Probability of passing through a parabolic barrier and thermal decay rate: Case of linear coupling both in momentum and in coordinate

Kuzyakin, R. A.; Sargsyan, V. V.; Adamian, G. G.; Antonenko, N. V.

doi:10.1103/physreva.84.032117

Cited by 19 publications

(6 citation statements)

References 30 publications

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“…According to Leggett’s terminology, coordinate and momentum couplings cause normal and anomalous dissipation, correspondingly, 50 and combined influence of normal and anomalous dissipation has been scrutinized for various harmonic systems. 50 − 58 Charged oscillators in magnetic field have been considered in ref ( 59 ), dynamics of classical spins have been studied in ref ( 60 ), and Kramers’ problem in the presence of coordinate and momentum couplings has been investigated in refs ( 61 and 62 ). However, all these position–momentum couplings were introduced in an ad hoc manner, and to our knowledge, harmonic systems were considered only.…”

Section: System–bath Approach For Momentum Couplingmentioning

confidence: 99%

Hierarchical Equations-of-Motion Method for Momentum System–Bath Coupling

2021

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For a broad class of quantum models of practical interest, we demonstrate that the Hamiltonian of the system nonlinearly coupled to a harmonic bath through the system and bath coordinates can be equivalently mapped into the Hamiltonian of the system bilinearly coupled to the bath through the system and bath momenta. We show that the Hamiltonian with bilinear system–bath momentum coupling can be treated by the hierarchical equations-of-motion (HEOM) method and present the corresponding proof-of-principle simulations. The developed methodology creates the opportunity to scrutinize a new family of nonlinear quantum systems by the numerically accurate HEOM method.

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Section: System–bath Approach For Momentum Couplingmentioning

confidence: 99%

Hierarchical Equations-of-Motion Method for Momentum System–Bath Coupling

2021

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“…Metastability in open quantum systems and relaxation processes from metastable states are a fundamental issue in many branches of physics and chemistry, and recently have been subject of increasing interest [23,79,80,81,82,83,84,85,86,87]. In this section, in order to analyze the evolution of a quantum particle, interacting with a thermal bath, initially placed in a metastable state we consider a time-independent asymmetric bistable potential.…”

Section: Quantum Metastable Systemmentioning

confidence: 99%

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Cognata

Spagnolo²,

Caldara

et al. 2012

Acta Phys. Pol. B

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Relaxation phenomena in three different classical and quantum systems are investigated. First, the role of multiplicative and additive noise in a classical metastable system is analyzed. The mean lifetime of the metastable state shows a nonmonotonic behavior with a maximum as a function of both the additive and multiplicative noise intensities. In the second system, the simultaneous action of thermal and non-Gaussian noise on the dynamics of an overdamped point Josephson junction is studied. The effect of a Lévy noise generated by a Cauchy-Lorentz distribution on the mean lifetime of the superconductive metastable state, in the presence of a periodic driving, is investigated. We find resonant activation and noise enhanced stability in the presence of Lévy noise. Finally, the time evolution of a quantum particle moving in a metastable potential and interacting with a thermal reservoir is analyzed. Within the Caldeira-Legget model and the Feynman-Vernon functional approach, we obtain the time evolution of the population distributions in the position eigenstates of the particle, for different values of the thermal bath coupling strength.

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“…The described theoretical framework was already studied in the more abstract context of dissipative position and momentum couplings [16][17][18][19][20][21][22][23][24][25][26]. In this work, we engineer the reservoirs for a current-biased Josephson system with two distinct dissipative interactions affecting respectively the phase and the charge variable.…”

Section: Introductionmentioning

confidence: 99%

Engineering the speedup of quantum tunneling in Josephson systems via dissipation

Maile,

Ankerhold,

Andergassen

et al. 2022

Preprint

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We theoretically investigate the escape rate occurring via quantum tunneling in a system affected by tailored dissipation. Specifically, we study the environmental assisted quantum tunneling of the superconducting phase in a current-biased Josephson junction. We consider Ohmic resistors inducing dissipation both in the phase and in the charge of the quantum circuit. We find that the charge dissipation leads to an enhancement of the quantum escape rate. This effect appears already in the low Ohmic regime and also occurs in the presence of phase dissipation that favors localization. Inserting realistic circuit parameters, we address the question of its experimental observability and discuss suitable parameter spaces for the observation of the enhanced rate.

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Probability of passing through a parabolic barrier and thermal decay rate: Case of linear coupling both in momentum and in coordinate

Cited by 19 publications

References 30 publications

Hierarchical Equations-of-Motion Method for Momentum System–Bath Coupling

Hierarchical Equations-of-Motion Method for Momentum System–Bath Coupling

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Engineering the speedup of quantum tunneling in Josephson systems via dissipation

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