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Mathematical Physics papers — page 241

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Reduced fluctuations for bosons in a double well
We review two recent results on the ground state properties of bosonic systems trapped by a double well external potential. In the limit of large population and large separation between the wells we…
Alessandro OlgiatiMar 1, 2022
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The Elliptic Ginibre Ensemble: A Unifying Approach to Local and Global Statistics for Higher Dimensions
The elliptic Ginibre ensemble of complex non-Hermitian random matrices allows to interpolate between the rotational invariant Ginibre ensemble and the Gaussian unitary ensemble of Hermitian random…
G. Akemann, M. Duits, L. D. MolagMar 1, 2022
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A Z2-Topological Index as a Z2-State Index
Within the setting of infinite dimensional self-dual CAR C*-algebras describing fermions in the Zd-lattice, we depart from the well-known Araki-Evans σ(P1,P2)…
N. J. B. Aza, L. C. P. A. M. Müssnich, A. F. Reyes-LegaMar 1, 2022
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Low-energy spectrum and dynamics of the weakly interacting Bose gas
We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates and dynamics, which provides…
Lea BoßmannMar 1, 2022
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Essential self-adjointness for the Klein-Gordon type operators on asymptotically static spacetime
Let X=R× M be the spacetime, where M is a closed manifold equipped with a Riemannian metric g, and we consider a symmetric Klein-Gordon type operator P on X, which is…
Shu Nakamura, Kouichi TairaMar 1, 2022
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Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations
This work concerns the relation between the geometry of Lagrangian Grassmannians and the CKP integrable hierarchy. The Lagrange map from the Lagrangian Grassmannian of maximal isotropic (Lagrangian)…
S. Arthamonov, J. Harnad, J. HurtubiseFeb 28, 2022
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Dilute Bose gas with three-body interaction: recent results and open questions
We review our recent study on the ground state energy of dilute Bose gases with three-body interactions. The main feature of our results is the emergence of the 3D energy-critical Schr\"odinger…
Phan Thành Nam, Julien Ricaud, Arnaud TriayFeb 28, 2022
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Reduction and reconstruction of multisymplectic Lie systems
A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional real Lie…
Javier de Lucas, Xavier Gràcia, Xavier Rivas et al.Feb 28, 2022
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Combinatorial Cobordism Theory
We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field…
Maxime SavoyFeb 28, 2022
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A Construction for Clifford Algebras
This paper is dedicated to the memory of Zbigniew Oziewicz, to his generosity, intelligence and intensity in the search that is science and mathematics. The paper begins with a basic construction…
Louis H. KauffmanFeb 28, 2022
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Multifractal eigenfunctions for quantum star graphs
We prove that the eigenfunctions of quantum star graphs exhibit multifractal self-similar structure in certain specified circumstances. In the semiclassical regime, when the spectral parameter and…
Jonathan P. Keating, Henrik UeberschaerFeb 28, 2022
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A remark on the essential self-adjointness for Klein-Gordon type operators
Here we discuss a new simplified proof of the essential self-adjointness for formally self-adjoint differential operators of real principal type, previously proved by Vasy (2020) and Nakamura-Taira…
Shu Nakamura, Kouichi TairaFeb 28, 2022
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Hamiltonian field theory close to the wave equation: from Fermi-Pasta-Ulam to water waves
In the present work we analyse the structure of the Hamiltonian field theory in the neighbourhood of the wave equation qtt=qxx. We show that, restricting to ``graded'' polynomial…
Matteo Gallone, Antonio PonnoFeb 27, 2022
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Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial…
Danilo Latini, Ian Marquette, Yao-Zhong ZhangFeb 27, 2022
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On applications of Herglotz-Nevanlinna functions in material sciences, II: extended applications and generalized theory
Part II of the review article focuses on the applications of Herglotz-Nevanlinna functions in material sciences. It presents a diverse set of applications with details and the role of…
Miao-Jung Yvonne Ou, Annemarie LugerFeb 26, 2022
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Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
In this paper we continue our derivation of the correlation functions of open quantum spin 1/2 chains with unparallel magnetic fields on the edges; this time for the more involved case of the XXZ…
G. Niccoli, V. TerrasFeb 25, 2022
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Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity
We study the Hamiltonian for a system of N identical bosons interacting with an impurity, i.e., a different particle, via zero-range forces in dimension three. It is well known that, following the…
Daniele Ferretti, Alessandro TetaFeb 25, 2022
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Mathematical structures of cohomological field theories
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing…
Shuhan JiangFeb 24, 2022
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Quantum Calculi: differential forms and vector fields in noncommutative geometry
In this paper, we revise the concept of noncommutative vector fields introduced previously in Ref. [1,2], extending the framework, adding new results and clarifying the old ones. Using appropriate…
Andrzej BorowiecFeb 24, 2022
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The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
Bogoliubov Theory provides important predictions for the low energy properties of the weakly interacting Bose gas. Recently, Bogoliubov's predictions could be justified rigorously in BBCS3…
Christian BrenneckeFeb 24, 2022
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On tetrahedron type equations associated with B3,C3, F4 and H3
Tetrahedron equation is a three dimensional analogue of the Yang-Baxter equation. It allows a formulation in terms of the Coxeter group A3. This short note includes miscellaneous remarks on the…
Atsuo KunibaFeb 24, 2022
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Spectral form factor in the Hadamard-Gutzwiller model: orbit pairs contributing in the third order
In this paper we consider orbit pairs contributing in the third order of the spectral form factor in the Hadamard-Gutzwiller model. We prove that periodic orbits including two 2-encounters in certain…
Huynh M. HienFeb 24, 2022
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NSR singular vectors from Uglov polynomials
It was conjectured in arXiv:1211.2788 that bosonization of singular vectors (in Neveu-Schwarz sector) of N=1 super analog of the Virasoro algebra can be identified with Uglov symmetric…
Mikhail Bershtein, Angelina VargulevichFeb 23, 2022
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Entanglement on Orbits
The study of multipartite entanglement is not only interesting but also important due to its wide application in quantum information processing. However, the complicated structure of the Hilbert…
Songbo XieFeb 23, 2022
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SPT indices emerging from translation invariance in two dimensional quantum spin systems
We consider SPT-phases with on-site G (where G is any finite group) symmetry for two-dimensional quantum spin systems. We then impose translation invariance in one direction and observe that on…
Tijl JappensFeb 23, 2022
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