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 Mathematical Physics

Regularizing divergences in the von Neumann entropy

J. C. Retamal, Lautaro Vergara

Published Feb 1, 2002• 0 citations
Publisher

Abstract

We study the decoherence process of a harmonic oscillator in a dissipative environment by considering the von Neumann entropy. Derivatives of the von Neumann entropy around the initial time exhibit divergences when the system is initially in a pure state. A regularization procedure based on the zeta function technique is considered in order to extract information about decoherence.

DOI
10.1063/1.1428809

Related papers

Uncertainty, Entropy and Decoherence of the Damped Harmonic Oscillator in the Lindblad Theory of Open Quantum Systems

Аурелиан Исар

In the framework of the Lindblad theory for open quantum systems, expressions for the density operator, von Neumann entropy and effective temperature of the damped harmonic oscillator are obtained. The entropy for a state characterized by a Wigner distribution function which is Gaussian in form is found to depend only on the variance of the distribution function. We give a series of inequalities, relating uncertainty to von Neumann entropy and linear entropy. We analyze the conditions for purity of states and show that for a special choice of the diffusion coefficients, the correlated coherent states (squeezed coherent states) are the only states which remain pure all the time during the evolution of the considered system. These states are also the most stable under evolution in the presence of the environment and play an important role in the description of environment induced decoherence.

arXiv:quant-ph/9910019•Fortschritte der Physik•Sep 1, 1999•31 citations

Decoherence of a dissipative Brownian charged magneto-anharmonic oscillator: an information theoretic approach

Suraka Bhattacharjee, Koushik Mandal, Supurna Sinha

Abstract We study the decoherence of an anisotropic anharmonic oscillator in a magnetic field, coupled to a bath of harmonic oscillators at high and low temperatures. We solve the anharmonic oscillator problem using perturbative techniques and derive the non-Markovian master equation in the weak coupling limit. The anharmonicity parameter α enhances decoherence due to the deconfining effect of anharmonicity. The oscillatory nature of the time evolution of heating function indicates information backflow. The von-Neumann entropy is also calculated for the system, which increases with α , consistent with the deconfining effect noted in the decoherence analysis. We have also proposed a cold ion experimental set up for testing our theoretical predictions. The study is of relevance to the domain of quantum technology where decoherence significantly affects the performance of a quantum computer.

arXiv:2510.19317•Journal of Physics A Mathematical and Theoretical•Dec 11, 2025•1 citation

von Neumann entropy and entropy production of a damped harmonic oscillator

Gabriel Artur Weiderpass, A. O. Caldeira

In this paper we analyze the entropy and entropy production of a nonisolated quantum system described within the quantum Brownian motion framework. This is a very general and paradigmatic framework for describing nonisolated quantum systems and can be used in any kind of coupling regime. We start by considering the application of von Neumann entropy to an arbitrarily damped quantum system making use of its reduced density operator. We argue that this application is formally valid and develop a path-integral method to evaluate that quantity analytically. We apply this technique to a harmonic oscillator in contact with a heat bath and obtain an exact form for its entropy. Then we study the entropy production of this system and enlighten important characteristics of its thermodynamical behavior on the pure quantum realm and also address their transition to the classical limit.

arXiv:2001.02261•Physical review. E•Sep 1, 2020•14 citations

Quantum dynamical entropy and decoherence rate

Robert Alicki, Artur ozi ski, Prot Pako ski +1 more

We investigate quantum dynamical systems defined on a finite dimensional Hilbert space and subjected to an interaction with an environment. The rate of decoherence of initially pure states, measured by the increase of their von Neumann entropy, averaged over an ensemble of random pure states, is proved to be bounded from above by the partial entropy used to define the ALF dynamical entropy. The rate of decoherence induced by the sequence of the von Neumann projectors measurements is shown to be maximal, if the measurements are performed in a randomly chosen basis. The numerically observed linear increase of entropies is attributed to free-independence of the measured observable and the unitary dynamical map.

arXiv:quant-ph/0309194•Journal of Physics A Mathematical and General•Apr 28, 2004•23 citations

Divergence of entanglement entropy in quantum systems: Zero-modes

S. Mahesh Chandran, S. Shankaranarayanan

To this day, von Neumann definition of entropy remains the most popular measure of quantum entanglement. Much of the literature on entanglement entropy, particularly in the context of field theory, has focused on isolating the UV divergences. Zero-mode divergences of the entanglement entropy are less studied in this context, and apart from being easier to isolate, they offer an interesting insight into the physics of the system. To gain a better understanding of the system in this limit, we develop the free particle approximation of harmonic oscillator, with which we investigate the properties of entropy divergence in continuous bi-partite quantum systems such as the coupled harmonic oscillators and the hydrogen atom. We also show zero-mode divergence of the entropy of environment-induced entanglement in a tri-partite oscillator system. We discuss the implications of our result for field theory and IR structure of gravity.

