A simple nonlinear dissipative quantum evolution equation

DOI10.1088/0305-4470/14/9/021zbMath0474.35040OpenAlexW2056578233MaRDI QIDQ3930108

Nicolas Gisin

Publication date: 1981

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/14/9/021

zbMATH Keywords

dissipationSchrödinger equationmaster equationquantum dynamicsdamped harmonic oscillatornon-linear dissipative evolution equationsemi-stable limit cycles

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Schrödinger operator, Schrödinger equation (35J10) General mathematical topics and methods in quantum theory (81Q99) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (23)

On the quantization of linearly damped harmonic oscillator ⋮ Split-operator technique for propagating phase space functions: exploring chaotic, dissipative and relativistic dynamics ⋮ Quantum dissipative systems. I: Canonical quantization and quantum Liouville equation ⋮ On nonlinear description of neutrino flavour evolution in solar matter ⋮ Longitudinal relaxation and quantum spin dynamics in Dzyaloshinsky-Moriya interaction spin spiral dimers ⋮ Nonlinear and non-CP gates for Bloch vector amplification ⋮ Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme ⋮ A comparison between models of gravity induced decoherence ⋮ Time-evolution of quantum systems via a complex nonlinear Riccati equation. II: Dissipative systems ⋮ A mathematical characterization of quantum Gaussian stochastic evolution schemes ⋮ Tensorial dynamics on the space of quantum states ⋮ Exact solutions of the general Doebner-Goldin equation ⋮ Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation ⋮ Connection between quantum mechanical and classical time evolution of certain dissipative systems via a dynamical invariant ⋮ Stochastic sequential reduction of commutative Hamiltonians ⋮ A generalization of the Lax equation ⋮ Integrable nonlinear evolution of the qubit ⋮ Stochastic Schrödinger evolution over piecewise enlarged filtrations ⋮ THE ATTRACTOR AND THE QUANTUM STATES ⋮ Understanding quantum measurement from the solution of dynamical models ⋮ NONLINEAR MARKOV SEMIGROUPS ON C*-ALGEBRAS ⋮ NON-HERMITIAN QUANTUM DYNAMICS OF A TWO-LEVEL SYSTEM AND MODELS OF DISSIPATIVE ENVIRONMENTS ⋮ Temporal correlation beyond quantum bounds in non-Hermitian PT- symmetric dynamics of a two level system

This page was built for publication: A simple nonlinear dissipative quantum evolution equation