1,360 research outputs found
Vlasov Equation In Magnetic Field
The linearized Vlasov equation for a plasma system in a uniform magnetic
field and the corresponding linear Vlasov operator are studied. The spectrum
and the corresponding eigenfunctions of the Vlasov operator are found. The
spectrum of this operator consists of two parts: one is continuous and real;
the other is discrete and complex. Interestingly, the real eigenvalues are
infinitely degenerate, which causes difficulty solving this initial value
problem by using the conventional eigenfunction expansion method. Finally, the
Vlasov equation is solved by the resolvent method.Comment: 15 page
Efficient computation of the first passage time distribution of the generalized master equation by steady-state relaxation
The generalized master equation or the equivalent continuous time random walk
equations can be used to compute the macroscopic first passage time
distribution (FPTD) of a complex stochastic system from short-term microscopic
simulation data. The computation of the mean first passage time and additional
low-order FPTD moments can be simplified by directly relating the FPTD moment
generating function to the moments of the local FPTD matrix. This relationship
can be physically interpreted in terms of steady-state relaxation, an extension
of steady-state flow. Moreover, it is amenable to a statistical error analysis
that can be used to significantly increase computational efficiency. The
efficiency improvement can be extended to the FPTD itself by modelling it using
a Gamma distribution or rational function approximation to its Laplace
transform
Depolarization channels with zero-bandwidth noises
A simple model describing depolarization channels with zero-bandwidth
environment is presented and exactly solved. The environment is modelled by
Lorentzian, telegraphic and Gaussian zero-bandwidth noises. Such channels can
go beyond the standard Markov dynamics and therefore can illustrate the
influence of memory effects of the noisy communication channel on the
transmitted information. To quantify the disturbance of quantum states the
entanglement fidelity between arbitrary input and output states is
investigated.Comment: 15 pages, 3 figure
Statistics of Entropy Production in Linearized Stochastic System
We consider a wide class of linear stochastic problems driven off the
equilibrium by a multiplicative asymmetric force. The force brakes detailed
balance, maintained otherwise, thus producing entropy. The large deviation
function of the entropy production in the system is calculated explicitly. The
general result is illustrated using an example of a polymer immersed in a
gradient flow and subject to thermal fluctuations.Comment: 4 pages, 1 figur
Dynamic disorder in receptor-ligand forced dissociation experiments
Recently experiments showed that some biological noncovalent bonds increase
their lifetimes when they are stretched by an external force, and their
lifetimes will decrease when the force increases further. Several specific
quantitative models have been proposed to explain the intriguing transitions
from the "catch-bond" to the "slip-bond". Different from the previous efforts,
in this work we propose that the dynamic disorder of the force-dependent
dissociation rate can account for the counterintuitive behaviors of the bonds.
A Gaussian stochastic rate model is used to quantitatively describe the
transitions observed recently in the single bond P-selctin glycoprotein ligand
1(PSGL-1)P-selectin force rupture experiment [Marshall, {\it et al.}, (2003)
Nature {\bf 423}, 190-193]. Our model agrees well to the experimental data. We
conclude that the catch bonds could arise from the stronger positive
correlation between the height of the intrinsic energy barrier and the distance
from the bound state to the barrier; classical pathway scenario or {\it a
priori} catch bond assumption is not essential.Comment: 4 pages, 2 figure
Entanglement and Quantum Noise Due to a Thermal Bosonic Field
We analyze the indirect exchange interaction between two two-state systems,
e.g., spins 1/2, subject to a common finite-temperature environment modeled by
bosonic modes. The environmental modes, e.g., phonons or cavity photons, are
also a source of quantum noise. We analyze the coherent vs noise-induced
features of the two-spin dynamics and predict that for low enough temperatures
the induced interaction is coherent over time scales sufficient to create
entanglement. A nonperturbative approach is utilized to obtain an exact
solution for the onset of the induced interaction, whereas for large times, a
Markovian scheme is used. We identify the time scales for which the spins
develop entanglement for various spatial separations. For large enough times,
the initially created entanglement is erased by quantum noise. Estimates for
the interaction and the level of quantum noise for localized impurity electron
spins in Si-Ge type semiconductors are given.Comment: 12 pages, 9 figures; typos correcte
Brownian rectifiers in the presence of temporally asymmetric unbiased forces
The efficiency of energy transduction in a temporally asymmetric rocked
ratchet is studied. Time asymmetry favours current in one direction and
suppresses it in the opposite direction due to which large efficiency ~ 50% is
readily obtained. The spatial asymmetry in the potential together with system
inhomogeneity may help in further enhancing the efficiency. Fine tuning of
system parameters considered leads to multiple current reversals even in the
adiabatic regime
Modelling background charge rearrangements near single-electron transistors as a Poisson process
Background charge rearrangements in metallic single-electron transistors are
modelled in two-level tunnelling systems as a Poisson process with a scale
parameter as only variable. The model explains the recent observation of
asymmetric Coulomb blockade peak spacing distributions in metallic
single-electron transistors. From the scale parameter we estimate the average
size of the tunnelling systems, their density of states, and the height of
their energy barrier. We conclude that the observed background charge
rearrangements predominantly take place in the substrate of the single-electron
transistor.Comment: 7 pages, 2 eps figures, used epl.cls macro include
Generalization of escape rate from a metastable state driven by external cross-correlated noise processes
We propose generalization of escape rate from a metastable state for
externally driven correlated noise processes in one dimension. In addition to
the internal non-Markovian thermal fluctuations, the external correlated noise
processes we consider are Gaussian, stationary in nature and are of
Ornstein-Uhlenbeck type. Based on a Fokker-Planck description of the effective
noise processes with finite memory we derive the generalized escape rate from a
metastable state in the moderate to large damping limit and investigate the
effect of degree of correlation on the resulting rate. Comparison of the
theoretical expression with numerical simulation gives a satisfactory agreement
and shows that by increasing the degree of external noise correlation one can
enhance the escape rate through the dressed effective noise strength.Comment: 9 pages, 1 figur
Completely positive maps with memory
The prevailing description for dissipative quantum dynamics is given by the
Lindblad form of a Markovian master equation, used under the assumption that
memory effects are negligible. However, in certain physical situations, the
master equation is essentially of a non-Markovian nature. This paper examines
master equations that possess a memory kernel, leading to a replacement of
white noise by colored noise. The conditions under which this leads to a
completely positive, trace-preserving map are discussed for an exponential
memory kernel. A physical model that possesses such an exponential memory
kernel is presented. This model contains a classical, fluctuating environment
based on random telegraph signal stochastic variables.Comment: 4 page
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