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

Journal of Chemical Education

Study of degenerate interacting levels by aid of the Liouville equation

Khalida Boulil, Olivier Henri‐Rousseau, Belkacem Boulil

Published Aug 1, 1990• 0 citations
Publisher

Abstract

This study will allow discussion of the steady and time-dependent states describing two degenerate interacting levels in terms of the first moments of the Hamiltonian.
DOI
10.1021/ed067p662

Related papers

Theory of Effective Hamiltonians with Stationary and Time-Dependent Interactions

Farhad H. M. Faisal

Springer eBooks•Jan 1, 1987•0 citations

Lindblad-driven discretized leads for nonequilibrium steady-state transport in quantum impurity models: Recovering the continuum limit

Frauke Schwarz, Moshe Goldstein, Antonius Dorda +3 more

The description of interacting quantum impurity models in steady-state nonequilibrium is an open challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing a truly open quantum system are seemingly incompatible. One possibility to bridge this gap is the use of Lindblad-driven discretized leads (LDDL): one couples auxiliary continuous reservoirs to the discretized lead levels and represents these additional reservoirs by Lindblad terms in the Liouville equation. For quadratic models governed by Lindbladian dynamics, we present an elementary approach for obtaining correlation functions analytically. In a second part, we use this approach to explicitly discuss the conditions under which the continuum limit of the LDDL approach recovers the correct representation of thermal reservoirs. As an analytically solvable example, the nonequilibrium resonant level model is studied in greater detail. Lastly, we present ideas towards a numerical evaluation of the suggested Lindblad equation for interacting impurities based on matrix product states. In particular, we present a reformulation of the Lindblad equation, which has the useful property that the leads can be mapped onto a chain where both the Hamiltonian dynamics and the Lindblad driving are local at the same time. Moreover, we discuss the possibility to combine the Lindblad approach with a logarithmic discretization needed for the exploration of exponentially small energy scales.

arXiv:1604.02050•Physical review. B./Physical review. B•Oct 27, 2016•72 citations

The Zel'dovich Electric Dipole Moment in Atoms

D. E. Krause

It is generally believed that both parity (P) and time reversal (T) invariance must be broken to produce a permanent electric dipole moment in a stable non-degenerate rotationally invariant system. However, Zel'dovich proposed that the P-violating weak interaction alone might be sufficient to produce an electric dipole moment in an unstable system, where the exponential decay law produces an "arrow of time" without explicit T-violation in the Hamiltonian. This "Zel'dovich moment" would be proportional to the linewidth of the unstable system. Subsequently, Bernreuther and Nachtmann explicitly calculated this Zel'dovich moment for deuterium. Here we use the master equation formalism to study the problem of the Zel'dovich moment. We apply a widely used master equation to a 3-level atom to obtain the results of Bernreuther and Nachtmann, and show that their effect may persist in steady-state situations. We then use a similar equation to study a 2-level atom, where we find an even more dramatic result. If true, it indicates that all atoms could have a Zel'dovich moment, even when they are in their ground states. We then show that these latter results are spurious--they arise because the master equation used neglected terms of the same order of magnitude as the Zel'dovich moment. When included, the Zel'dovich moment disappears in the 2-level atom. Since Bernreuther and Nachtmann's result was obtained in a similar manner, it is also called into question.

•Jan 1, 1994•0 citations

Moment-equation representation of the dissipative quantum Liouville equation

Michael A. Stroscio

Superlattices and Microstructures•Jan 1, 1986•21 citations

On the time dependence of a degenerate two-level system interacting with a pulse of radiation

Gerald F. Thomas, William J. Meath

Physics Letters A•Apr 1, 1979•9 citations

Fast trajectory tracking of the steady state of open quantum systems

S. L. Wu, X. L. Huang, X. X. Yi

We present a control strategy to speed up the steady-state tracking for open quantum systems governed by a time-dependent Markovian master equation. With this fast trajectory tracking strategy, the quantum state strictly follows the instantaneous steady state of open quantum systems and evolves into the target state without any fidelity loss. A compact expression for the counterdiabatic term is derived in terms of a superoperator formalism in Liouville space. To be specific, we utilize a universal method to transform the counterdiabatic superoperator into the ordinary operator form. It can be seen from the operator form that in addition to the coherent control field, an incoherent control is required for the fast trajectory tracking. The control strategy is successfully applied in two examples: One is a two-level quantum system with a time-dependent Hamiltonian coupling to a heat bath, the other is a two-level system following an isothermal process.

Physical Review A•Apr 19, 2019•11 citations
The description of interacting quantum impurity models in steady-state nonequilibrium is an open challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing a truly open quantum system are seemingly incompatible. One possibility to bridge this gap is the use of Lindblad-driven discretized leads (LDDL): one couples auxiliary continuous reservoirs to the discretized lead levels and represents these additional reservoirs by Lindblad terms in the Liouville equation. For quadratic models governed by Lindbladian dynamics, we present an elementary approach for obtaining correlation functions analytically. In a second part, we use this approach to explicitly discuss the conditions under which the continuum limit of the LDDL approach recovers the correct representation of thermal reservoirs. As an analytically solvable example, the nonequilibrium resonant level model is studied in greater detail. Lastly, we present ideas towards a numerical evaluation of the suggested Lindblad equation for interacting impurities based on matrix product states. In particular, we present a reformulation of the Lindblad equation, which has the useful property that the leads can be mapped onto a chain where both the Hamiltonian dynamics and the Lindblad driving are local at the same time. Moreover, we discuss the possibility to combine the Lindblad approach with a logarithmic discretization needed for the exploration of exponentially small energy scales.
It is generally believed that both parity (P) and time reversal (T) invariance must be broken to produce a permanent electric dipole moment in a stable non-degenerate rotationally invariant system. However, Zel'dovich proposed that the P-violating weak interaction alone might be sufficient to produce an electric dipole moment in an unstable system, where the exponential decay law produces an "arrow of time" without explicit T-violation in the Hamiltonian. This "Zel'dovich moment" would be proportional to the linewidth of the unstable system. Subsequently, Bernreuther and Nachtmann explicitly calculated this Zel'dovich moment for deuterium. Here we use the master equation formalism to study the problem of the Zel'dovich moment. We apply a widely used master equation to a 3-level atom to obtain the results of Bernreuther and Nachtmann, and show that their effect may persist in steady-state situations. We then use a similar equation to study a 2-level atom, where we find an even more dramatic result. If true, it indicates that all atoms could have a Zel'dovich moment, even when they are in their ground states. We then show that these latter results are spurious--they arise because the master equation used neglected terms of the same order of magnitude as the Zel'dovich moment. When included, the Zel'dovich moment disappears in the 2-level atom. Since Bernreuther and Nachtmann's result was obtained in a similar manner, it is also called into question.
We present a control strategy to speed up the steady-state tracking for open quantum systems governed by a time-dependent Markovian master equation. With this fast trajectory tracking strategy, the quantum state strictly follows the instantaneous steady state of open quantum systems and evolves into the target state without any fidelity loss. A compact expression for the counterdiabatic term is derived in terms of a superoperator formalism in Liouville space. To be specific, we utilize a universal method to transform the counterdiabatic superoperator into the ordinary operator form. It can be seen from the operator form that in addition to the coherent control field, an incoherent control is required for the fast trajectory tracking. The control strategy is successfully applied in two examples: One is a two-level quantum system with a time-dependent Hamiltonian coupling to a heat bath, the other is a two-level system following an isothermal process.