arXiv:1810.03888•Physical review. D/Physical review. D.•Feb 19, 2019•27 citations

Dissipative quantum dynamics: solution of the generalized von Neumann equation for the damped harmonic oscillator

Martin Hensel, H. J. Korsch

A recently proposed generalized von Neumann equation describing dissipative time evolution of quantum systems is applied to a damped and driven harmonic oscillator. Utilizing Lie algebraic methods the nonlinear operator equation is solved and from this solution the behaviour of the mean value (x) is extracted, including both amplitude and phaseshift relative to the driving force. A differential equation for (x) is derived and the damping constant is identified.

Journal of Physics A Mathematical and General•Apr 7, 1992•14 citations
We study the decoherence process of a harmonic oscillator in a dissipative environment by considering the von Neumann entropy. Derivatives of the von Neumann entropy around the initial time exhibit divergences when the system is initially in a pure state. A regularization procedure based on the zeta function technique is considered in order to extract information about decoherence.
In the framework of the Lindblad theory for open quantum systems, expressions for the density operator, von Neumann entropy and effective temperature of the damped harmonic oscillator are obtained. The entropy for a state characterized by a Wigner distribution function which is Gaussian in form is found to depend only on the variance of the distribution function. We give a series of inequalities, relating uncertainty to von Neumann entropy and linear entropy. We analyze the conditions for purity of states and show that for a special choice of the diffusion coefficients, the correlated coherent states (squeezed coherent states) are the only states which remain pure all the time during the evolution of the considered system. These states are also the most stable under evolution in the presence of the environment and play an important role in the description of environment induced decoherence.
Abstract We study the decoherence of an anisotropic anharmonic oscillator in a magnetic field, coupled to a bath of harmonic oscillators at high and low temperatures. We solve the anharmonic oscillator problem using perturbative techniques and derive the non-Markovian master equation in the weak coupling limit. The anharmonicity parameter α enhances decoherence due to the deconfining effect of anharmonicity. The oscillatory nature of the time evolution of heating function indicates information backflow. The von-Neumann entropy is also calculated for the system, which increases with α , consistent with the deconfining effect noted in the decoherence analysis. We have also proposed a cold ion experimental set up for testing our theoretical predictions. The study is of relevance to the domain of quantum technology where decoherence significantly affects the performance of a quantum computer.
In this paper we analyze the entropy and entropy production of a nonisolated quantum system described within the quantum Brownian motion framework. This is a very general and paradigmatic framework for describing nonisolated quantum systems and can be used in any kind of coupling regime. We start by considering the application of von Neumann entropy to an arbitrarily damped quantum system making use of its reduced density operator. We argue that this application is formally valid and develop a path-integral method to evaluate that quantity analytically. We apply this technique to a harmonic oscillator in contact with a heat bath and obtain an exact form for its entropy. Then we study the entropy production of this system and enlighten important characteristics of its thermodynamical behavior on the pure quantum realm and also address their transition to the classical limit.
We investigate quantum dynamical systems defined on a finite dimensional Hilbert space and subjected to an interaction with an environment. The rate of decoherence of initially pure states, measured by the increase of their von Neumann entropy, averaged over an ensemble of random pure states, is proved to be bounded from above by the partial entropy used to define the ALF dynamical entropy. The rate of decoherence induced by the sequence of the von Neumann projectors measurements is shown to be maximal, if the measurements are performed in a randomly chosen basis. The numerically observed linear increase of entropies is attributed to free-independence of the measured observable and the unitary dynamical map.
To this day, von Neumann definition of entropy remains the most popular measure of quantum entanglement. Much of the literature on entanglement entropy, particularly in the context of field theory, has focused on isolating the UV divergences. Zero-mode divergences of the entanglement entropy are less studied in this context, and apart from being easier to isolate, they offer an interesting insight into the physics of the system. To gain a better understanding of the system in this limit, we develop the free particle approximation of harmonic oscillator, with which we investigate the properties of entropy divergence in continuous bi-partite quantum systems such as the coupled harmonic oscillators and the hydrogen atom. We also show zero-mode divergence of the entropy of environment-induced entanglement in a tri-partite oscillator system. We discuss the implications of our result for field theory and IR structure of gravity.