Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Acta Physica Sinica

VARIATIONAL STUDY FOR A COUPLED SYSTEM OF A QUANTUM TUNNELING STATE WITH PHONONS

Shi Yun-Long, Nie Yi-Hang, Chen Hong, Xiang Xia Wu, (1)同济大学物理系,上海200092; (2)雁北师范学院物理系,大同037000

Published Jan 1, 1992• 0 citations
Publisher

Abstract

The ground state energy of a coupled system of a quantum tunneling state with phonons is investegated by a variational approach. We find that the ground state of the system may be described by two variation states-displaced state and displaced-squeezed state, and the transition of the stable ground state from displaced state to displaced-squeezed state will occur as coupling strength increases. The phase diagram of the transition is also given.

DOI
10.7498/aps.41.1499

Related papers

VARIATIONAL STUDY ON CORRELATED-SQUEEZED GROUND STATE OF QUANTUM TUNNELING SYSTEM INTERACTING WITH TWO PHONONS

GAO YANG, Yumei Zhang, 同济大学物理系，上海　200092

The variational approach is applied to the study of the ground state of quantum tunneling system interacting with two phonons by use of a correlated-squeezed transformation. We fine: 1) For the two phonons bath, the ground state energy of the phonons with correlation effect is lower than that without correlation effect; 2) The effect of correlation varies with the mode parameters: In the resonant regime of the phonons and two-state system, the correlation effect is more significant and will be strengthened together with the increase of coupling coefficient.

Acta Physica Sinica•Jan 1, 1999•0 citations

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

Hong Chen, Yumei Zhang, Xiang Xia Wu

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.

Physical review. B, Condensed matter•Dec 1, 1989•29 citations

VARIATIONAL STUDY OF A DISSIPATIVE QUANTUMTUNNELING SYSTEM

Shi Yun-Long, Chen Hong, Wu Xiang +1 more

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.

Acta Physica Sinica•Jan 1, 1993•0 citations

DEPENDENCE OF THE DEFORMATION IN DISSIPATIVE QUANTUM TUNNELING SYSTEM ON THE COUPLING INDEX

Shi Yun-Long, Nie Yi-Hang, Chen Hong +1 more

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

Acta Physica Sinica•Jan 1, 1994•0 citations

Symmetry-breaking transition in a two-level system coupled to an Ohmic bath: A squeezed-state approach

Biswadeb Dutta, A. M. Jayannavar

Displaced squeezed states are proposed as variational ground states for phonons (Bose fields) coupled to two-level systems (spin systems). We have investigated the zero-temperature phase diagram for the localization-delocalization transition of a tunneling particle interacting with an Ohmic heat bath. Our results are compared with known existing approximate treatments. A modified phase diagram using the displaced squeezed state is presented.

Physical review. B, Condensed matter•Feb 1, 1994•9 citations

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

T. P. Pareek, A. M. Jayannavar

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.

arXiv:cond-mat/9505089•International Journal of Modern Physics B•May 15, 1995•3 citations
The ground state energy of a coupled system of a quantum tunneling state with phonons is investegated by a variational approach. We find that the ground state of the system may be described by two variation states-displaced state and displaced-squeezed state, and the transition of the stable ground state from displaced state to displaced-squeezed state will occur as coupling strength increases. The phase diagram of the transition is also given.
The variational approach is applied to the study of the ground state of quantum tunneling system interacting with two phonons by use of a correlated-squeezed transformation. We fine: 1) For the two phonons bath, the ground state energy of the phonons with correlation effect is lower than that without correlation effect; 2) The effect of correlation varies with the mode parameters: In the resonant regime of the phonons and two-state system, the correlation effect is more significant and will be strengthened together with the increase of coupling coefficient.
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.
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.
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
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.