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

Physical Review A

Exact density-matrix calculations for simple open systems

Matthew J. Collett

Published Sep 1, 1988• 62 citations
Publisher

Abstract

Explicit density-matrix solutions are obtained for several simple open quantum systems without the usual trace being taken over the thermal bath. This is achieved using a representation of the density matrix in terms of the dynamic operators of the system. The results are compared with those from conventional reduced calculations. Different types of irreversible behavior are found, and the implications of this distinction for models of quantum measurement are considered.

DOI
10.1103/physreva.38.2233

Related papers

Exact dynamics and thermalization of open quantum systems coupled to reservoirs through particle exchanges

Fei-Lei Xiong, Wei-Min Zhang

In this paper, we study the exact dynamics of general open systems interacting with their environments through particle exchanges. The paper includes two main results. First, by taking advantage of the propagating function in the coherent state representation, we obtain the exact solution of the reduced density matrix, which is expressed in terms of the nonequilibrium Green functions. Second, in the dynamical perspective, we provide a rigorous thermalization process of open quantum systems.

arXiv:2003.09598•Physical Review A•Aug 18, 2020•9 citations

Dynamical and thermodynamical approaches to open quantum systems

Vitalii Semin, Francesco Petruccione

The non-Markovian dynamics of open quantum systems is studied from two different points of view. The first one coincides with the traditional tracing out of the environmental degrees of freedom, presented in classical textbooks on open quantum systems. The second one is an approximation of the exact density operator with the knowledge of only several dynamical variables in the spirit of non-equilibrium thermodynamics. The approximation is based on the principle of maximal entropy. We discuss the information and the Renyi entropies, which lead to different approximations. The time-convolutionless master equation governs the dynamics of both traditional and approximated reduced density operator with a particular projection operator. Considering the example of two interacting qubits in a thermal environment, we compare the traditional and thermodynamical approaches.

Scientific Reports•Feb 13, 2020•12 citations

Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation

Takashi Mori, Seiji Miyashita

We study the structure of the time evolution of the density matrix in contact with a thermal bath in a standard projection operator sheme. The reduced density matrix of the system in the steady state is obtained by tracing out the degree of freedom of the thermal bath from the equilibrium density matrix of the total system. This reduced density matrix is modified by the interaction, and is different from that of the equilibrium of the system alone. We explicitly calculate the contribution of each term in quantum master equation to the realization of the steady state density matrix, and make clear roles of each term. By making use of the role of each term, the properties of the commonly used quantum master equation are examined.

arXiv:0810.0626•Journal of the Physical Society of Japan•Nov 25, 2008•58 citations

Decoherence in open quantum systems: influence of the intrinsic bath dynamics

V. V. Ignatyuk, V. G. Morozov

The non-Markovian master equation for open quantum systems is obtained by generalization of the standard Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations is written for the reduced density matrices of the bath ϱB(t) and of the system ϱS(t). A formal solution of the equation for ϱB(t) in the 2nd approximation in interaction yields a specific extra term related to the intrinsic bath dynamics. This term is nonlinear in the reduced density matrix ϱS(t), and vanishes in the Markovian limit. To verify the consistence and robustness of our approach, we apply the generalized ZN projection scheme to a simple dephasing model. We study the obtained kinetic equation both in the Markovian approximation and beyond it (for the term related to the intrinsic bath dynamics) and compare the results with the exact ones.

arXiv:2112.05595•Condensed Matter Physics•Jan 1, 2022•4 citations

Dynamics of Open Quantum Systems Using Parametric Representation with Coherent States

Dario Calvani, Alessandro Cuccoli, Nikitas I. Gidopoulos +1 more

Open quantum systems and their dynamics are usually studied in terms of reduced density matrices. This approach allows a nonsymmetric description, which is useful when one of the two subsystems is to be considered an environment, at the expense of a loss of information, as tracing out the environmental degrees of freedom is an irreversible process. This has a series of consequences which can be severe. In this work we present an alternative description, which is still nonsymmetric but yet exact: It is based on a parametric representation of composite systems, as obtained by introducing environmental coherent states, such that the principal system get to be described by a set of pure states parametrically dependent on environmental variables. The representation allows one to relate properties which typically arise in studying systems with parametrically dependent Hamiltonians, such as the emergence of geometrical phases, with features which specifically characterize open quantum systems, such as decoherence and entanglement generation.

