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 $U$ 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 $U$, 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 $U$ 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 $L_2$ 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

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

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

Comparison of solar photospheric bright points between SUNRISE observations and MHD simulations

Bright points (BPs) in the solar photosphere are radiative signatures of magnetic elements described by slender flux tubes located in the darker intergranular lanes. They contribute to the ultraviolet (UV) flux variations over the solar cycle and hence may influence the Earth's climate. Here we combine high-resolution UV and spectro-polarimetric observations of BPs by the SUNRISE observatory with 3D radiation MHD simulations. Full spectral line syntheses are performed with the MHD data and a careful degradation is applied to take into account all relevant instrumental effects of the observations. It is demonstrated that the MHD simulations reproduce the measured distributions of intensity at multiple wavelengths, line-of-sight velocity, spectral line width, and polarization degree rather well. Furthermore, the properties of observed BPs are compared with synthetic ones. These match also relatively well, except that the observations display a tail of large and strongly polarized BPs not found in the simulations. The higher spatial resolution of the simulations has a significant effect, leading to smaller and more numerous BPs. The observation that most BPs are weakly polarized is explained mainly by the spatial degradation, the stray light contamination, and the temperature sensitivity of the Fe I line at 5250.2 \AA{}. The Stokes $V$ asymmetries of the BPs increase with the distance to their center in both observations and simulations, consistent with the classical picture of a production of the asymmetry in the canopy. This is the first time that this has been found also in the internetwork. Almost vertical kilo-Gauss fields are found for 98 % of the synthetic BPs. At the continuum formation height, the simulated BPs are on average 190 K hotter than the mean quiet Sun, their mean BP field strength is 1750 G, supporting the flux-tube paradigm to describe BPs.Comment: Accepted for publication in Astronomy & Astrophysics on May 30 201

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

Work probability distribution and tossing a biased coin

We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modelling other physical phenomena where rare events play an important role.Comment: 6 pages, 4 figures