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Title: Classical and quantum stochastic models of resistive and memristive circuits
Authors: Gough, JE
Zhang, GF 
Issue Date: 2017
Publisher: American Institute of Physics
Source: Journal of mathematical physics, 2017, v. 58, no. 7, 73505 How to cite?
Journal: Journal of mathematical physics 
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 standard Wiener 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. Published by AIP Publishing.
ISSN: 0022-2488
EISSN: 1089-7658
DOI: 10.1063/1.4995392
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