Classical and Quantum Stochastic Models of Resistive and Memristive Circuits
arXiv:1510.08243 · doi:10.1063/1.4995392
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 for which is canonical in the sense that the underlying Poisson Brackets 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.
12 pages, 5 figures
References in corpus (6)
- Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems
- Lagrange formalism of memory circuit elements: classical and quantum formulations
- The Langevin equation from Markovian Quantum Central Limits
- On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurements
- On the Stochastic Limit of Quantum Field Theory
- Symplectic Noise & The Classical Analog of the Lindblad Generator