© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Pointer state dynamics of dissipative quantum systems

Lutz Sörgel

Published Oct 26, 2016• 0 citations

Abstract

In the present work, I identify the pointer states of quantum Brownian motion as rotated Gaussian states in phase space. By means of a particular piecewise deterministic unraveling, the pointer state unraveling, I determine the trajectories of the position and momentum expectation of the pointer states. They turn out to be described by a diffusion process in phase space and, in the semiclassical limit, they turn into the Langevin equation of classical Brownian motion. For collisional decoherence, the non-dissipative limit of the quantum linear Boltzmann equation, which describes the dynamics of a marker particle in an ideal gaseous environment, I examine the width of the pointer states and thereby extend previous results to more than one dimension. Crucially, it follows that pointer states do not exist for all parameter values in that case. By expanding the Lindblad operators of the quantum linear Boltzmann equation, I derive a new Lindblad master equation, dissipative collisional decoherence, which shows a decoherence behavior similar to that of collisional decoherence and also incorporates frictional as well as diffusion effects. Moreover this equation exhibits soliton-like solutions as candidates for the pointer states.

Related papers

Unraveling quantum Brownian motion: Pointer states and their classical trajectories

Lutz Sörgel, Klaus Hornberger

We characterize the pointer states generated by the master equation of quantum Brownian motion and derive stochastic equations for the dynamics of their trajectories in phase space. Our method is based on a Poissonian unraveling of the master equation whose deterministic part exhibits soliton-like solutions that can be identified with the pointer states. In the semiclassical limit, their equations of motion in phase space turn into those of classical diffusion, yielding a clear picture of the quantum-classical transition induced by environmental decoherence.

arXiv:1509.02392•Physical Review A•Dec 9, 2015•12 citations

Master Equation for a Quantum Particle in a Gas

Klaus Hornberger

The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts nonperturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.

arXiv:quant-ph/0607085•Physical Review Letters•Aug 7, 2006•92 citations

Rotational Friction and Diffusion of Quantum Rotors

Benjamin A. Stickler, Björn Schrinski, Klaus Hornberger

We present the Markovian quantum master equation describing rotational decoherence, friction, diffusion, and thermalization of planar, linear, and asymmetric rotors in contact with a thermal environment. It describes how an arbitrary initial rotation state decoheres and evolves toward a Gibbs-like thermal ensemble, as we illustrate numerically for the linear and the planar top, and it yields the expected rotational Fokker-Planck equation of Brownian motion in the semiclassical limit.

arXiv:1712.05163•Physical Review Letters•Jul 23, 2018•49 citations

Dissipation and decoherence in Brownian motion

Bruno Bellomo, Stephen Mark Barnett, John Jeffers

We consider the evolution of a Brownian particle described by a measurement-based master equation. We derive the solution to this equation for general initial conditions and apply it to a Gaussian initial state. We analyse the effects of the diffusive terms, present in the master equation, and describe how these modify uncertainties and coherence length. This allows us to model dissipation and decoherence in quantum Brownian motion.

Journal of Physics Conference Series•May 1, 2007•1 citation

Monitoring derivation of the quantum linear Boltzmann equation

Klaus Hornberger, Bassano Vacchini

We show how the effective equation of motion for a distinguished quantum particle in an ideal gas environment can be obtained by means of the monitoring approach introduced by Hornberger [EPL 77, 50007 (2007)]. The resulting Lindblad master equation accounts for the quantum effects of the scattering dynamics in a nonperturbative fashion and it describes decoherence and dissipation in a unified framework. It incorporates various established equations as limiting cases and reduces to the classical linear Boltzmann equation once the state is diagonal in momentum.

arXiv:0711.3109•Physical Review A•Feb 19, 2008•45 citations

Frictional quantum decoherence

Bruno Bellomo, Stephen Mark Barnett, John Jeffers

The dynamics associated with a measurement-based master equation for quantum Brownian motion are investigated. A scheme for obtaining time evolution from general initial conditions is derived. This is applied to analyze dissipation and decoherence in the evolution of both a Gaussian and a Schrödinger cat initial state. Dependence on the diffusive terms present in the master equation is discussed with reference to both the coordinate and momentum representations.

arXiv:0707.2912•Journal of Physics A Mathematical and Theoretical•Jul 19, 2007•7 citations

In the present work, I identify the pointer states of quantum Brownian motion as rotated Gaussian states in phase space. By means of a particular piecewise deterministic unraveling, the pointer state unraveling, I determine the trajectories of the position and momentum expectation of the pointer states. They turn out to be described by a diffusion process in phase space and, in the semiclassical limit, they turn into the Langevin equation of classical Brownian motion. For collisional decoherence, the non-dissipative limit of the quantum linear Boltzmann equation, which describes the dynamics of a marker particle in an ideal gaseous environment, I examine the width of the pointer states and thereby extend previous results to more than one dimension. Crucially, it follows that pointer states do not exist for all parameter values in that case. By expanding the Lindblad operators of the quantum linear Boltzmann equation, I derive a new Lindblad master equation, dissipative collisional decoherence, which shows a decoherence behavior similar to that of collisional decoherence and also incorporates frictional as well as diffusion effects. Moreover this equation exhibits soliton-like solutions as candidates for the pointer states.

We characterize the pointer states generated by the master equation of quantum Brownian motion and derive stochastic equations for the dynamics of their trajectories in phase space. Our method is based on a Poissonian unraveling of the master equation whose deterministic part exhibits soliton-like solutions that can be identified with the pointer states. In the semiclassical limit, their equations of motion in phase space turn into those of classical diffusion, yielding a clear picture of the quantum-classical transition induced by environmental decoherence.

The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts nonperturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.

We show how the effective equation of motion for a distinguished quantum particle in an ideal gas environment can be obtained by means of the monitoring approach introduced by Hornberger [EPL 77, 50007 (2007)]. The resulting Lindblad master equation accounts for the quantum effects of the scattering dynamics in a nonperturbative fashion and it describes decoherence and dissipation in a unified framework. It incorporates various established equations as limiting cases and reduces to the classical linear Boltzmann equation once the state is diagonal in momentum.