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math-phDec 13, 2016
authors
  • R. Sinuvasan
  • A. Paliathanasis
  • R. M. Morris
  • P. G. L. Leach
institutions
  • Austral University of Chile
  • Durban University of Technology
  • Pondicherry University
  • University of KwaZulu-Natal
arXiv abstractPDF
paper

Solution of the Master Equation for Quantum Brownian Motion given by the Schrödinger Equation

arXiv:1612.04070 · doi:10.3390/math5010001

Abstract

We consider the master equation of quantum Brownian motion and with the application of the group invariant transformation we show that there exists a surface on which the solution of the master equation is given by an autonomous one-dimensional Schrödinger Equation.

arXiv comment7 pages, to be published in Mathematics (MDPI)

References in corpus (8)

  • General non-Markovian dynamics of open quantum systems
  • Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
  • Alternative Derivation of the Hu-Paz-Zhang Master Equation for Quantum Brownian Motion
  • Exact solution of the Hu-Paz-Zhang master equation
  • Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
  • Non-Markovian Dynamics Impact on the Foundations of Statistical Mechanics
  • The geometric origin of Lie point symmetries of the Schrödinger and the Klein Gordon equations
  • Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities
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