Quantum theory of a mutual-inductance-coupled circuit including Josephson junctions studied via the entangled state representation

We generalize the Moyal equation, which describes the dynamics of quantum observables in phase space, to quantum systems coupled to a reservoir. It is shown that phase space observables become functionals of fluctuating noise forces introduced by the coupling to the reservoir. For Markovian reservoirs, the Moyal equation turns into a functional differential equation in which the reservoir's effect can be described by a single parameter.

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“…It remains to perform transformation (14). By using e LRt F (t ′ ) = F (t ′ − t) and approximation (27) we obtain…”

Section: Free Particle Coupled To a Reservoirmentioning

confidence: 99%

“…In this section we repeat the calculations of Sec. IV A without making the Markov approximation (27). This amounts to solving Eq.…”

Section: Appendix C: Solution For Canonical Observables Without Markomentioning

confidence: 99%

The Moyal equation for open quantum systems

Marzlin

Deering²

2015

J. Phys. A: Math. Theor.

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“…In recent years, the phenomenon of superconductivity has been the focus of considerable theoretical and experimental study in the literature. The origin of this great interest is due to its potential application in various branches of physics [1][2][3][4][5][6]. This phenomenon was first observed in Leiden by Onnes in 1911 [7] when he noted that the resistance of a rod of frozen mercury suddenly drops to zero when cooled to the boiling point of helium, 4.2 K, and in 1933 [8], Meissner and Ochsenfeld discovered that this phenomenon expels the magnetic field from within the superconductor.…”

Section: Introductionmentioning

confidence: 98%

“…This author has studied the quantum effects of a nondissipative mesoscopic LC circuit with a source and expressed its fluctuations in the vacuum state. Based on Louisell's work and with the progress of quantum information and quantum computa-tion, many articles concerned with mesoscopic or nanoscale circuits have been published in the literature [1][2][3][4][5][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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London superconductor and time-varying mesoscopic LC circuits

Pedrosa

Nascimento

2021

Rev. Mex. Fís.

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In this work we study the classical and quantum dynamics of a London superconductor and of a time-dependent mesoscopic or nanoscale LC circuit by assuming that the inductance and capacitance vary exponentially with time at constant rate. Surprisingly, we find that the behavior of these two systems are equivalent, both classically and quantum mechanically, and can be mapped into a standard damped harmonic oscillator which is described by the Caldirola-Kanai Hamiltonian. With the aid of the dynamical invariant method and Fock states, we solve the time-dependent Schr\"odinger equation associated with this Hamiltonian and calculate some important physical properties of these systems such as expectation values of the charge and magnetic flux, their variances and the respective uncertainty principle.

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