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Physical review. B, Condensed matter

Variational ground state of the model of a two-state system coupled with phonons

Hong Chen, Yumei Zhang, Xiang Xia Wu

Published Dec 1, 1989• 29 citations
Publisher

Abstract

The ground state of the model of a two-state system coupled with phonons is studied by a variational method. Two trial states, the displaced state, and the displaced-squeezed state, for the phonon subsystem are compared, and their dependence on tunneling parameter \ensuremath{\Delta}, phonon frequency \ensuremath{\omega}, and coupling strength g is analyzed. We find that for \ensuremath{\Delta}/\ensuremath{\omega}\ensuremath{\ll}1 the displaced state is more stable for g/\ensuremath{\omega}<1, while the displaced-squeezed state is preferable for g/\ensuremath{\omega}>1.

DOI
10.1103/physrevb.40.11326

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Physical review. B, Condensed matter•Sep 1, 1991•20 citations
The ground state of the model of a two-state system coupled with phonons is studied by a variational method. Two trial states, the displaced state, and the displaced-squeezed state, for the phonon subsystem are compared, and their dependence on tunneling parameter \ensuremath{\Delta}, phonon frequency \ensuremath{\omega}, and coupling strength g is analyzed. We find that for \ensuremath{\Delta}/\ensuremath{\omega}\ensuremath{\ll}1 the displaced state is more stable for g/\ensuremath{\omega}<1, while the displaced-squeezed state is preferable for g/\ensuremath{\omega}>1.
Two variational states, the displaced state and the displaced-squeezed state, are compared for a two-state system with super-Ohmic dissipation, and their dependence on the form of the coupling strength gl{\mathit{g}}_{\mathit{l}}gl​\ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}^{\ensuremath{\lambda}}$ (${\mathrm{\ensuremath{\omega}}}_{\mathit{l}}$ is the phonon frequency) is analyzed. We find that, in the strong-coupling region, the displaced-squeezed state is more stable and the ground-state properties depend not only on the spectral density but also on the index \ensuremath{\lambda}. Moreover, we find that the stable area of the displaced-squeezed state increases as \ensuremath{\lambda} decreases.
摘要 采用变分方法，比较了超欧姆耗散两能态系统中位移变分态和位移－压缩变分态的特性。通过研究发现，在强耦合区域，位移－压缩态较稳定，其基态性质不仅取决于谱密度，而且还依赖于耦合强度ｇ1～ω1λ的指数λ；位移－压缩态稳定的区域将随λ减小而增加。对于欧姆耗散两能态系统，在位移－压缩态退局域相区域亦有同样的特性，且该区域亦随λ减小而增加。 Abstract The properties of two variational states, the displaced state and the displaced-squeezed state, are compared for a two-state system with superohmic dissipation by a variational approach. We find that, in strong coupling region, the displaced-squeezed state is the more stable and the ground-state properties depend not only on the spectral density but also on the index λ of the coupling strength ｇ1～ω1λ(ω1 is phonon frequenceis). Moreover, we obtain that the stable area of the displaced-squeezed state increases as λ reduces. Similar properties have been obtained for ohmic dissipation and it is shown that the delocalization area of the displaced-squeezed state increases as λ reduces. 作者及机构信息 石云龙2, 聂一行2, 陈鸿1, 吴翔1 (1)同济大学物理系; (2)雁北师范学院物理系 基金项目: 国家自然科学基金和山西省自然科学基金资助的课题. Authors and contacts SHI YUN-LONG2, NIE YI-HANG2, CHEN HONG1, WU XIANG1 (1)同济大学物理系; (2)雁北师范学院物理系 参考文献 施引文献
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 generalize the variational approach proposed by Chen, Zhang, and Wu [Phys. Rev. B 40, 11 326 (1989)] to the ground state of a two-level system coupled to a single boson mode. The resulting displaced-squeezed state is compared to the true ground state (calculated numerically), and to further variational states, by computing energy differences and overlaps. These states are able to describe a bifurcation occurring in the ground state of the quantum system as well as in the equilibrium state of its classical limit, and they are excellent approximations to the true ground state.