The quantum to classical crossover for a weak link capacitor

Physics Letters A, 1999

We consider the tunneling of a wave packet through a potential barrier which is coupled to a nonintegrable classical system and study the interplay of classical chaos and dissipation in the tunneling dynamics. We show that chaos-assisted tunneling is further enhanced by dissipation, while tunneling is suppressed by dissipation when the classical subsystem is regular.

Pramana, 2007

We present a numerical investigation of the tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier which is coupled to a non-integrable classical system and study the interplay between classical chaos and barrier fluctuation in the tunneling dynamics. We found that the coupling of the quantum system with the classical subsystem decreases the tunneling rate irrespective of whether the classical subsystem is regular or chaotic and also irrespective of the fact that whether the barrier fluctuates or not. Presence of classical chaos always enhances the tunneling rate constant. The effect of barrier fluctuation on the tunneling rate in a mixed quantum-classical system is to suppress the tunneling rate. In contrast to the case of regular subsystem, the suppression arising due to barrier fluctuation is more visible when the subsystem is chaotic.

2014

We derive fluctuation-dissipation relations for a tunnel junction driven by a high impedance microwave resonator, displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical forces hold, provided the effect of the circuit's quantum fluctuations is incorporated into a modified non-linear I(V ) curve. We also demonstrate that all quantities measured under a coherent time dependent bias can be reconstructed from their dc counterpart with a photo-assisted tunneling relation. We confirm these predictions by implementing the circuit and measuring the dc current through the junction, its high frequency admittance and its current noise at the frequency of the resonator. arXiv:1409.6696v1 [cond-mat.mes-hall]

2012 International Conference on Electromagnetics in Advanced Applications, 2012

The quantum mechanical rate equations for a general class of circuits consisting of lossless memory elements embedded in a general lossless linear reciprocal circuit have been derived. The embedding circuit is described by a canonical Foster multiport circuit c. The approach is general since any lossless linear reciprocal embedding network can be formulated in this way. The presented circuit model is the framework for a general quantum circuit theory for lossless reciprocal circuits including also nonlinear elements. As an example two-state memreactances described by a spin model have been considered.

Physics Letters A, 1985

We propose a framework of a quantum mechanical description of current driven tunnel junctions. Based on this description we predict several new effects. These effects can be observed for k B T < E T < e 2 /C, where for a normal tunnel junction and for a Josephson junction, ...

Physical Review B, 2003

We analyze the dynamics of a nanomechanical oscillator coupled to an electrical tunnel junction with an arbitrary voltage applied to the junction and arbitrary temperature of electrons in leads. We obtain the explicit expressions for the fluctuations of oscillator position, its damping/decoherence rate, and the current through the structure. It is shown that quantum heating of the oscillator results in nonlinearity of the current-voltage characteristics. The effects of mechanical vacuum fluctuations are also discussed.

2009

Due to the progress made in the control and the manipulation of mesoscopic structures driven by high frequency periodic voltages, the ac regime has been recently experimentally investigated [1] and consequently its theoretical interest has been renewed. We consider here, a quantum chaotic cavity that is coupled via tunnel barriers and gates to a macroscopic circuit which contains ac-sources [2]. By extending to the ac-transport, the recent trajectory-based semiclassical theory of quantum chaotic transport in presence of tunnel barrier [3], we derive for arbitrary tunneling rates and arbitrary positive Ehrenfest time, the averaged and the weak-localization correction to the screened conductance. Then we use these results to investigate the effect of dephasing on the relaxation resistance of a chaotic capacitor in the linear low frequency regime. This last investigation are in principle relevant to the recent measure of the admittance at zero magnetic flux of a mesoscopic capacitor [1,4].References[2][t]1cm#1[t]14cm#2 [1] J. Gabelli et al., Science 313, 499 (2006).[2] C. Petitjean et al, in preparation (2008).[3] R.S. Whitney, Phys. Rev. B, 75, 235404 (2007).[4] S. Nigg and M. B"uttiker, Phys. Rev. B 77, 085312 (2008).

Physical Review B, 2010

We present a theoretical study of time-dependent quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator within the non-equilibrium Green's function technique. An arbitrary voltage is applied to the tunnel junction and electrons in the leads are considered to be at zero temperature. The transient and the steady state behavior of the system is considered here in order to explore the quantum dynamics of the oscillator as a function of time. The properties of the phonon distribution of the nanomechnical oscillator strongly coupled to the electrons on the dot are investigated using a non-perturbative approach. We consider both the energy transferred from the electrons to the oscillator and the Fano factor as a function of time. We discuss the quantum dynamics of the nanomechanical oscillator in terms of pure and mixed states. We have found a significant difference between a quantum and a classical oscillator. In particular, the energy of a classical oscillator will always be dissipated by the electrons whereas the quantum oscillator remains in an excited state. This will provide useful insight for the design of experiments aimed at studying the quantum behavior of an oscillator.

Physical Review Letters, 2005