamical system…
Jean-François Bougron, Alain Joye, Claude-Alain PilletFeb 10, 2022
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On the number and sums of eigenvalues of Schr\"odinger-type operators with degenerate kinetic energy
We estimate sums of functions of negative eigenvalues of Schr\"odinger-type operators whose kinetic energy vanishes on a codimension one submanifold. Our main technical tool is the Stein-Tomas…
Jean-Claude Cuenin, Konstantin MerzFeb 10, 2022
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Lieb's most useful contribution to density functional theory?
The importance of the Lieb-Simon proof of the relative exactness of Thomas-Fermi theory in the large-Z limit to modern density functional theory (DFT) is explored. The principle, that there is a…
Kieron BurkeFeb 10, 2022
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Self-Adjointness of Toeplitz Operators on the Segal-Bargmann Space
We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. Our criterion applies, in particular, to symbols with Lipschitz continuous…
Wolfram Bauer, Lauritz van Luijk, Alexander Stottmeister et al.Feb 9, 2022
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A Birman-Schwinger principle in galactic dynamics
These are the (somewhat extended) lecture notes for four lectures delivered at the spring school during the thematic programme "Mathematical Perspectives of Gravitation beyond the Vacuum…
Markus KunzeFeb 9, 2022
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On the algebraic solutions of the Painleve-III (D7) equation
The D7 degeneration of the Painleve-III equation has solutions that are rational functions of x1/3 for certain parameter values. We apply the isomonodromy method to obtain a Riemann-Hilbert…
Robert J. Buckingham, Peter D. MillerFeb 9, 2022
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Dimer model on the square lattice with interface
In this exposition, we consider the dimer problem on an infinite square lattice with partially non-periodic edge weights, which we refer to as the square lattice with interface. In particular, we…
Meredith SheaFeb 9, 2022
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2D discrete Hodge-Dirac operator on the torus
We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace…
Volodymyr SushchFeb 8, 2022
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An Application of Singular Traces to Crystals and Percolation
For a certain class of discrete metric spaces, we provide a formula for the density of states. This formula involves Dixmier traces and is proven using recent advances in operator theory. Various…
N. Azamov, E. Hekkelman, E. McDonald et al.Feb 8, 2022
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Towards modified bimetric theories within non-product spectral geometry
We discuss class of doubled geometry models with diagonal metrics. Based on the analysis of known examples we formulate a hypothesis that supports treating them as modified bimetric gravity theories.…
Arkadiusz BochniakFeb 8, 2022
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Magnetic quantum currents in the presence of a Neumann wall
We consider the Schrödinger operator with constant transverse magnetic field on a half-plane, endowed with Neumann boundary conditions. We study the low energy currents flowing along the boundary and…
Nicolas Raymond, Éric SoccorsiFeb 8, 2022
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Quantum KdV hierarchy and quasimodular forms
Dubrovin has shown that the spectrum of the quantization (with respect to the first Poisson structure) of the dispersionless Korteweg-de Vries (KdV) hierarchy is given by shifted symmetric functions;…
Jan-Willem M. van Ittersum, Giulio RuzzaFeb 7, 2022
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Proper condensates and off-diagonal long range order
Within the framework of the algebra of canonical commutation relations in Euclidean space, a long range order between particles in bounded regions is established in states with a sufficiently large…
Detlev BuchholzFeb 7, 2022
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A note on continuous entropy
Von Neumann entropy has a natural extension to the case of an arbitrary semifinite von Neumann algebra, as was considered by I. E. Segal. We relate this entropy to the relative entropy and show that…
Roberto Longo, Edward WittenFeb 7, 2022
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Absolutely Continuous Spectrum For Schrödinger Operators With Random Decaying Matrix Potentials on The Strip
We consider a family of random Schrödinger operators on the discrete strip with decaying random 2 matrix potential. We prove that the spectrum is almost surely pure absolutely continuous,…
Hernan Gonzales, Christian SadelFeb 7, 2022
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Painleve-type asymptotics for the defocusing Hirota equation in transition region
We consider the Cauchy problem for the classical Hirota equation on the line with decaying initial data. Based on the spectral analysis of the Lax pair of the Hirota equation, we first expressed the…
Weikang Xun, Luman Ju, Engui FanFeb 6, 2022
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Notes on the Twistor P1
Remarkably, the twistor P1 occurs as a fundamental object in both four-dimensional space-time geometry and in number theory. In Euclidean signature twistor theory it is how one describes…
Peter WoitFeb 5, 2022
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Nonstandard Null Lagrangians and Gauge Functions and Dissipative Forces in Dynamics
Standard and non-standard Lagrangians that give the same equation of motion are significantly different in their forms, as the latter do not have terms that clearly discernable energy-like…
A. L. Segovia, L. C. Vestal, Z. E. MusielakFeb 5, 2022
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Asymptotic behavior of a stochastic particle system of 5 neighbors
We analyze a stochastic particle system of 5 neighbors. Considering eigenvalue problem of transition matrix, we propose a conjecture that asymptotic distribution of the system is determined by the…
Kazushige EndoFeb 5, 2022
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