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

Progress of Theoretical Physics Supplement

Nonadiabatic Transition Probabilities in the Presence of Strong Dissipation

Keiji Saito

Published Jan 1, 2002• 0 citations
Publisher

Abstract

Strong dissipative effects on the nonadiabatic transition for the two level system are studied. We focus on a strong dissipation for the diabatic states, and derive the exact transition probability making use of the effective master equation. We consider the case where the external field is swept from not only a negative large value but also from the resonant field, and the exact transition probabilities in these cases are derived.

DOI
10.1143/ptps.145.403

Related papers

Nonadiabatic transition probabilities in the presence of strong dissipation at an avoided-level crossing point

Keiji Saito, Yōsuke Kayanuma

Dissipative effects on the nonadiabatic transition for the two- and three-level systems are studied. When the system is affected by a strong dissipation through the diabatic states, the exact transition probability is enumerated making use of the effective master equation. In the two-level system, we consider the case where the external field is swept from not only a negative large value but also from the resonant field, and the exact transition probabilities in these cases are derived. The transition probabilities are derived for the three-level system where the three diabatic states form only one avoided-level crossing point. These probabilities are compared with that in the pure quantum case obtained by Carroll and Hioe.

arXiv:cond-mat/0111420•Physical Review A•Feb 8, 2002•29 citations

Nonadiabatic Transitions in Level Crossing with Energy Fluctuation. I. Analytical Investigations

Yōsuke Kayanuma

A simple stochastic model is proposed describing the nonadiabatic transitions in level crossing with energy fluctuation. The model is an extension of Zener's model having a diagonal energy term fluctuating as a Markoffian Gaussian process. The transition rate P ∞ defined in terms of the diabatic basis is calculated exactly by the formal perturbation expansion with respect to the off-diagonal coupling in the two limiting cases: In the slow fluctuation limit, P ∞ coincides with the Landau-Zener formula, \(P_{\infty}=P_{\text{LZ}} \equiv 1 - \exp (-2 \pi J^{2}/\hbar |v|)\), where J is the off-diagonal coupling constant and v is the velocity of the change of the mean energy difference. In the strong damping limit, which is a limiting case of large fluctuation amplitude in the rapid fluctuation limit, P ∞ is given by the formula, \(P_{\infty}=P_{\text{SD}} \equiv \{1 - \exp (-4 \pi J^{2}/\hbar |v|)\}/2\).

Journal of the Physical Society of Japan•Jan 1, 1984•121 citations

Nonadiabatic transition probabilities for quantum systems in electromagnetic fields: Dephasing and population relaxation due to contact with a bath

Sara D. Jovanovski, Anirban Mandal, Katharine L. C. Hunt

We contrast Dirac's theory of transition probabilities and the theory of nonadiabatic transition probabilities, applied to a perturbed system that is coupled to a bath. In Dirac's analysis, the presence of an excited state |k0⟩ in the time-dependent wave function constitutes a transition. In the nonadiabatic theory, a transition occurs when the wave function develops a term that is not adiabatically connected to the initial state. Landau and Lifshitz separated Dirac's excited-state coefficients into a term that follows the adiabatic theorem of Born and Fock and a nonadiabatic term that represents excitation across an energy gap. If the system remains coherent, the two approaches are equivalent. However, differences between the two approaches arise when coupling to a bath causes dephasing, a situation that was not treated by Dirac. For two-level model systems in static electric fields, we add relaxation terms to the Liouville equation for the time derivative of the density matrix. We contrast the results obtained from the two theories. In the analysis based on Dirac's transition probabilities, the steady state of the system is not an equilibrium state; also, the steady-state population ρkk,s increases with increasing strength of the perturbation and its value depends on the dephasing time T2. In the nonadiabatic theory, the system evolves to the thermal equilibrium with the bath. The difference is not simply due to the choice of basis because the difference remains when the results are transformed to a common basis.

The Journal of Chemical Physics•Apr 26, 2023•2 citations

Stochastic Theory for Nonadiabatic Level Crossing with Fluctuating Off-Diagonal Coupling

Yōsuke Kayanuma

A simple stochastic model is presented describing the nonadiabatic transitions in the level crossing with fluctuating off-diagonal coupling, in which the fluctuation is assumed to obey the Markoffian Gaussian process. The probability P that the transition occurs from one diabatic state to another is calculated exactly in the two limiting situations: In the slow fluctuation limit, P is given by \(P{=}1-\{1+(4{\pi}J^{2}/\hbar|v|)\}^{-1/2}\), where J is the averaged amplitude of the off-diagonal term and v is the velocity of the change of the energy difference between the crossing levels. In the rapid fluctuation limit, P is given by \(P{=}\{1-{\exp}(-4{\pi}J^{2}/\hbar|v|)\}/2\). The intermediate case is studied numerically by the Wiener-Hermite expansion method. Generally, P approaches not 1 but 1/2 in the limit of slow passage, namely, v →0.

Journal of the Physical Society of Japan•May 15, 1985•62 citations

Control of Time-Dependent Nonadiabatic Processes by an External Field

Yoshiaki Teranishi, Hiroki Nakamura

A new idea of controlling nonadiabatic transitions by an external field is proposed. The basic principle is to periodically sweep an external field at each level crossing to make the overall transition probability from an initial state to any desirable final state equal to unity. The recently completed semiclassical theory of nonadiabatic transition enables us to analytically deal with this problem. The present idea may be applicable to various physical and chemical problems, whenever level crossings are created by an external field.

