5,827 research outputs found
Quantum quench dynamics of the Bose-Hubbard model at finite temperatures
We study quench dynamics of the Bose-Hubbard model by exact diagonalization.
Initially the system is at thermal equilibrium and of a finite temperature. The
system is then quenched by changing the on-site interaction strength
suddenly. Both the single-quench and double-quench scenarios are considered. In
the former case, the time-averaged density matrix and the real-time evolution
are investigated. It is found that though the system thermalizes only in a very
narrow range of the quenched value of , it does equilibrate or relax well in
a much larger range. Most importantly, it is proven that this is guaranteed for
some typical observables in the thermodynamic limit. In order to test whether
it is possible to distinguish the unitarily evolving density matrix from the
time-averaged (thus time-independent), fully decoherenced density matrix, a
second quench is considered. It turns out that the answer is affirmative or
negative according to the intermediate value of is zero or not.Comment: preprint, 20 pages, 7 figure
The delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation
It has been alleged in several papers that the so called delayed
continuous-time random walks (DCTRWs) provide a model for the one-dimensional
telegraph equation at microscopic level. This conclusion, being widespread now,
is strange, since the telegraph equation describes phenomena with finite
propagation speed, while the velocity of the motion of particles in the DCTRWs
is infinite. In this paper we investigate how accurate are the approximations
to the DCTRWs provided by the telegraph equation. We show that the diffusion
equation, being the correct limit of the DCTRWs, gives better approximations in
norm to the DCTRWs than the telegraph equation. We conclude therefore
that, first, the DCTRWs do not provide any correct microscopic interpretation
of the one-dimensional telegraph equation, and second, the kinetic (exact)
model of the telegraph equation is different from the model based on the
DCTRWs.Comment: 12 pages, 9 figure
On possible violation of the CHSH Bell inequality in a classical context
It has been shown that there is a small possibility to experimentally violate
the CHSH Bell inequality in a 'classical' context. The probability of such a
violation has been estimated in the framework of a classical probabilistic
model in the language of a random-walk representation.Comment: 9 pages, 1 figur
Entwicklung eines Prognosemodells für den N-Düngebedarf im ökologischen Gemüsebau
Several field grown vegetables are known to have a short vegetation period coupled with a high nitrogen demand. The proposed amendment of the German fertilization ordinance provides several changes. Thus in future organic vegetable farmers have to adapt their fertilization to reduce nitrogen surplus but still produce vegetables with good quality. The aim of our work was to predict the nitrogen supply in organic vegetable production with a simple model. This should allow organic farmers to reduce the nitrogen surplus and facilitate them to meet the regulation of the new fertilization ordinance. Therefore the parameters to predict the maximal nitrogen supply in organic fertilizers and their mineralization constants were estimated by single kinetic functions. We now have the possibility to predict the nitrogen mineralization or immobilization dependent on fertilizer quality. Finally, the calculated parameters are implemented in the N-Expert software and give organic vegetable farmers the possibility to predict the nitrogen demand in their production systems
Analytical Solution to Transport in Brownian Ratchets via Gambler's Ruin Model
We present an analogy between the classic Gambler's Ruin problem and the
thermally-activated dynamics in periodic Brownian ratchets. By considering each
periodic unit of the ratchet as a site chain, we calculated the transition
probabilities and mean first passage time for transitions between energy minima
of adjacent units. We consider the specific case of Brownian ratchets driven by
Markov dichotomous noise. The explicit solution for the current is derived for
any arbitrary temperature, and is verified numerically by Langevin simulations.
