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

International Journal of Circuit Theory and Applications

On state equations of two‐level quantum systems in a thermal environment

Pier Paolo Civalleri, Marco Gilli

Published Nov 1, 2004• 1 citation
Publisher

Abstract

Abstract The state equations of open two‐level quantum systems, which form the building blocks of quantum cellular neural networks, are studied in arbitrary representations. It is shown that the dissipation matrix, that under the usual assumptions is diagonal in the energy representation, such remains if and only if the coupling between the states induced by an external field is real and infinitesimal. Copyright © 2004 John Wiley & Sons, Ltd.

DOI
10.1002/cta.298

Related papers

On state equations of two-level quantum systems in a thermal environment: Research Articles

Pier Paolo Civalleri, Marco Gilli

The state equations of open two-level quantum systems, which form the building blocks of quantum cellular neural networks, are studied in arbitrary representations. It is shown that the dissipation matrix, that under the usual assumptions is diagonal in the energy representation, such remains if and only if the coupling between the states induced by an external field is real and infinitesimal. Copyright © 2004 John Wiley & Sons, Ltd.

International Journal of Circuit Theory and Applications•Nov 1, 2004•0 citations

Coherence in a network of two-level systems coupled to a bosonic field

S. Fischer, Heinz‐Peter Breuer

We study the quantum dynamics of an open network of two-level systems which is coupled to a correlated common environment represented by a bosonic field in a thermal equilibrium state. Extensive numerical simulations of the full second-order time-convolutionless quantum master equation for the density matrix of various types of networks are performed, in order to investigate dissipation and decoherence processes and, in particular, their dependence on the spatial separation of the network sites and on the speed of the bosonic field modes. In the limit of an infinite speed the influence of the environment disappears due to the emergence of a decoherence-free subspace, while the limit of zero speed corresponds to the case in which the network sites are coupled to independent reservoirs, a case which is much easier to treat numerically. The main result of the paper is a general intuitive criterion which states that the simpler model of independent reservoirs can be used as long as the network relaxation time is smaller than the time it takes for the modes to travel the minimal distance between the network sites.

Physical Review A•Dec 13, 2013•10 citations

Jordan block structure of two-dimensional quantum neural cellular network

Bi Qiao, Harry E. Ruda

We present a Jordan type spectral decomposition for the Hamiltonian operator of a two-dimensional (2D) Ising model driven by a local external field. The results reveal that the external field induces a dynamic contribution to the Jordan block structure, while the interaction between lattice spins contributes to the energy spectrum, tending to attract the system to a minimum energy state. Both interactions contributing to the principle vectors of the Hamiltonian operator reflect their correlation. Since we adopt a first-principle approach the results are useful to general 2D Ising spin systems subject to time-independent external fields irrespective of whether the system is in equilibrium.

Journal of Applied Physics•Jul 1, 1999•2 citations

Theory of open quantum systems

Rui‐Xue Xu, YiJing Yan

A quantum dissipation theory is constructed with the system–bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition. The theory is valid for arbitrary bath correlation functions and time-dependent external driving fields, and satisfies correlated detailed-balance relation at any temperatures. The general formulation assumes a particularly simple form in driven Brownian oscillator systems in which the correlated driving-dissipation effects can be accounted for exactly in terms of local-field correction. Remarks on a class of widely used phenomenological quantum master equations that neglects the bath dispersion-induced dissipation are also made in contact with the present theory.

The Journal of Chemical Physics•May 9, 2002•5,903 citations

Decoherence in quantum systems and the network paradigm

Wolfgang M. Mathis, K. Pahlke, Xu‐Bo Zou

Abstract Since quantum systems interact with their environment permanently or within a measurement process, there is much interest in concepts of open quantum system modelling. In this paper we give an overview on three different concepts in order to address this problem in the context of the network paradigm. Furthermore the modelling of spatially localized decoherence processes within the stochastic diffusion wave equation approach of Gisin et al. is briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.

International Journal of Circuit Theory and Applications•Jan 1, 2003•3 citations

Basic concepts of quantum systems versus classical networks

Pier Paolo Civalleri, Marco Gilli, Michele Bonnin

Abstract The paper is intended to establish a conceptual bridge between Classical Network Theory and Quantum Mechanics. The concept of time‐reversal symmetry is extended from Quantum Mechanics to Network Theory (in the state equations description), while concepts of passivity and losslessness are extended from Network Theory to Quantum Mechanics. Copyright © 2004 John Wiley & Sons, Ltd.

International Journal of Circuit Theory and Applications•Sep 1, 2004•4 citations
Abstract The state equations of open two‐level quantum systems, which form the building blocks of quantum cellular neural networks, are studied in arbitrary representations. It is shown that the dissipation matrix, that under the usual assumptions is diagonal in the energy representation, such remains if and only if the coupling between the states induced by an external field is real and infinitesimal. Copyright © 2004 John Wiley & Sons, Ltd.
We study the quantum dynamics of an open network of two-level systems which is coupled to a correlated common environment represented by a bosonic field in a thermal equilibrium state. Extensive numerical simulations of the full second-order time-convolutionless quantum master equation for the density matrix of various types of networks are performed, in order to investigate dissipation and decoherence processes and, in particular, their dependence on the spatial separation of the network sites and on the speed of the bosonic field modes. In the limit of an infinite speed the influence of the environment disappears due to the emergence of a decoherence-free subspace, while the limit of zero speed corresponds to the case in which the network sites are coupled to independent reservoirs, a case which is much easier to treat numerically. The main result of the paper is a general intuitive criterion which states that the simpler model of independent reservoirs can be used as long as the network relaxation time is smaller than the time it takes for the modes to travel the minimal distance between the network sites.
We present a Jordan type spectral decomposition for the Hamiltonian operator of a two-dimensional (2D) Ising model driven by a local external field. The results reveal that the external field induces a dynamic contribution to the Jordan block structure, while the interaction between lattice spins contributes to the energy spectrum, tending to attract the system to a minimum energy state. Both interactions contributing to the principle vectors of the Hamiltonian operator reflect their correlation. Since we adopt a first-principle approach the results are useful to general 2D Ising spin systems subject to time-independent external fields irrespective of whether the system is in equilibrium.
A quantum dissipation theory is constructed with the system–bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition. The theory is valid for arbitrary bath correlation functions and time-dependent external driving fields, and satisfies correlated detailed-balance relation at any temperatures. The general formulation assumes a particularly simple form in driven Brownian oscillator systems in which the correlated driving-dissipation effects can be accounted for exactly in terms of local-field correction. Remarks on a class of widely used phenomenological quantum master equations that neglects the bath dispersion-induced dissipation are also made in contact with the present theory.
Abstract Since quantum systems interact with their environment permanently or within a measurement process, there is much interest in concepts of open quantum system modelling. In this paper we give an overview on three different concepts in order to address this problem in the context of the network paradigm. Furthermore the modelling of spatially localized decoherence processes within the stochastic diffusion wave equation approach of Gisin et al. is briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.