Physical Review Letters•Sep 1, 1998•53 citations

Dissipative quantum tunneling of two-level systems driven by dc-ac fields

Hao Wang, V. N. Freire, Xian-Geng Zhao

The time-dependent average population in a two-level system interacting with an Ohmic boson bath and driven by a dc-ac field is obtained. The study is performed within the noninteracting-blip approximation and for the high-frequency driving case. The integro-differential master equation and the exact formal solution for the average transition probability are obtained. The dissipative quantum decay and the transition temperature from the coherent to the incoherent motion are investigated. The effect of the external electric field on the the dissipative two-level system is found to destroy its coherence.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 1, 1998•2 citations
Strong dissipative effects on the nonadiabatic transition for the two level system are studied. We focus on a strong dissipation for the diabatic states, and derive the exact transition probability making use of the effective master equation. We consider the case where the external field is swept from not only a negative large value but also from the resonant field, and the exact transition probabilities in these cases are derived.
Dissipative effects on the nonadiabatic transition for the two- and three-level systems are studied. When the system is affected by a strong dissipation through the diabatic states, the exact transition probability is enumerated making use of the effective master equation. In the two-level system, we consider the case where the external field is swept from not only a negative large value but also from the resonant field, and the exact transition probabilities in these cases are derived. The transition probabilities are derived for the three-level system where the three diabatic states form only one avoided-level crossing point. These probabilities are compared with that in the pure quantum case obtained by Carroll and Hioe.
A simple stochastic model is proposed describing the nonadiabatic transitions in level crossing with energy fluctuation. The model is an extension of Zener's model having a diagonal energy term fluctuating as a Markoffian Gaussian process. The transition rate P ∞ defined in terms of the diabatic basis is calculated exactly by the formal perturbation expansion with respect to the off-diagonal coupling in the two limiting cases: In the slow fluctuation limit, P ∞ coincides with the Landau-Zener formula, P∞=PLZ≡1−exp⁡(−2πJ2/ℏ∣v∣)P_{\infty}=P_{\text{LZ}} \equiv 1 - \exp (-2 \pi J^{2}/\hbar |v|)P∞​=PLZ​≡1−exp(−2πJ2/ℏ∣v∣), where J is the off-diagonal coupling constant and v is the velocity of the change of the mean energy difference. In the strong damping limit, which is a limiting case of large fluctuation amplitude in the rapid fluctuation limit, P ∞ is given by the formula, P∞=PSD≡{1−exp⁡(−4πJ2/ℏ∣v∣)}/2P_{\infty}=P_{\text{SD}} \equiv \{1 - \exp (-4 \pi J^{2}/\hbar |v|)\}/2P∞​=PSD​≡{1−exp(−4πJ2/ℏ∣v∣)}/2.
We contrast Dirac's theory of transition probabilities and the theory of nonadiabatic transition probabilities, applied to a perturbed system that is coupled to a bath. In Dirac's analysis, the presence of an excited state |k0⟩ in the time-dependent wave function constitutes a transition. In the nonadiabatic theory, a transition occurs when the wave function develops a term that is not adiabatically connected to the initial state. Landau and Lifshitz separated Dirac's excited-state coefficients into a term that follows the adiabatic theorem of Born and Fock and a nonadiabatic term that represents excitation across an energy gap. If the system remains coherent, the two approaches are equivalent. However, differences between the two approaches arise when coupling to a bath causes dephasing, a situation that was not treated by Dirac. For two-level model systems in static electric fields, we add relaxation terms to the Liouville equation for the time derivative of the density matrix. We contrast the results obtained from the two theories. In the analysis based on Dirac's transition probabilities, the steady state of the system is not an equilibrium state; also, the steady-state population ρkk,s increases with increasing strength of the perturbation and its value depends on the dephasing time T2. In the nonadiabatic theory, the system evolves to the thermal equilibrium with the bath. The difference is not simply due to the choice of basis because the difference remains when the results are transformed to a common basis.
A simple stochastic model is presented describing the nonadiabatic transitions in the level crossing with fluctuating off-diagonal coupling, in which the fluctuation is assumed to obey the Markoffian Gaussian process. The probability P that the transition occurs from one diabatic state to another is calculated exactly in the two limiting situations: In the slow fluctuation limit, P is given by P=1−{1+(4πJ2/ℏ∣v∣)}−1/2P{=}1-\{1+(4{\pi}J^{2}/\hbar|v|)\}^{-1/2}P=1−{1+(4πJ2/ℏ∣v∣)}−1/2, where J is the averaged amplitude of the off-diagonal term and v is the velocity of the change of the energy difference between the crossing levels. In the rapid fluctuation limit, P is given by P={1−exp⁡(−4πJ2/ℏ∣v∣)}/2P{=}\{1-{\exp}(-4{\pi}J^{2}/\hbar|v|)\}/2P={1−exp(−4πJ2/ℏ∣v∣)}/2. The intermediate case is studied numerically by the Wiener-Hermite expansion method. Generally, P approaches not 1 but 1/2 in the limit of slow passage, namely, v →0.
A new idea of controlling nonadiabatic transitions by an external field is proposed. The basic principle is to periodically sweep an external field at each level crossing to make the overall transition probability from an initial state to any desirable final state equal to unity. The recently completed semiclassical theory of nonadiabatic transition enables us to analytically deal with this problem. The present idea may be applicable to various physical and chemical problems, whenever level crossings are created by an external field.
The time-dependent average population in a two-level system interacting with an Ohmic boson bath and driven by a dc-ac field is obtained. The study is performed within the noninteracting-blip approximation and for the high-frequency driving case. The integro-differential master equation and the exact formal solution for the average transition probability are obtained. The dissipative quantum decay and the transition temperature from the coherent to the incoherent motion are investigated. The effect of the external electric field on the the dissipative two-level system is found to destroy its coherence.