Results 61 to 70 of about 166 (151)

Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential

Symmetry, Integrability and Geometry: Methods and Applications, 2005
The complex WKB-Maslov method is used to consider an approach to the semiclassical integrability of the multidimensional Gross-Pitaevskii equation with an external field and nonlocal nonlinearity previously developed by the authors.
Alexander Shapovalov, Andrey Trifonov, Alexander Lisok   +2 more
doaj  

Nonlinear Fokker-Planck Equation in the Model of Asset Returns

Symmetry, Integrability and Geometry: Methods and Applications, 2008
The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets.
Alexander Shapovalov, Andrey Trifonov, Elena Masalova   +2 more
doaj  

Semiclassical asymptotics, gauge fields, and quantum chaos

Journal of Functional Analysis, 1989
A gauge field is given by a connection on a principal bundle P → M. We consider the semiclassical behavior of a family of Schrödinger operators associated with a gauge field, in the limit as . We relate the spectral theory of such operators to behavior of the Hamiltonian flow on the natural phase space associated to a gauge field, examining in ...
Schrader, Robert, Taylor, Michael E
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Quantum scattering with semiclassical asymptotic motion

, 2018
Conventional scattering theory is incomplete in that it does not adequately describe the behaviour of the wave function at macroscopic distances from the scattering reaction volume. In scattering experiments particles are incident from sources at macroscopic distance and measured at macroscopic distance from the microscopic reaction volume.
Briggs, John S., Feagin, James M.
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Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation

Symmetry, Integrability and Geometry: Methods and Applications, 2005
The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method.
Alexey Borisov, Alexander Shapovalov, Andrey Trifonov   +2 more
doaj  

Semiclassical asymptotics of the Bloch–Torrey operator in two dimensions

Journal of the Mathematical Society of Japan
The Bloch--Torrey operator $-h^2Δ+e^{iα}x_1$ on a bounded smooth planar domain, subject to Dirichlet boundary conditions, is analyzed. Assuming $α\in\left[0,\frac{3π}{5}\right)$ and a non-degeneracy assumption on the left-hand side of the domain, asymptotics of the eigenvalues with the smallest real part in the limit $h \to 0$ are derived. The strategy
Hérau, Frédéric, Krejcirik, David, Raymond, Nicolas   +2 more
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On the Spectral Form Factor for Random Matrices. [PDF]

Commun Math Phys, 2023
Cipolloni G, Erdős L, Schröder D.
europepmc   +1 more source

Unitarity and Page Curve for Evaporation of 2D AdS Black Holes. [PDF]

Entropy (Basel), 2022
Cadoni M, Sanna AP.
europepmc   +1 more source

Semiclassical Asymptotics of Eigenvalues for Schrödinger Operators with Magnetic Fields

Journal of Functional Analysis, 1995
The author studies the semi-classical asymptotics of eigenvalues for Schrödinger operators \(H(\lambda)\) with magnetic fields either on two-dimensional compact manifolds \(M\) or on \(\mathbb{R}^2\). Here \(H(\lambda)=1/2\nabla^{A_*}_\lambda\nabla^A_{\lambda}+\lambda^2V+\lambda v\), \(\lambda>0\), with \(\nabla^A_\lambda u=du+i\lambda uA\) \((i=\sqrt{-
openaire   +1 more source

Differences Between Robin and Neumann Eigenvalues. [PDF]

Commun Math Phys, 2021
Rudnick Z, Wigman I, Yesha N.
europepmc   +1 more source