© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1310.7199 · Communications in Mathematical Sciences

Decoherence for a heavy particle interacting with a light particle: New analysis and numerics

Riccardo Adami, Maxime Hauray, Claudia Negulescu

Published Jan 1, 2016• 7 citations

Abstract

We study the dynamics of a quantum heavy particle undergoing a repulsive interaction with a light one. The main motivation is the detailed description of the loss of coherence induced on a quantum system (in our model, the heavy particle) by the interaction with the environment (the light particle). The content of the paper is analytical and numerical. Concerning the analytical contribution, we show that an approximate description of the dynamics of the heavy particle can be carried out in two steps: first comes the interaction, then the free evolution. In particular, all effects of the interaction can be embodied in the action of a collision operator that acts on the initial state of the heavy particle. With respect to previous analytical results on the same topics, we turn our focus from the M{\o}ller wave operator to the full scattering operator, whose analysis proves to be simpler. Concerning the numerical contribution, we exploit the previous analysis to construct an efficient numerical scheme that turns the original, multiscale, two-body problem in two one-body problems which can be solved separately. This leads to a considerable gain in simulation time. We present and interpret some simulations carried out on specific one-dimensional systems by using the new scheme. Finally, we propose a new description of the mechanism of decoherence induced by scattering: decoherence is produced by an interference-free bump which arises from the initial state of the heavy particle immediately after the collision. We support such a picture by numerical evidence as well as by an approximation theorem.

DOI: 10.4310/cms.2016.v14.n5.a8

Related papers

On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles

Riccardo Adami, Rodolfo Figari, Domenico Finco +1 more

Abstract. We consider a non relativistic quantum system consisting of K heavy and N light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential αV. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming α sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K = 1 the result is extended to arbitrary α. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrödinger group. Exploiting the asymptotic formula, it is also outlined an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones. 1.

•Jan 1, 2006•16 citations

Decoherence in a two-particle model

Detlef Dürr, Rodolfo Figari, Alessandro Teta

We consider a simple one-dimensional quantum system consisting of a heavy and a light particle interacting via a point interaction. The initial state is chosen to be a product state, with the heavy particle described by a coherent superposition of two spatially separated wave packets with opposite momentum and the light particle localized in the region between the two wave packets. We characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. We derive the corresponding reduced density matrix for the heavy particle and explicitly compute the (partial) decoherence effect for the heavy particle induced by the presence of the light one for a particular set up of the parameters.

arXiv:quant-ph/0210199•Journal of Mathematical Physics•Mar 17, 2004•24 citations

Adding Decoherence to the Wigner Equation

Luigi Barletti, Giovanni Frosali, Elisa Giovannini

Starting from the detailed description of the single-collision decoherence mechanism proposed by Adami, Hauray and Negulescu (2016 R. Adami, M. Hauray, C. Negulescu. 2016. Decoherence for a heavy particle interacting with a light particle: new analysis and numerics. Comm. Math. Sci. 14 (5):1373–1415.[Crossref], [Web of Science ®] , [Google Scholar]), we derive a Wigner equation endowed with a decoherence term of a fairly general form. This equation is shown to contain well known decoherence models, such as the Wigner–Fokker–Planck equation, as particular cases. The effect of the decoherence mechanism on the dynamics of the macroscopic moments (density, current, energy) is illustrated by deriving the corresponding set of balance laws. The issue of large-time asymptotics of our model is addressed in the particular, although physically relevant, case of Gaussian solutions. It is shown that the addition of a Caldeira–Legget friction term provides the asymptotic behavior that one expects on the basis of physical considerations.

arXiv:2006.01121•Journal of Computational and Theoretical Transport•Apr 16, 2018•3 citations

Decoherence induced by scattering: a three-dimensional model

Claudio Cacciapuoti, Raffaele Carlone, Rodolfo Figari

The dynamical process of generation of entanglement between subsystems of an evolving quantum system is analysed in this paper. We consider one of the simplest possible continuous systems in which such a process can be rigorously studied: a quantum ‘heavy’ particle (the system) interacting via zero range forces with a lighter particle (the environment). In a three-dimensional model we study the asymptotic dynamics when the ratio between the masses of the light and the heavy particle is very small. The effect of decoherence on the heavy particle induced by the interaction is explicitly computed.

Journal of Physics A Mathematical and General•May 18, 2005•15 citations

A Numerical Study of Quantum Decoherence

Riccardo Adami, Claudia Negulescu

The present paper provides a numerical investigation of the decoherence effect induced on a quantum heavy particle by the scattering with a light one. The time dependent two-particle Schrödinger equation is solved by means of a time-splitting method. The damping undergone by the non-diagonal terms of the heavy particle density matrix is estimated numerically, as well as the error in the Joos-Zeh approximation formula.

