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

Stationary states of two-level open quantum systems

Bart Lomiej Gardas, Zbigniew Pucha La

Published Aug 15, 2016• 3 citations
OpenAlex

Abstract

A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two-level open quantum systems under certain conditions applied on both the qubit and the surrounding.

Related papers

Stationary states of two-level open quantum systems

Bartłomiej Gardas, Zbigniew Puchała

A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two-level open quantum systems under certain conditions applied on both the qubit and the surrounding.

arXiv:1006.3328•Journal of Physics A Mathematical and Theoretical•May 3, 2011•2 citations

Open quantum systems and quantum information dynamics

́Angel Rivas

In the first part of this thesis we extensively review the general theory of open quantum systems. We introduce new approaches to describe, in a hopefully more transparent way, some aspects which are usually misleading in a broad range of the literature. In addition, we revise new concepts and methods developed in recent years that complement the general theory mainly developed in the 1970s. In the second part, we focus our attention on the so-called Markovian processes which have been described in the previous part. We study the validity of typical equations used in simple systems such as harmonic oscillators, and propose and check different strategies to describe Markovian dynamics in more complicated interacting systems. Finally we propose a counter-intuitive situation where some level of noise can be actually useful for information tasks. In the third and last part, we approach the problem of the non-Markovian description of open quantum systems. To quantify how non-Markovian an open quantum system is we introduce a computable measure and apply it to some relevant situations. We also propose a way of probing the complexity of an environment by visualizing properties of a pair of qubits embedded in it. In addition, we develop a technique based on orthogonal polynomial theory to transform a wide range of environments into simple chains of particles which can be efficiently simulated with numerical techniques.

•Jan 1, 2011•1 citation

CONTROLLABILITY OF OPEN QUANTUM SYSTEMS

Andreea Grigoriu, HERSCHEL A. RABITZ, Gabriel Turinici

The problem of controllability of open quantum systems (i.e., quantum systems interacting with an environment), whose dynamics is described by a non-Markowian master equation is addressed. The manipulations of the dynamics is realized with both a laser eld and a tailored nonequilibrium, and generally time-dependent, state of the surrounding environment. Lie algebra theory is used to characterize the structures of the reachable states sets and to prove controllability. The theoretical results are supported by examples.

•May 11, 2012•1 citation

Non-Hermitian Quantum Mechanics of Open Quantum Systems: Revisiting The One-Body Problem

Naomichi Hatano, Gonzalo Ordonez

We review analyses of open quantum systems. We show how non-Hermiticity arises in an open quantum system with an infinite environment, focusing on the one-body problem. One of the reasons for taking the present approach is that we can solve the problem completely, making it easier to see the structures of problems involving open quantum systems. We show that this results in the discovery of a new complete set, which is one of the main topics of the present article. Another reason for focusing on the one-body problem is that the theory permits the strong coupling between the system and the environment. In the current research landscape, it is valuable to revisit the one-body problem for open quantum systems, which can be solved accurately for arbitrary strengths of the system-environment couplings. A rigorous understanding of the problem structures in the present approach will be helpful when we tackle problems with many-body interactions. First, we consider potential scattering and directly define the resonant state as an eigenstate of the Schrödinger equation under the Siegert outgoing boundary condition. We show that the resonant eigenstate can have a complex energy eigenvalue, even though the Hamiltonian is seemingly Hermitian. Second, we introduce the Feshbach formalism, which eliminates the infinite degrees of freedom of the environment and represents its effect as a complex potential. The resulting effective Hamiltonian is explicitly non-Hermitian. By unifying these two ways of defining resonant states, we obtain a new complete set of bases for the scattering problem that contains all discrete eigenstates, including resonant states. We finally mention the non-Markovian dynamics of open quantum systems. We emphasize the time-reversal symmetry of the dynamics that continuously connects the past and the future. We can capture it using the new complete set that we develop here.

quant-pharXiv:2602.14105•Feb 17, 2026•0 citations

Finding Stationary Solutions of the Lindblad Equation by Analyzing the Entropy Production Functional

Anton Sergeevich Trushechkin

A necessary and sufficient condition is derived for a density operator to be a stationary solution for a certain class of Lindblad equations in the theory of open quantum systems. This condition is based on the properties of a functional that in some cases corresponds to entropy production. Examples are given where this condition is used to find stationary solutions.

