1,081 research outputs found
Effective coupling between two Brownian particles
We use the system-plus-reservoir approach to study the dynamics of a system
composed of two independent Brownian particles. We present an extension of the
well-known model of a bath of oscillators which is capable of inducing an
effective coupling between the two particles depending on the choice made for
the spectral function of the bath oscillators. The coupling is non-linear in
the variables of interest and an exponential dependence on these variables is
imposed in order to guarantee the translational invariance of the model if the
two particles are not subject to any external potential. The effective
equations of motion for the particles are obtained by the Laplace transform
method and besides recovering all the local dynamical properties for each
particle we end up with an effective interaction potential between them. We
explicitly analyze one of its possible forms.Comment: 4 pages, 1 figur
Dynamical decoupling induced renormalization of the non-Markovian dynamics
In this work we develop a numerical framework to investigate the
renormalization of the non-Markovian dynamics of an open quantum system to
which dynamical decoupling is applied. We utilize a non-Markovian master
equation which is derived from the non-Markovian quantum trajectories
formalism. It contains incoherent Markovian dynamics and coherent Schr\"odinger
dynamics as its limiting cases and is capable of capture the transition between
them. We have performed comprehensive simulations for the cases in which the
system is either driven by the Ornstein-Uhlenbeck noise or or is described by
the spin-boson model. The renormalized dynamics under bang-bang control and
continuous dynamical decoupling are simulated. Our results indicate that the
renormalization of the non-Markovian dynamics depends crucially on the spectral
density of the environment and the envelop of the decoupling pulses. The
framework developed in this work hence provides an unified approach to
investigate the efficiency of realistic decoupling pulses. This work also opens
a way to further optimize the decoupling via pulse shaping
The mobility and diffusion of a particle coupled to a Luttinger liquid
We study the mobility of a particle coupled to a one dimensional interacting
fermionic system, a Luttinger liquid. We bosonize the Luttinger liquid and find
the effective interaction between the particle and the bosonic system. We show
that the dynamics of this system is completely equivalent to the acoustic
polaron problem where the interaction has purely electronic origin. This
problem has a zero mode excitation, or soliton, in the strong coupling limit
which corresponds to the formation of a polarization cloud due to the
fermion-fermion interaction around the particle. We obtain that, due to the
scattering of the residual bosonic modes, the soliton has a finite mobility and
diffusion coefficient at finite temperatures which depend on the
fermion-fermion interaction. We show that at low temperatures the mobility and
the diffusion coefficient are proportional to and respectively
and at high temperatures the mobility vanishes as while the diffusion
increases as .Comment: 9 pages, Revtex, UIUC preprin
Thermal equilibrium of two quantum Brownian particles
The influence of the environment in the thermal equilibrium properties of a
bipartite continuous variable quantum system is studied. The problem is treated
within a system-plus-reservoir approach. The considered model reproduces the
conventional Brownian motion when the two particles are far apart and induces
an effective interaction between them, depending on the choice of the spectral
function of the bath. The coupling between the system and the environment
guarantees the translational invariance of the system in the absence of an
external potential. The entanglement between the particles is measured by the
logarithmic negativity, which is shown to monotonically decrease with the
increase of the temperature. A range of finite temperatures is found in which
entanglement is still induced by the reservoir.Comment: 8 pages, 1 figur
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