Dynamics of a set of quantum states generated by a nonlinear Liouville-von Neumann equation

DOI10.1134/S0965542520080096zbMath1450.35238OpenAlexW3092137842MaRDI QIDQ2206373

V. Zh. Sakbaev, A. D. Grekhneva

Publication date: 22 October 2020

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542520080096

zbMATH Keywords

regularizationnonlinear Schrödinger equationquantum stategradient catastrophe

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) NLS equations (nonlinear Schrödinger equations) (35Q55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Blow-up of states in the dynamics given by the Schrödinger equation with a power-law nonlinearity in the potential ⋮ Nonlinear Schrödinger equation with delay and its regularization

Cites Work

• Unnamed Item
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• Notion of blowup of the solution set of differential equations and averaging of random semigroups
• Diffusion and quantum dynamics on graphs
• L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
• Invariant measures for the defocusing nonlinear Schrödinger equation
• Functional analysis, Sobolev spaces and partial differential equations
• On quantum dynamics on \(C^\ast\)-algebras
• Phase flows generated by Cauchy problem for nonlinear Schrödinger equation and dynamical mappings of quantum states
• Hamiltonian Feynman measures, Kolmogorov integral, and infinite-dimensional pseudodifferential operators
• On the collapse of solutions of the Cauchy problem for the cubic Schrödinger evolution equation
• Gradient blow-up of solutions to the Cauchy problem for the Schrödinger equation
• Geometric properties of systems of vector states and expansion of states in Pettis integrals
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory

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