Proceedings of the Steklov Institute of Mathematics•May 1, 2018•11 citations

On the relationship between quantum entanglement and classical synchronization in open systems

E. D. Vol

We propose a simple model of classical open system consisting of two subsystems all stationary states of which correspond to phase synchronization between the subsystems. The model is generalized to quantum systems in a finite-dimensional Hilbert space. The analysis of the simplest two qubit version of the quantum model shows that all its stationary states are nonseparable.

arXiv:1004.5497•Apr 30, 2010•0 citations
A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two-level open quantum systems under certain conditions applied on both the qubit and the surrounding.
In the first part of this thesis we extensively review the general theory of open quantum systems. We introduce new approaches to describe, in a hopefully more transparent way, some aspects which are usually misleading in a broad range of the literature. In addition, we revise new concepts and methods developed in recent years that complement the general theory mainly developed in the 1970s. In the second part, we focus our attention on the so-called Markovian processes which have been described in the previous part. We study the validity of typical equations used in simple systems such as harmonic oscillators, and propose and check different strategies to describe Markovian dynamics in more complicated interacting systems. Finally we propose a counter-intuitive situation where some level of noise can be actually useful for information tasks. In the third and last part, we approach the problem of the non-Markovian description of open quantum systems. To quantify how non-Markovian an open quantum system is we introduce a computable measure and apply it to some relevant situations. We also propose a way of probing the complexity of an environment by visualizing properties of a pair of qubits embedded in it. In addition, we develop a technique based on orthogonal polynomial theory to transform a wide range of environments into simple chains of particles which can be efficiently simulated with numerical techniques.
The problem of controllability of open quantum systems (i.e., quantum systems interacting with an environment), whose dynamics is described by a non-Markowian master equation is addressed. The manipulations of the dynamics is realized with both a laser eld and a tailored nonequilibrium, and generally time-dependent, state of the surrounding environment. Lie algebra theory is used to characterize the structures of the reachable states sets and to prove controllability. The theoretical results are supported by examples.
We review analyses of open quantum systems. We show how non-Hermiticity arises in an open quantum system with an infinite environment, focusing on the one-body problem. One of the reasons for taking the present approach is that we can solve the problem completely, making it easier to see the structures of problems involving open quantum systems. We show that this results in the discovery of a new complete set, which is one of the main topics of the present article. Another reason for focusing on the one-body problem is that the theory permits the strong coupling between the system and the environment. In the current research landscape, it is valuable to revisit the one-body problem for open quantum systems, which can be solved accurately for arbitrary strengths of the system-environment couplings. A rigorous understanding of the problem structures in the present approach will be helpful when we tackle problems with many-body interactions. First, we consider potential scattering and directly define the resonant state as an eigenstate of the Schrödinger equation under the Siegert outgoing boundary condition. We show that the resonant eigenstate can have a complex energy eigenvalue, even though the Hamiltonian is seemingly Hermitian. Second, we introduce the Feshbach formalism, which eliminates the infinite degrees of freedom of the environment and represents its effect as a complex potential. The resulting effective Hamiltonian is explicitly non-Hermitian. By unifying these two ways of defining resonant states, we obtain a new complete set of bases for the scattering problem that contains all discrete eigenstates, including resonant states. We finally mention the non-Markovian dynamics of open quantum systems. We emphasize the time-reversal symmetry of the dynamics that continuously connects the past and the future. We can capture it using the new complete set that we develop here.