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Mathematical Physics papers — page 180

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A New Non-Linear Density Fluctuations Stochastic Partial Differential Equation With a Singular Coefficient of Relevance to Polymer Dynamics and Rheology: Discussions, Proofs of Solution Existence, Uniqueness, and a Conjecture
In this paper we consider an entirely new - previously unstudied to the best of our knowledge - type of density fluctuations stochastic partial differential equation with a singular coefficient…
Ludovic Goudenège, Liviu Iulian PaladeJun 9, 2023
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An introduction to the analysis of gradients systems
The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4…
Alexander MielkeJun 8, 2023
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Eigenstates and spectral projection for quantized baker's map
We extend the approach from [arXiv:2110.15301] to prove windowed spectral projection estimates and a generalized Weyl law for the (Weyl) quantized baker's map on the torus. The spectral window is…
Laura ShouJun 8, 2023
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Approximate Analytical Solution using Power Series Method for the Propagation of Blast Waves in a Rotational Axisymmetric non-ideal Gas
In this paper, the propagation of the blast (shock) waves in non-ideal gas atmosphere in rotational medium is studied using a power series method in cylindrical geometry. The flow variables are…
Nandita, Rajan AroraJun 8, 2023
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Stellar dynamics within the virial theorem: asymptotic small-parameters time expansion of the Ermakov-Lewis-Leach invariant as an infinite series of conservation laws
The regime of undamped oscillations characterizing the stellar dynamics of virialised systems is analysed within the framework of a new approach to the study of the integrals of motion. The method is…
Orchidea Maria Lecian, Brunello TirozziJun 7, 2023
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Symplectic and variational formulations of compressible and incompressible Navier-Stokes equation
In a previous paper, we proposed a symplectic version of Brezis-Ekeland-Nayroles principle based on the concepts of Hamiltonian inclusions and symplectic polar functions. We illustrated it by…
Géry de SaxcéJun 7, 2023
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The U(1) BF functional measure and the Dirac distribution on the space of quantum fields
In this letter, we explain how the U(1) BF measure can be related to the Fourier transform of a Dirac distribution defined on the Z-module of quantum fields. Then, we revisit the U(1) BF…
Frank ThuillierJun 7, 2023
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Bifurcations of Riemann Ellipsoids
We give an account of the various changes in the stability character in the five types of Riemann ellipsoids by establishing the occurrence of different quasi-periodic Hamiltonian bifurcations.…
Fahimeh Mokhtari, Jesús F. Palacián, Patricia YanguasJun 7, 2023
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Beyond Superoscillation: General Theory of Approximation with Bandlimited Functions
We give a general strategy to construct superoscillating/growing functions using an orthogonal polynomial expansion of a bandlimited function. The degree of superoscillation/growth is controlled by…
Tathagata Karmakar, Andrew N. JordanJun 6, 2023
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Counting eigenvalues of Schr\"odinger operators using the landscape function
We prove an upper and a lower bound on the rank of the spectral projections of the Schr\"odinger operator - + V in terms of the volume of the sublevel sets of an effective potential…
Sven Bachmann, Richard Froese, Severin SchravenJun 6, 2023
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Extended Series of Correlation Inequalities in Quantum Systems
A systematic derivation provides extended series of correlation inequalities in quantum systems. Each order in truncated Taylor expansion of the spectral representation for the Duhamel correlation…
Chigak Itoi, Hiroto Ishimori, Kota Sato et al.Jun 6, 2023
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Reconstruction of shear force in Atomic Force Microscopy from measured displacement of the cone-shaped cantilever tip
In this paper, a dynamic model of reconstruction of the shear force g(t) in the Atomic Force Microscopy (AFM) cantilever tip-sample interaction is proposed. The interaction of the cone-shaped…
Alemdar Hasanov, Onur Baysal, Alexandre KawanoJun 5, 2023
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Stability analysis of nonlinear localized modes in the coupled Gross-Pitaevskii equations with PT-symmetric Scarf-II potential
We study the nonlinear localized modes in two-component Bose-Einstein condensates with parity-time-symmetric Scarf-II potential, which can be described by the coupled Gross-Pitaevskii equations.…
Jia-Rui Zhang, Xia WangJun 5, 2023
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Degenerate flat bands in twisted bilayer graphene
We prove that in the chiral limit of the Bistritzer--MacDonald Hamiltonian, there exist magic angles at which the Hamiltonian exhibits flat bands of multiplicity four instead of two. We analyse the…
Simon Becker, Tristan Humbert, Maciej ZworskiJun 5, 2023
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Decay of the Green's function of the fractional Anderson model and connection to long-range SAW
We prove a connection between the Green's function of the fractional Anderson model and the two point function of a self-avoiding random walk with long range jumps, adapting a strategy proposed by…
Margherita Disertori, Roberto Maturana Escobar, Constanza Rojas-MolinaJun 5, 2023
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Low energy spectrum of the XXZ model coupled to a magnetic field
For a class of Hamiltonians of XXZ spin chains in a uniform external magnetic field that are small quantum perturbations of an Ising Hamiltonian, it is shown that the spectral gap above the…
Simone Del Vecchio, Jürg Fröhlich, Alessandro Pizzo et al.Jun 5, 2023
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Convergence of operators with deficiency indices (k,k) and of their self-adjoint extensions
We consider an abstract sequence \An\n=1∞ of closed symmetric operators on a separable Hilbert space H. It is assumed that all An's have equal deficiency indices (k,k)…
August BjergJun 5, 2023
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Superspace realizations of the Bannai-Ito algebra
A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the three-fold tensor product of the basic realization of the Lie superalgebra osp(1|2) in terms of operators in…
N. Crampe, H. De Bie, P. Iliev et al.Jun 5, 2023
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Post-Lie algebras of derivations and regularity structures
Given a commutative algebra A, we exhibit a canonical structure of post-Lie algebra on the space A Der(A) where Der(A) is the space of…
Jean-David Jacques, Lorenzo ZambottiJun 4, 2023
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Generalised Br\`egman relative entropies: a brief introduction
We present some basic elements of the theory of generalised Br\`egman relative entropies over nonreflexive Banach spaces. Using nonlinear embeddings of Banach spaces together with the…
Ryszard Paweł KosteckiJun 4, 2023
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Multiplication of distributions in a linear gain and loss system
We consider a model of coupled oscillators which can be seen as a gain and loss system. In the attempt to quantize the system we propose a new definition of multiplication between distributions, and…
Fabio BagarelloJun 4, 2023
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Inviscid Water-Waves and interface modeling
We present a rigorous mathematical analysis of the modeling of inviscid water waves. The free-surface is described as a parametrized curve. We introduce a numerically stable algorithm which accounts…
Emmanuel Dormy, Christophe LacaveJun 4, 2023
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Semiclassical resonances for matrix Schr\"odinger operators with vanishing interactions at crossings of classical trajectories
We study the semiclassical distribution of resonances of a 2 × 2 matrix Schr\"odinger operator, obtained as a reduction of an Hamiltonian when studying molecular predissociation models under…
Vincent LouatronJun 4, 2023
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Random matrix theory and the loss surfaces of neural networks
Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world…
Nicholas P BaskervilleJun 3, 2023
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Thermal time as an unsharp observable
We show that the Connes-Rovelli thermal time associated with the quantum harmonic oscillator can be described as an (unsharp) observable, that is, as a positive operator valued measure. We…
Jan van Neerven, Pierre PortalJun 3, 2023
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