The conditions for vanishing current and current reversal in the ratchet are
obtained and discussed.Comment: 4 pages, 3 figure
Spatiotemporally Complete Condensation in a Non-Poissonian Exclusion Process
We investigate a non-Poissonian version of the asymmetric simple exclusion
process, motivated by the observation that coarse-graining the interactions
between particles in complex systems generically leads to a stochastic process
with a non-Markovian (history-dependent) character. We characterize a large
family of one-dimensional hopping processes using a waiting-time distribution
for individual particle hops. We find that when its variance is infinite, a
real-space condensate forms that is complete in space (involves all particles)
and time (exists at almost any given instant) in the thermodynamic limit. The
mechanism for the onset and stability of the condensate are both rather subtle,
and depends on the microscopic dynamics subsequent to a failed particle hop
attempts.Comment: 5 pages, 5 figures. Version 2 to appear in PR
Small violations of full correlation Bell inequalities for multipartite pure random states
We estimate the probability of random -qudit pure states violating
full-correlation Bell inequalities with two dichotomic observables per site.
These inequalities can show violations that grow exponentially with , but we
prove this is not the typical case. For many-qubit states the probability to
violate any of these inequalities by an amount that grows linearly with is
vanishingly small. If each system's Hilbert space dimension is larger than two,
on the other hand, the probability of seeing \emph{any} violation is already
small. For the qubits case we discuss furthermore the consequences of this
result for the probability of seeing arbitrary violations (\emph i.e., of any
order of magnitude) when experimental imperfections are considered.Comment: 16 pages, one colum
Transport in a Levy ratchet: Group velocity and distribution spread
We consider the motion of an overdamped particle in a periodic potential
lacking spatial symmetry under the influence of symmetric L\'evy noise, being a
minimal setup for a ``L\'evy ratchet.'' Due to the non-thermal character of the
L\'evy noise, the particle exhibits a motion with a preferred direction even in
the absence of whatever additional time-dependent forces. The examination of
the L\'evy ratchet has to be based on the characteristics of directionality
which are different from typically used measures like mean current and the
dispersion of particles' positions, since these get inappropriate when the
moments of the noise diverge. To overcome this problem, we discuss robust
measures of directionality of transport like the position of the median of the
particles displacements' distribution characterizing the group velocity, and
the interquantile distance giving the measure of the distributions' width.
Moreover, we analyze the behavior of splitting probabilities for leaving an
interval of a given length unveiling qualitative differences between the noises
with L\'evy indices below and above unity. Finally, we inspect the problem of
the first escape from an interval of given length revealing independence of
exit times on the structure of the potential.Comment: 9 pages, 12 figure
Model for Folding and Aggregation in RNA Secondary Structures
We study the statistical mechanics of RNA secondary structures designed to
have an attraction between two different types of structures as a model system
for heteropolymer aggregation. The competition between the branching entropy of
the secondary structure and the energy gained by pairing drives the RNA to
undergo a `temperature independent' second order phase transition from a molten
to an aggregated phase'. The aggregated phase thus obtained has a
macroscopically large number of contacts between different RNAs. The partition
function scaling exponent for this phase is \theta ~ 1/2 and the crossover
exponent of the phase transition is \nu ~ 5/3. The relevance of these
calculations to the aggregation of biological molecules is discussed.Comment: Revtex, 4 pages; 3 Figures; Final published versio
Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation
It is shown that the energy of a mode of a classical chaotic field, following
the continuous exponential distribution as a classical random variable, can be
uniquely decomposed into a sum of its fractional part and of its integer part.
The integer part is a discrete random variable (we call it Planck variable)
whose distribution is just the Bose distribution yielding the Planck law of
black-body radiation. The fractional part is the dark part (we call is dark
variable) with a continuous distribution, which is, of course, not observed in
the experiments. It is proved that the Bose distribution is infinitely
divisible, and the irreducible decomposition of it is given. The Planck
variable can be decomposed into an infinite sum of independent binary random
variables representing the binary photons (more accurately photo-molecules or
photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons
follow the Fermi statistics. Consequently, the black-body radiation can be
viewed as a mixture of statistically and thermodynamically independent fermion
gases consisting of binary photons. The binary photons give a natural tool for
the dyadic expansion of arbitrary (but not coherent) ordinary photon
excitations. It is shown that the binary photons have wave-particle
fluctuations of fermions. These fluctuations combine to give the wave-particle
fluctuations of the original bosonic photons expressed by the Einstein
fluctuation formula.Comment: 29 page
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