570 research outputs found
Breakdown of a conservation law in incommensurate systems
We show that invariance properties of the Lagrangian of an incommensurate
system, as described by the Frenkel Kontorova model, imply the existence of a
generalized angular momentum which is an integral of motion if the system
remains floating. The behavior of this quantity can therefore monitor the
character of the system as floating (when it is conserved) or locked (when it
is not). We find that, during the dynamics, the non-linear couplings of our
model cause parametric phonon excitations which lead to the appearance of
Umklapp terms and to a sudden deviation of the generalized momentum from a
constant value, signalling a dynamical transition from a floating to a pinned
state. We point out that this transition is related but does not coincide with
the onset of sliding friction which can take place when the system is still
floating.Comment: 7 pages, 6 figures, typed with RevTex, submitted to Phys. Rev. E
Replaced 27-03-2001: changes to text, minor revision of figure
Quantum trajectories for Brownian motion
We present the stochastic Schroedinger equation for the dynamics of a quantum
particle coupled to a high temperature environment and apply it the dynamics of
a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on
the environmental memory time scale, in the mean, our result recovers the
solution of the known non-Lindblad quantum Brownian motion master equation. A
remarkable feature of our approach is its localization property: individual
quantum trajectories remain localized wave packets for all times, even for the
classically chaotic system considered here, the localization being stronger the
smaller .Comment: 4 pages, 3 eps figure
A perturbative approach to non-Markovian stochastic Schr\"odinger equations
In this paper we present a perturbative procedure that allows one to
numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations,
for a wide range of memory functions. To illustrate this procedure numerical
results are presented for a classically driven two level atom immersed in a
environment with a simple memory function. It is observed that as the order of
the perturbation is increased the numerical results for the ensembled average
state approach the exact reduced state found via
Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].Comment: 17 pages, 4 figure
Influence of Complex Exciton-Phonon Coupling on Optical Absorption and Energy Transfer of Quantum Aggregates
We present a theory that efficiently describes the quantum dynamics of an
electronic excitation that is coupled to a continuous, highly structured phonon
environment. Based on a stochastic approach to non-Markovian open quantum
systems, we develop a dynamical framework that allows us to handle realistic
systems where a fully quantum treatment is desired yet the usual approximation
schemes fail. The capability of the method is demonstrated by calculating
spectra and energy transfer dynamics of mesoscopic molecular aggregates,
elucidating the transition from fully coherent to incoherent transfer
On the driven Frenkel-Kontorova model: II. Chaotic sliding and nonequilibrium melting and freezing
The dynamical behavior of a weakly damped harmonic chain in a spatially
periodic potential (Frenkel-Kontorova model) under the subject of an external
force is investigated. We show that the chain can be in a spatio-temporally
chaotic state called fluid-sliding state. This is proven by calculating
correlation functions and Lyapunov spectra. An effective temperature is
attributed to the fluid-sliding state. Even though the velocity fluctuations
are Gaussian distributed, the fluid-sliding state is clearly not in equilibrium
because the equipartition theorem is violated. We also study the transition
between frozen states (stationary solutions) and=7F molten states
(fluid-sliding states). The transition is similar to a first-order phase
transition, and it shows hysteresis. The depinning-pinning transition
(freezing) is a nucleation process. The frozen state contains usually two
domains of different particle densities. The pinning-depinning transition
(melting) is caused by saddle-node bifurcations of the stationary states. It
depends on the history. Melting is accompanied by precursors, called
micro-slips, which reconfigurate the chain locally. Even though we investigate
the dynamics at zero temperature, the behavior of the Frenkel-Kontorova model
is qualitatively similar to the behavior of similar models at nonzero
temperature.Comment: Written in RevTeX, 13 figures in PostScript, appears in PR
Comparison of Stochastic Methods for the Variability Assessment of Technology Parameters
This paper provides and compares two alternative solutions for the simulation of cables and interconnects with the inclusion of the effects of parameter uncertainties, namely the Polynomial Chaos (PC) method and the Response Surface Modeling (RSM). The problem formulation applies to the telegraphers equations with stochastic coefficients. According to PC, the solution requires an expansion of the unknown parameters in terms of orthogonal polynomials of random variables. On the contrary, RSM is based on a least-square polynomial fitting of the system response. The proposed methods offer accuracy and improved efficiency in computing the parameter variability effects on system responses with respect to the conventional Monte Carlo approach. These approaches are validated by means of the application to the stochastic analysis of a commercial multiconductor flat cable. This analysis allows us to highlight the respective advantages and disadvantages of the presented method
Non-Markovian stochastic Schr\"odinger equations: Generalization to real-valued noise using quantum measurement theory
Do stochastic Schr\"odinger equations, also known as unravelings, have a
physical interpretation? In the Markovian limit, where the system {\em on
average} obeys a master equation, the answer is yes. Markovian stochastic
Schr\"odinger equations generate quantum trajectories for the system state
conditioned on continuously monitoring the bath. For a given master equation,
there are many different unravelings, corresponding to different sorts of
measurement on the bath. In this paper we address the non-Markovian case, and
in particular the sort of stochastic \sch equation introduced by Strunz, Di\'
osi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum measurement
theory approach, we rederive their unraveling which involves complex-valued
Gaussian noise. We also derive an unraveling involving real-valued Gaussian
noise. We show that in the Markovian limit, these two unravelings correspond to
heterodyne and homodyne detection respectively. Although we use quantum
measurement theory to define these unravelings, we conclude that the stochastic
evolution of the system state is not a true quantum trajectory, as the identity
of the state through time is a fiction.Comment: 17 pages, 3 figure
Viscoelastic Depinning of Driven Systems: Mean-Field Plastic Scallops
We have investigated the mean field dynamics of an overdamped viscoelastic
medium driven through quenched disorder. The model introduced incorporates
coexistence of pinned and sliding degrees of freedom and can exhibit continuous
elastic depinning or first order hysteretic depinning. Numerical simulations
indicate mean field instabilities that correspond to macroscopic stick-slip
events and lead to premature switching. The model is relevant for the dynamics
of driven vortex arrays in superconductors and other extended disordered
systems.Comment: 4 pages, 2 figure
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