1,721,057 research outputs found
Quantum description of Einstein's Brownian motion
No full textA fully quantum treatment of Einstein's Brownian motion is given, stressing in particular the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature of the medium. The former leads to a clearcut relationship with a generator of translation-covariant quantum-dynamical semigroups recently characterized by Holevo, the latter to a formulation of the fluctuation- dissipation theorem in terms of the dynamic structure factor, a two-point correlation function introduced in seminal work by Van Hove, directly related to density fluctuations in the medium and therefore to its atomistic, discrete nature. A microphysical expression for the generally temperature dependent friction coefficient is given in terms of the dynamic structure factor and of the interaction potential describing the single collisions. A comparison with the Caldeira-Leggett model is drawn, especially in view of the requirement of translational invariance, further characterizing general structures of reduced dynamics arising in the presence of symmetry under translations
Kinetic description of quantum Brownian motion
No full textWe stress the relevance of the two features of translational invariance and atomic nature of the gas in the quantum description of the motion of a massive test particle in a gas, corresponding to the original picture of
Einstein used in the characterization of Brownian motion. The master equation describing the reduced dynamics of the test particle is of Lindblad form and complies with the requirement of covariance under
translations
Initial correlations effects on decoherence at zero temperature
No full textWe consider a free charged particle interacting with an electromagnetic bath at zero temperature. The dipole approximation is used to treat the bath wavelengths larger than the width of the particle wave packet. The effect of these wavelengths is then described by a linear Hamiltonian whose form is analogous to the phenomenological Hamiltonians previously adopted to describe the free particle-bath interaction. We study how the time dependence of decoherence evolution is related with initial particle-bath correlations. We show that decoherence is related to the time dependent dressing of the particle. Moreover, because decoherence induced by the T ≤ 0 bath is very rapid, we make some considerations on the conditions under which interference may be experimentally observed
Loss of coherence and dressing in QED
Full text linkThe dynamics of a free charged particle, initially described by a coherent wave packet, interacting with an environment, i.e., the electromagnetic field characterized by a temperature T, is studied. Using the dipole approximation, the exact expressions for the evolution of the reduced density matrix both in momentum and configuration space and the vacuum and the thermal contribution to decoherence are obtained. The time behavior of the coherence lengths in the two representations are given. Through the analysis of the dynamic of the field structure associated with the particle the vacuum contribution is shown to be linked to the birth of correlations between the single momentum components of the particle wave packet and the virtual photons of the dressing clou
Stochastic Schrödinger equations with coloured noise
No full textA natural non-Markovian extension of the theory of white noise quantum trajectories is presented. In order to introduce memory effects in the formalism an Ornstein-Uhlenbeck coloured noise is considered as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, non-Markovian stochastic Schrödinger equations which unravel non-Markovian master equations are derived. As a prototypical example, an harmonic oscillator is considered, able to emit light and with memory terms in the dynamics. The signature of the non-Markovian dynamics is seen in the spectrum of the emitted light
Stochastic Schrödinger Equations for Markovian and non-Markovian Cases
Full text linkFirstly, the Markovian stochastic Schroedinger equations are presented, together with their connections with the theory of measurements in continuous time. Moreover, the stochastic evolution equations are translated into a simulation algorithm, which is illustrated by two concrete examples - the damped harmonic oscillator and a two-level atom with homodyne photodetection. We then consider how to introduce memory effects in the stochastic Schroedinger equation via coloured noise. Specifically, the approach by using the Ornstein-Uhlenbeck process is illustrated and a simulation for the non-Markovian process proposed. Finally, an analytical approximation technique is tested with the help of the stochastic simulation in a model of a dissipative qubit
Theoretical analysis of a recent experiment on mesoscopic state superpositions in cavity QED
Full text linkQuite recently quantum features exhibited by a mesoscopic field interacting with a single Rydberg atom in a microwave cavity has been observed (A. Auffeves et al., Phys. Rev. Lett. 91, 230405, 2003). In this paper
we theoretically analyze all the phases of this articulated experiment considering from the very beginning cavity losses. Fully applying the theory of quantum open systems, our modelization succeeds in predicting fine aspects of the measured quantity, reaching qualitative and quantitative good agreement with the experimental
results. This fact validates our theoretical approach based on the fundamental atom-cavity interaction model and simple mathematical structure of dissipative superoperators
Sochastic Schrödinger equations and memory
No full textBy starting from the stochastic Schröödinger equation and quantum trajectory theory, we introduce memory effects by considering stochastic adapted coefficients. As an example of a natural non-Markovian extension of the theory of white noise
quantum trajectories we use an Ornstein-Uhlenbeck coloured noise as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, we show that our non-Markovian stochastic Schröödinger equations unravel some master equations with memory kernels
Non-Markovian wave function simulations of quantum Brownian motion
No full textThe non-Markovian wave function method (NMWF) using the stochastic unravelling of the master equation in the doubled Hilbert space is implemented for quantum Brownian motion. A comparison between the simulation and the analytical results shows that the method can be conveniently used to study the non-Markovian dynamics of the system
Scaling of non-Markovian Monte Carlo wave-function methods
Full text linkWe demonstrate a scaling method for non-Markovian Monte Carlo wave-function simulations used to study open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values of arbitrary operators of interest can be calculated, all the quantities in the equation being easily obtainable from the scaled Monte Carlo wave-function simulations. In the optimal case, the scaling method can be used, within the weak coupling approximation, to reduce the size of the generated Monte Carlo ensemble by several orders of magnitude. Thus, the developed method allows faster simulations and makes it possible to solve the dynamics of the certain class of non-Markovian systems whose simulation would be otherwise too tedious because of the requirement for large computational resources
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