Classical and quantum stochastic models of resistive and memristive circuits

John E. Gough, Guofeng Zhang

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Abstract

The purpose of this paper is to examine stochastic Markovian models for circuits in phase space for which the drift term is equivalent to the standard circuit equations. In particular, we include dissipative components corresponding to both a resistor and a memristor in series. We obtain a dilation of the problem which is canonical in the sense that the underlying Poisson bracket structure is preserved under the stochastic flow.We do this first of all for standardWiener noise but also treat the problem using a new concept of symplectic noise, where the Poisson structure is extended to the noise as well as the circuit variables, and in particular where we have canonically conjugate noises. Finally, we construct a dilation which describes the quantum mechanical analogue.
Original languageEnglish
Article number073505
JournalJournal of Mathematical Physics
Volume58
Issue number7
DOIs
Publication statusPublished - 1 Jul 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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