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Mathematics 2017, 5(1), 1; doi:10.3390/math5010001

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

1
Department of Mathematics, Pondicherry University, Kalapet Puducherry 605 014, India
2
Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia 5090000, Chile
3
Institute of Systems Science, Durban University of Technology, PO Box 1334, Durban 4000, South Africa
4
Department of Mathematics and Institute of Systems Science, Research and Postgraduate Support, Durban University of Technology, PO Box 1334, Durban 4000, South Africa
5
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Palle E.T. Jorgensen
Received: 24 September 2016 / Revised: 6 December 2016 / Accepted: 13 December 2016 / Published: 22 December 2016
View Full-Text   |   Download PDF [351 KB, uploaded 22 December 2016]

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. View Full-Text
Keywords: quantum Brownian motion; master equation; group invariant transformations quantum Brownian motion; master equation; group invariant transformations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Sinuvasan, R.; Paliathanasis, A.; Morris, R.M.; Leach, P.G.L. Solution of the Master Equation for Quantum Brownian Motion Given by the Schrödinger Equation. Mathematics 2017, 5, 1.

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