Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/76205
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Title: Classical and quantum stochastic models of resistive and memristive circuits
Authors: Gough, JE
Zhang, GF 
Issue Date: Jul-2017
Source: Journal of mathematical physics, July 2017, v. 58, no. 7, 73505, p. 073505-1-073505-18
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.
Publisher: American Institute of Physics
Journal: Journal of mathematical physics 
ISSN: 0022-2488
EISSN: 1089-7658
DOI: 10.1063/1.4995392
Rights: © 2017 Author(s).
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. E. Gough and G. F. Zhang, J. Math. Phys. 58, 73505 (2017) and may be found at https://dx.doi.org/10.1063/1.4995392
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