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arXiv:cond-mat/9505089 · International Journal of Modern Physics B

GROUND STATE PROPERTIES OF A DISSIPATIVE TWO STATE SYSTEM COUPLED TO PHONONS

T. P. Pareek, A. M. Jayannavar

Published May 15, 1995• 3 citations
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Abstract

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.

DOI
10.1142/s0217979295000574

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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.
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.
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We present some characteristic properties of the ground state of a two-level system linearly coupled to a phonon field. Such properties are valid over the whole range of the parameters appearing in the Hamiltonian of the system. The knowledge of these exact results provides a physical basis for an accurate variational determination of the ground state. A physical picture of the self-trapping transition is discussed in terms of particle-field correlations. Our treatment is based on operator methods combining symmetry considerations with some general properties of the lowest energy state.
The properties of a two-state chain interacting with a phonon bath is studied in this paper. We discuss the renormalization of the single pseudospin tunneling parameter by phonons' interaction, as well as other pseudospins' correlation. We find that for Ohmic dissipation, the correlation between pseudospins vanishes and the phonons' interaction induces the localization–delocalization transition. For our discussed super-Ohmic dissipation, the phonons' interaction only reduces the tunneling parameter and does not induce phase transition. In this case the pseudospins' correlation has its effect and reduces the tunneling parameter at weak coupling. In addition, some application of our results is also discussed.