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Europhysics Letters (EPL)

Quantum fluctuating barriers

Joachim Ankerhold, Philip Pechukas

Published Nov 1, 2000• 22 citations
Publisher

Abstract

\n \nTunneling dynamics in metastable and bistable potentials driven by\ncorrelated noise is studied. For barriers fluctuating randomly in time\nwe show by exact numerical and approximate analytical calculations\nthe significant impact on the incoherent and coherent decay. Thereby\nwe make use of both a stochastic Schrödinger equation and the\ncorresponding exact master equation. The crucial role of\nsynchronization of barrier flippings with intrinsic system dynamics is\nrevealed.\n\n

DOI
10.1209/epl/i2000-00433-3

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\n \nTunneling dynamics in metastable and bistable potentials driven by\ncorrelated noise is studied. For barriers fluctuating randomly in time\nwe show by exact numerical and approximate analytical calculations\nthe significant impact on the incoherent and coherent decay. Thereby\nwe make use of both a stochastic Schrödinger equation and the\ncorresponding exact master equation. The crucial role of\nsynchronization of barrier flippings with intrinsic system dynamics is\nrevealed.\n\n
Quantum decay rates for barrier potentials driven by external stochastic and periodic forces in the strong damping regime are studied. Based on the quantum Smoluchowski equation derived recently by Ankerhold, Pechukas, and Grabert [Phys. Rev. Lett. 87, 086802 (2001)] explicit analytical and numerical results are presented for the case of the resonant activation phenomenon in a bistable potential and the escape from a metastable well with oscillating barrier, respectively. The significant impact of quantum fluctuations is revealed.
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We investigate the problem of tunneling across a randomly fluctuating barrier in the presence of dissipation in the two-level approximation. The barrier fluctuations are induced by a random telegraph noise whose switching rate nu is taken as a control parameter. For infinitely fast fluctuations the dynamics of the system is similar to the static case, while, for very small nu, the barrier evolution is a superposition of static solutions for both configurations. This leads to a resonant beating or long-time periodic localization. For an intermediate value of nu we have found a resonancelike suppression of coherent tunneling. When the system levels are detuned, a resonant enhancement of decay in the incoherent regime also occurs.
We study the real time dynamics of a dissipative quantum system in a metastable state which may decay by crossing a potential barrier. Starting from an initial state where the system is in thermal equilibrium on one side of the barrier, the time evolution of the density matrix is evaluated analytically in the semiclassical approximation for coordinates near the barrier top. In a region about a critical temperature Tc{\mathrm{T}}_{\mathrm{c}}Tc​ large quantum fluctuations render the harmonic approximation of the potential insufficient and anharmonicities become essential. Accounting for non-Gaussian fluctuation modes, we show that the density matrix approaches a quasistationary state with a constant flux across the barrier. This extends our earlier results [Phys. Rev. E 51, 4267 (1995)] on the quantum generalization of the Kramers flux state to the region about Tc{\mathrm{T}}_{\mathrm{c}}Tc​. By matching the flux state onto the equilibrium state on one side of the barrier, we determine the decay rate out of the metastable state. The rate constant shows a changeover from thermally activated decay to quantum tunneling for temperatures below Tc{\mathrm{T}}_{\mathrm{c}}Tc​.
We develop a stochastic Schrödinger equation (SSE) framework to simulate the real-time dynamics of Anderson-Holstein (AH) impurities coupled to a continuous Fermionic bath. The bath degrees of freedom are incorporated through fluctuating terms determined by exact system-bath correlations, which is derived in an ab initio manner. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and macroscopic master equations. Computationally, the SSE model enables efficient numerical methods for propagating stochastic trajectories. We demonstrate that this approach not only naturally provides microscopically detailed information unavailable from reduced models but also captures effects beyond master equations, thus serving as a promising tool to study open quantum dynamics emerging in physics and chemistry.