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Physical review. B, Condensed matter

Variational approach for tunneling diffusion of a particle interacting with phonons

Guangming Zhang, Hong Chen, Xiang Xia Wu

Published Jun 1, 1990• 4 citations
Publisher

Abstract

Displaced-squeezed states are proposed as the variational ground states of phonons coupled with a particle moving in a tight-binding band. The narrowing effect of the phonon overlapping integral on the renormalized bandwidth of the tunneling particle is investigated. We find that, for Ohmic dissipation, the conditions for the localization-delocalization transition of the tunneling particle are modified compared with the previous studies.

DOI
10.1103/physrevb.41.11600

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Journal of Physics Condensed Matter•Apr 2, 1990•3 citations
Displaced-squeezed states are proposed as the variational ground states of phonons coupled with a particle moving in a tight-binding band. The narrowing effect of the phonon overlapping integral on the renormalized bandwidth of the tunneling particle is investigated. We find that, for Ohmic dissipation, the conditions for the localization-delocalization transition of the tunneling particle are modified compared with the previous studies.
The ground states of phonons in a dissipative quantum tunneling system and their influences on the localiza ion-delocalization transtion are investigated by a variational approach. We find that: 1. There are two kind of influences, displacement and deformation, on phonon states due to coupling with a tunneling particle, and displaced -squeezed states are proposed to describe both these influences. 2. The localization-delocahzation transition depends on the choice of phonon ground state. The transition will occur at strong coupling as the energy of the ground state decreases.
We propose a correlated squeezed-state approach to study the dissipative two-state system at zero temperature. We have found that the ground state of this system can be better described by the correlated squeezed-state ansatz than those given in earlier variational treatments. In this new ground state the suppression effect of the phonon overlapping integral on the renormalized tunneling parameter is much more alleviated. Thus, the condition for the localization-delocalization transition of the two-state system is significantly modified in this correlated squeezed state, when compared with previous studies.
We present a systematic analysis of the ground state properties of a tunneling system coupled to an Ohmic bath. The nonadiabatic effects induced by coupling with tunneling particle, on the ground state properties of phonons are taken into account. For this we have considered both displacement and deformation of phonons via a variational treatment. The symmetry breaking transition, or the delocalization-localization transition, of the tunneling particle is presented and is compared with earlier known results. We also show that in the critical regime a gap will be opened near the zero momentum in the spectrum of the phonons. The modified phonon spectrum along with the phonon displacement field correlation functions have been calculated. It is shown that in the critical regime the tunneling system stabilizes the lattice against long wavelength fluctuations.