Communications in Computational Physics•May 22, 2012•7 citations

Quantum decoherence: a study applied to quarkonium-like bound states in strongly interacting matter

Gabriele Coci, Salvatore Plumari, Giuseppe Falci

We study the quantum decoherence of a bound state interacting with a reservoir of strongly interacting matter within the framework of open quantum systems. The bound state is modeled as a quantum harmonic oscillator whose parameters are tuned to reproduce the root-mean-square radius of $J/Ψ$ particle. The surrounding medium, representing the many degrees of freedom of strongly interacting matter, acts as an environment that induces dissipation and decoherence through system-reservoir coupling. By analyzing the time evolution of the reduced density matrix, we quantify the loss of quantum coherence and its dependence on medium properties. Subsequently, we extend the model by introducing a time dependence in the system-thermal bath coupling, thereby simulating a temperature evolution similar to that occurring during the expansion of a fireball in the central region of heavy-ion collisions. We find that a temperature evolution has a relevant impact on the way the system loses coherence through the coupling with the expanding medium. Finally, we estimate the impact of the time-dependent temperature on the decoherence process, also analyzing a scenario that includes viscous effects without finding a significant change with respect to ideal hydrodynamical evolution.

hep-phCross-listedarXiv:2607.06137•Jul 8, 2026•0 citations

We study the dynamics of a quantum heavy particle undergoing a repulsive interaction with a light one. The main motivation is the detailed description of the loss of coherence induced on a quantum system (in our model, the heavy particle) by the interaction with the environment (the light particle). The content of the paper is analytical and numerical. Concerning the analytical contribution, we show that an approximate description of the dynamics of the heavy particle can be carried out in two steps: first comes the interaction, then the free evolution. In particular, all effects of the interaction can be embodied in the action of a collision operator that acts on the initial state of the heavy particle. With respect to previous analytical results on the same topics, we turn our focus from the M{\o}ller wave operator to the full scattering operator, whose analysis proves to be simpler. Concerning the numerical contribution, we exploit the previous analysis to construct an efficient numerical scheme that turns the original, multiscale, two-body problem in two one-body problems which can be solved separately. This leads to a considerable gain in simulation time. We present and interpret some simulations carried out on specific one-dimensional systems by using the new scheme. Finally, we propose a new description of the mechanism of decoherence induced by scattering: decoherence is produced by an interference-free bump which arises from the initial state of the heavy particle immediately after the collision. We support such a picture by numerical evidence as well as by an approximation theorem.

Abstract. We consider a non relativistic quantum system consisting of K heavy and N light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential αV. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming α sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K = 1 the result is extended to arbitrary α. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrödinger group. Exploiting the asymptotic formula, it is also outlined an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones. 1.

We consider a simple one-dimensional quantum system consisting of a heavy and a light particle interacting via a point interaction. The initial state is chosen to be a product state, with the heavy particle described by a coherent superposition of two spatially separated wave packets with opposite momentum and the light particle localized in the region between the two wave packets. We characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. We derive the corresponding reduced density matrix for the heavy particle and explicitly compute the (partial) decoherence effect for the heavy particle induced by the presence of the light one for a particular set up of the parameters.

Starting from the detailed description of the single-collision decoherence mechanism proposed by Adami, Hauray and Negulescu (2016 R. Adami, M. Hauray, C. Negulescu. 2016. Decoherence for a heavy particle interacting with a light particle: new analysis and numerics. Comm. Math. Sci. 14 (5):1373–1415.[Crossref], [Web of Science ®] , [Google Scholar]), we derive a Wigner equation endowed with a decoherence term of a fairly general form. This equation is shown to contain well known decoherence models, such as the Wigner–Fokker–Planck equation, as particular cases. The effect of the decoherence mechanism on the dynamics of the macroscopic moments (density, current, energy) is illustrated by deriving the corresponding set of balance laws. The issue of large-time asymptotics of our model is addressed in the particular, although physically relevant, case of Gaussian solutions. It is shown that the addition of a Caldeira–Legget friction term provides the asymptotic behavior that one expects on the basis of physical considerations.

The dynamical process of generation of entanglement between subsystems of an evolving quantum system is analysed in this paper. We consider one of the simplest possible continuous systems in which such a process can be rigorously studied: a quantum ‘heavy’ particle (the system) interacting via zero range forces with a lighter particle (the environment). In a three-dimensional model we study the asymptotic dynamics when the ratio between the masses of the light and the heavy particle is very small. The effect of decoherence on the heavy particle induced by the interaction is explicitly computed.

We study the quantum decoherence of a bound state interacting with a reservoir of strongly interacting matter within the framework of open quantum systems. The bound state is modeled as a quantum harmonic oscillator whose parameters are tuned to reproduce the root-mean-square radius of

J/Ψ

particle. The surrounding medium, representing the many degrees of freedom of strongly interacting matter, acts as an environment that induces dissipation and decoherence through system-reservoir coupling. By analyzing the time evolution of the reduced density matrix, we quantify the loss of quantum coherence and its dependence on medium properties. Subsequently, we extend the model by introducing a time dependence in the system-thermal bath coupling, thereby simulating a temperature evolution similar to that occurring during the expansion of a fireball in the central region of heavy-ion collisions. We find that a temperature evolution has a relevant impact on the way the system loses coherence through the coupling with the expanding medium. Finally, we estimate the impact of the time-dependent temperature on the decoherence process, also analyzing a scenario that includes viscous effects without finding a significant change with respect to ideal hydrodynamical evolution.