Open Systems & Information Dynamics•Sep 1, 2013•5 citations

Exact solutions of open integrable quantum spin chains

Enej Ilievski

In the thesis we present an analytic approach towards exact description for steady state density operators of nonequilibrium quantum dynamics in the framework of open systems. We employ the so-called quantum Markovian semi-group evolution, i.e. a general form of time-autonomous positivity and trace-preserving dynamical equation for reduced density operators, by only allowing unitarity-breaking dissipative terms acting at the boundaries of a system. Such setup enables to simulate macroscopic reservoirs for different values of effective thermodynamic potentials, causing incoherent transitions between quantum states which are modeled with aid of the Lindblad operators. This serves as a simple minimalistic model for studying quantum transport properties, either in the linear response domain or in more general regimes far from canonical equilibrium. We are mainly exploring possibilities of identifying nonequilibrium situations which are amenable to exact description within matrix product state representation, by exclusively focusing on steady states, i.e. fixed points of the Lindblad equation, of certain prototypic interacting integrable spin chains driven by incoherent polarizing processes. Finally, we define a concept of pseudo-local extensive almost-conserved quantities by allowing a violation of time-invariance up to boundary-localized terms. We elucidate the role of such quantities on non-ergodic behaviour of temporal correlation functions rendering anomalous transport properties. It turns out that such conservation laws can be generated by means of boundary universal quantum transfer operators of the fundamental integrable models.

arXiv:1410.1446•Oct 6, 2014•16 citations
Explicit density-matrix solutions are obtained for several simple open quantum systems without the usual trace being taken over the thermal bath. This is achieved using a representation of the density matrix in terms of the dynamic operators of the system. The results are compared with those from conventional reduced calculations. Different types of irreversible behavior are found, and the implications of this distinction for models of quantum measurement are considered.
The non-Markovian dynamics of open quantum systems is studied from two different points of view. The first one coincides with the traditional tracing out of the environmental degrees of freedom, presented in classical textbooks on open quantum systems. The second one is an approximation of the exact density operator with the knowledge of only several dynamical variables in the spirit of non-equilibrium thermodynamics. The approximation is based on the principle of maximal entropy. We discuss the information and the Renyi entropies, which lead to different approximations. The time-convolutionless master equation governs the dynamics of both traditional and approximated reduced density operator with a particular projection operator. Considering the example of two interacting qubits in a thermal environment, we compare the traditional and thermodynamical approaches.
We study the structure of the time evolution of the density matrix in contact with a thermal bath in a standard projection operator sheme. The reduced density matrix of the system in the steady state is obtained by tracing out the degree of freedom of the thermal bath from the equilibrium density matrix of the total system. This reduced density matrix is modified by the interaction, and is different from that of the equilibrium of the system alone. We explicitly calculate the contribution of each term in quantum master equation to the realization of the steady state density matrix, and make clear roles of each term. By making use of the role of each term, the properties of the commonly used quantum master equation are examined.
The non-Markovian master equation for open quantum systems is obtained by generalization of the standard Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations is written for the reduced density matrices of the bath ϱB(t) and of the system ϱS(t). A formal solution of the equation for ϱB(t) in the 2nd approximation in interaction yields a specific extra term related to the intrinsic bath dynamics. This term is nonlinear in the reduced density matrix ϱS(t), and vanishes in the Markovian limit. To verify the consistence and robustness of our approach, we apply the generalized ZN projection scheme to a simple dephasing model. We study the obtained kinetic equation both in the Markovian approximation and beyond it (for the term related to the intrinsic bath dynamics) and compare the results with the exact ones.
Open quantum systems and their dynamics are usually studied in terms of reduced density matrices. This approach allows a nonsymmetric description, which is useful when one of the two subsystems is to be considered an environment, at the expense of a loss of information, as tracing out the environmental degrees of freedom is an irreversible process. This has a series of consequences which can be severe. In this work we present an alternative description, which is still nonsymmetric but yet exact: It is based on a parametric representation of composite systems, as obtained by introducing environmental coherent states, such that the principal system get to be described by a set of pure states parametrically dependent on environmental variables. The representation allows one to relate properties which typically arise in studying systems with parametrically dependent Hamiltonians, such as the emergence of geometrical phases, with features which specifically characterize open quantum systems, such as decoherence and entanglement generation.
In the thesis we present an analytic approach towards exact description for steady state density operators of nonequilibrium quantum dynamics in the framework of open systems. We employ the so-called quantum Markovian semi-group evolution, i.e. a general form of time-autonomous positivity and trace-preserving dynamical equation for reduced density operators, by only allowing unitarity-breaking dissipative terms acting at the boundaries of a system. Such setup enables to simulate macroscopic reservoirs for different values of effective thermodynamic potentials, causing incoherent transitions between quantum states which are modeled with aid of the Lindblad operators. This serves as a simple minimalistic model for studying quantum transport properties, either in the linear response domain or in more general regimes far from canonical equilibrium. We are mainly exploring possibilities of identifying nonequilibrium situations which are amenable to exact description within matrix product state representation, by exclusively focusing on steady states, i.e. fixed points of the Lindblad equation, of certain prototypic interacting integrable spin chains driven by incoherent polarizing processes. Finally, we define a concept of pseudo-local extensive almost-conserved quantities by allowing a violation of time-invariance up to boundary-localized terms. We elucidate the role of such quantities on non-ergodic behaviour of temporal correlation functions rendering anomalous transport properties. It turns out that such conservation laws can be generated by means of boundary universal quantum transfer operators of the fundamental integrable models.