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

Chemical Physics Letters

Density matrix formulation of complex geometric quantum phases in dissipative systems

Shih‐I Chu, Zhong Chao Wu, Eric G. Layton

Published Apr 1, 1989• 30 citations
Publisher
DOI
10.1016/0009-2614(89)87225-2

Related papers

Complex geometrical phases for dissipative systems

J. C. Garrison, Ewan M. Wright

Physics Letters A•Mar 1, 1988•266 citations

Geometric phases in dissipative quantum

Yuriy Makhlin

Les Houches/Les Houches•Jan 1, 2005•0 citations

Adiabatic Approximation in the Density Matrix Approach: Non-Degenerate Systems

A.C. Aguiar Pinto, K. M. Fonseca-Romero, M. T. Thomaz

We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric phases for periodic Hamiltonians obtained previously by M.V. Berry are recovered in the present approach. We determine the necessary condition satisfied by the coefficients of the linear expansion of the non-unitary part of the Liouvillian in order to the imaginary phases acquired by the elements of the density matrix, due to dissipative effects, be geometric. The results derived are model-independent. We apply them to spin 1/2 model coupled to reservoir at thermodynamic equilibrium.

•Jan 1, 2002•5 citations

Geometric phase of mixed states for three-level open systems

Yanyan Jiang, Y. H. Ji, Hualan Xu +4 more

Geometric phase of mixed state for three-level open system is defined by establishing in connecting density matrix with nonunit vector ray in a three-dimensional complex Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. Under the limiting of pure state, our approach is in agreement with the Berry phase, Pantcharatnam phase, and Aharonov and Anandan phase. We find that, furthermore, the Berry phase of mixed state correlated to population inversions of three-level open system.

Physical Review A•Dec 8, 2010•14 citations

Phase diagram of a dissipative quantum system

S. A. Bulgadaev

•Mar 1, 1984•11 citations

Geometric phases in non-Hermitian quantum mechanics

Xiaodong Cui, Yujun Zheng

We generally derive complex geometric phases in non-Hermitian quantum mechanics. The formalism of complex geometric phases for non-Hermitian quantum systems is general and can be applied in the cases of cyclic and noncyclic states in non-Hermitian quantum mechanics. As an example, we show the interpretation of complex geometric phases by a generalized density matrix defined on a two-level non-Hermitian quantum system and the two-level Bethe-Lamb model. Also, in the Hermitian case, our theoretical framework of a complex geometric phase reduces to the counterpart of the Pancharatnam phase.

Physical Review A•Dec 20, 2012•44 citations
We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric phases for periodic Hamiltonians obtained previously by M.V. Berry are recovered in the present approach. We determine the necessary condition satisfied by the coefficients of the linear expansion of the non-unitary part of the Liouvillian in order to the imaginary phases acquired by the elements of the density matrix, due to dissipative effects, be geometric. The results derived are model-independent. We apply them to spin 1/2 model coupled to reservoir at thermodynamic equilibrium.
Geometric phase of mixed state for three-level open system is defined by establishing in connecting density matrix with nonunit vector ray in a three-dimensional complex Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. Under the limiting of pure state, our approach is in agreement with the Berry phase, Pantcharatnam phase, and Aharonov and Anandan phase. We find that, furthermore, the Berry phase of mixed state correlated to population inversions of three-level open system.
We generally derive complex geometric phases in non-Hermitian quantum mechanics. The formalism of complex geometric phases for non-Hermitian quantum systems is general and can be applied in the cases of cyclic and noncyclic states in non-Hermitian quantum mechanics. As an example, we show the interpretation of complex geometric phases by a generalized density matrix defined on a two-level non-Hermitian quantum system and the two-level Bethe-Lamb model. Also, in the Hermitian case, our theoretical framework of a complex geometric phase reduces to the counterpart of the Pancharatnam phase.