dorsal/arxiv
View SchemaQuantum dynamics of the dissipative two-state system coupled with a sub-Ohmic bath
| Authors | Zhiguo Lü, Hang Zheng |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612042 |
| URL | https://arxiv.org/abs/quant-ph/0612042 |
| DOI | 10.1103/PhysRevB.75.054302 |
| Journal | PhysRevB.75.054302 (2007) |
Abstract
The decoherence of a two-state system coupled with a sub-Ohmic bath is investigated theoretically by means of the perturbation approach based on a unitary transformation. It is shown that the decoherence depends strongly and sensitively on the structure of environment. Nonadiabatic effect is treated through the introduction of a function $\xi_k$ which depends on the boson frequency and renormalized tunneling. The results are as follows:(1) the non-equilibrium correlation function $P(t)$, the dynamical susceptibility $\chi''(\omega)$ and the equilibrium correlation function $C(t)$ are analytically obtained for $s\leq 1$; (2) the phase diagram of thermodynamic transition shows the delocalized-localized transition point $\alpha_l$ which agrees with exact results and numerical data from the Numerical Renormalization Group; (3) the dynamical transition point $\alpha_c$ between coherent and incoherent phase is explicitly given for the first time. A crossover from the coherent oscillation to incoherent relaxation appears with increasing coupling (for $\alpha > \alpha_c $, the coherent dynamics disappear); (4) the Shiba's relation and sum rule are exactly satisfied when $\alpha \leq \alpha_c $; (5) an underdamping-overdamping transition point $\alpha_c^{*}$ exists in the function $S(\omega)$. Consequently, the dynamical phase diagrams in both ohmic and sub-Ohmic case are mapped out. For $\Delta \ll \omega_c$, the critical couplings ($\alpha_l, \alpha_c$ and $\alpha_c^{*}$) are proportional to $\Delta^{1-s}$.
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"abstract": "The decoherence of a two-state system coupled with a sub-Ohmic bath is\ninvestigated theoretically by means of the perturbation approach based on a\nunitary transformation. It is shown that the decoherence depends strongly and\nsensitively on the structure of environment. Nonadiabatic effect is treated\nthrough the introduction of a function $\\xi_k$ which depends on the boson\nfrequency and renormalized tunneling. The results are as follows:(1) the\nnon-equilibrium correlation function $P(t)$, the dynamical susceptibility\n$\\chi\u0027\u0027(\\omega)$ and the equilibrium correlation function $C(t)$ are\nanalytically obtained for $s\\leq 1$; (2) the phase diagram of thermodynamic\ntransition shows the delocalized-localized transition point $\\alpha_l$ which\nagrees with exact results and numerical data from the Numerical Renormalization\nGroup; (3) the dynamical transition point $\\alpha_c$ between coherent and\nincoherent phase is explicitly given for the first time. A crossover from the\ncoherent oscillation to incoherent relaxation appears with increasing coupling\n(for $\\alpha \u003e \\alpha_c $, the coherent dynamics disappear); (4) the Shiba\u0027s\nrelation and sum rule are exactly satisfied when $\\alpha \\leq \\alpha_c $; (5)\nan underdamping-overdamping transition point $\\alpha_c^{*}$ exists in the\nfunction $S(\\omega)$. Consequently, the dynamical phase diagrams in both ohmic\nand sub-Ohmic case are mapped out. For $\\Delta \\ll \\omega_c$, the critical\ncouplings ($\\alpha_l, \\alpha_c$ and $\\alpha_c^{*}$) are proportional to\n$\\Delta^{1-s}$.",
"arxiv_id": "quant-ph/0612042",
"authors": [
"Zhiguo L\u00fc",
"Hang Zheng"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevB.75.054302",
"journal_ref": "PhysRevB.75.054302 (2007)",
"title": "Quantum dynamics of the dissipative two-state system coupled with a sub-Ohmic bath",
"url": "https://arxiv.org/abs/quant-ph/0612042"
},
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