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Mathematical Physics papers — page 225

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One dimensional discrete Schrödinger operators with resonant embedded eigenvalues
In this paper, we introduce a new family of functions to construct Schrödinger operators with embedded eigenvalues. This particularly allows us to construct discrete Schrödinger operators with…
Wencai Liu, Kang LyuJul 1, 2022
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Discrete integrable systems and random Lax matrices
We study properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. Specifically, we investigate the spectral behaviour of the corresponding Lax…
Massimo Gisonni, Tamara Grava, Giorgio Gubbiotti et al.Jun 30, 2022
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A proof of the Lieb-Thirring inequality via the Besicovitch covering lemma
We give a proof of the Lieb-Thirring inequality on the kinetic energy of orthonormal functions by using a microlocal technique, in which the uncertainty and exclusion principles are combined through…
Phan Thành NamJun 30, 2022
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Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential
We consider a gas of weakly interacting bosons in three dimensions subject to an external potential in the mean field regime. Assuming that the initial state of our system is a product state, we show…
Charlotte Dietze, Jinyeop LeeJun 30, 2022
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The Floquet Baxterisation
Quantum integrability has proven to be a useful tool to study quantum many-body systems out of equilibrium. In this paper we construct a generic framework for integrable quantum circuits through the…
Yuan Miao, Vladimir Gritsev, Denis V. KurlovJun 30, 2022
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The ionization problem in quantum mechanics
While it is well-known experimentally that a neutral atom can bind at most one or two extra electrons, deriving this fact rigorously from first principles of quantum mechanics remains a very…
Phan Thành NamJun 30, 2022
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Dip-ramp-plateau for Dyson Brownian motion from the identity on U(N)
In a recent work the present authors have shown that the eigenvalue probability density function for Dyson Brownian motion from the identity on U(N) is an example of a newly identified class of…
Peter J. Forrester, Mario Kieburg, Shi-Hao Li et al.Jun 29, 2022
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Symplectic duality for topological recursion
We consider weighted double Hurwitz numbers, with the weight given by arbitrary rational function times an exponent of the completed cycles. Both special singularities are arbitrary, with the lengths…
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian et al.Jun 29, 2022
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On the global minimum of the energy-momentum relation for the polaron
For the Fr\"ohlich 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…
Jonas Lampart, David Mitrouskas, Krzysztof MyśliwyJun 29, 2022
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Boundary structure of gauge and matter fields coupled to gravity
The boundary structure of 3+1-dimensional gravity (in the Palatini-Cartan formalism) coupled to to gauge (Yang-Mills) and matter (scalar and spinorial) fields is described through the use of the…
Giovanni Canepa, Alberto S. Cattaneo, Filippo Fila-RobattinoJun 29, 2022
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Exact sum rules for spectral zeta functions of homogeneous 1D quantum oscillators, revisited
We survey sum rules for spectral zeta functions of homogeneous 1D Schr\"odinger operators, that mainly result from the exact WKB method.
André VorosJun 29, 2022
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Integrability of planar-algebraic models
The Quantum Inverse Scattering Method is a scheme for solving integrable models in 1+1 dimensions, building on an R-matrix that satisfies the Yang--Baxter equation and in terms of which one…
Xavier Poncini, Jorgen RasmussenJun 29, 2022
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Renewal approach for the energy-momentum relation of the Fröhlich polaron
We study the qualitative behaviour of the energy-momentum relation of the Fröhlich polaron at fixed coupling strength. Among other properties, we show that it is non-decreasing and that the…
Steffen PolzerJun 29, 2022
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Complexity of representations of coefficients of power series in classical statistical mechanics. Their classification and complexity criteria
It is declared that the aim of simplifying representations of coefficients of power series of classical statistical mechanics is to simplify a process of obtaining estimates of the coefficients using…
G. I. KalmykovJun 29, 2022
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Fixed points of an infinite dimensional operator related to Gibbs measures
We describe fixed points of an infinite dimensional non-linear operator related to a hard core (HC) model with a countable set N of spin values on the Cayley tree. This operator is defined…
U. R. Olimov, U. A. RozikovJun 28, 2022
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A comment on the solutions of the generalized Faddeev-Volkov model
We consider two recent generalizations of the Faddeev-Volkov model, which is exactly solvable Ising-type lattice spin model. The first generalization based on using of the non-compact quantum…
Mehmet DedeJun 28, 2022
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Critical points of discrete periodic operators
We study the spectra of operators on periodic graphs using methods from combinatorial algebraic geometry. Our main result is a bound on the number of complex critical points of the Bloch variety,…
Matthew Faust, Frank SottileJun 27, 2022
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On the Effective Quasi-Bosonic Hamiltonian of the Electron Gas: Collective Excitations and Plasmon Modes
We consider an effective quasi-bosonic Hamiltonian of the electron gas which emerges naturally from the random phase approximation and describes the collective excitations of the gas. By a rigorous…
Martin Ravn Christiansen, Christian Hainzl, Phan Thành NamJun 27, 2022
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R\'enyi's entropy on Lorentzian spaces. Timelike curvature-dimension conditions
For a Lorentzian space measured by m in the sense of Kunzinger, S\"amann, Cavalletti, and Mondino, we introduce and study synthetic notions of timelike lower Ricci curvature bounds by…
Mathias BraunJun 27, 2022
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Quantum Diffusion via an Approximate Semigroup Property
In this paper we introduce a new approach to the diffusive limit of the weakly random Schrodinger equation, first studied by L. Erdos, M. Salmhofer, and H.T. Yau. Our approach is based on a…
Felipe HernándezJun 27, 2022
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Deformation quantization of contact manifolds
We extend Fedosov deformation quantization to general contact manifolds. Unlike the case of symplectic manifolds, not every classical observable on a contact manifold is generally quantized. On…
Boris M. Elfimov, Alexey A. SharapovJun 27, 2022
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Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system
We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by HN = p12 + p22 +Σn=1N γn(q1 p1 + q2 p2)n , where qi and pi are…
Alfonso Blasco, Ivan Gutierrez-Sagredo, Francisco J. HerranzJun 25, 2022
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Nambu mechanics viewed as a Clebsch parameterized Poisson algebra -- toward canonicalization and quantization
In his pioneering paper [Phys. Rev. E 7, 2405 (1973)], Nambu proposed the idea of multiple Hamiltonian systems. The explicit example examined there is equivalent to the so(3) Lie-Poisson system,…
Zensho YoshidaJun 25, 2022
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Algebraic area enumeration for open lattice walks
We calculate the number of open walks of fixed length and algebraic area on a square planar lattice by an extension of the operator method used for the enumeration of closed walks. The open walk area…
Stephane Ouvry, Alexios PolychronakosJun 24, 2022
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On super cluster algebras based on super Pl\"ucker and super Ptolemy relations
We study super cluster algebra structure arising in examples provided by super Pl\"ucker and super Ptolemy relations. We develop the super cluster structure of the super Grassmannians…
Ekaterina ShemyakovaJun 24, 2022
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