Transmission spectrum of a tunneling particle interacting with dynamical fields: real-time functional-integral approach

Details Transmission spectrum of a tunneling particle interacting with dynamical fields: real-time functional-integral approach Transmission spectrum of a tunneling particle interacting with dynamical fields: real-time functional-integral approach

1996-07-26

arxiv.org/abs/cond-mat/9607189v1

Physics

Condensed Matter

RevTeX3.0, 18 pages, two figures (not included) are available upon request from the author. Accepted for publication in Phys.

Scientific paper

10.1103/PhysRevB.54.8676

A real-time functional-integral method is used to derive an effective action that gives the transmission spectrum of a tunneling particle interacting with a bath of harmonic oscillators. The transmission spectum is expressed in terms of double functional integrals with respect to the coordinate of the particle which are evaluated by means of stationary-phase approximation. The equations of motion for the stationary-phase trajectories are solved exactly for an arbitrary spectral density function of the bath, and the obtained solutions are used to find the transmission spectra for specific examples. For a bath with single frequency $\omega$, an analytic expression of the transmission spectrum is obtained which covers from sudden tunneling ($\omega T_0\ll 1$) to adiabatic one ($\omega T_0\gg 1$), where $T_0$ is the time it would take a classical particle to traverse the inverted bare potential barrier. For a bath with Ohmic spectrum, the differential tunneling conductance at low bias voltage $V$ and for $\eta T_0\ll 1$ is found to obey a power law $\sim(eVT_0/\hbar)^{\eta T_0S_0/2\pi\hbar}$, where $\eta$ is the friction coefficient and $S_0$ is the tunneling exponent in the absence of interaction.

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