Latest Papers in Condensed Matter Physics
Statistical Mechanics
Izaak Neri, Edgar Roldán, Simone Pigolotti, Frank Jülicher
2019-03-19
A stopping time 
is the first time when a trajectory of a stochastic process satisfies a certain criterion, which does not anticipate future events. In this paper, we derive using martingale theory the integral fluctuation relation 
for the stochastic entropy production 
at stopping times of a non-equilibrium steady-state physical system. This fluctuation relation implies a law of thermodynamics at stopping times, which is similar to the second law and states that it is not possible to reduce entropy on average, even when stopping a stochastic process at a cleverly chosen moment. Applying the integral fluctuation relation to different examples of stopping times we derive universal equalities and inequalities for the fluctuations of entropy production. For example, we bound the probability of entropy decreases by deriving bounds on the statistics of negative records of entropy production and we derive generic bounds for splitting probabilities of entropy production. For continuous processes we derive equalities for fluctuation properties of entropy production, such as, splitting probabilities and the statistics of negative records of entropy production. The integral fluctuation relation at stopping times can serve as a proxy for the exponential martingale structure of the stochastic entropy production, and we solve the problem of finite statistics for the integral fluctuation relation at stopping times, which is relevant for empirical tests of this relation.
Catalin Pascu Moca, Márton Kormos, Gergely Zaránd
2016-09-04
We develop a hybrid semiclassical method to study the time evolution of one dimensional quantum systems in and out of equilibrium. Our method handles internal degrees of freedom completely quantum mechanically by a modified time evolving block decimation method, while treating orbital quasiparticle motion classically. We can follow dynamics up to timescales well beyond the reach of standard numerical methods to observe the crossover between pre-equilibrated and locally phase equilibrated states. As an application, we investigate the quench dynamics and phase fluctuations of a pair of tunnel coupled one dimensional Bose condensates. We demonstrate the emergence of soliton-collision induced phase propagation, soliton-entropy production and multistep thermalization. Our method can be applied to a wide range of gapped one-dimensional systems.
Konrad Jerzy Kapcia, Romuald Lemański, Stanisław Robaszkiewicz
2019-03-19
The extended Falicov-Kimball model (EFKM) is analyzed exactly for finite temperatures in the limit of large dimensions. The onsite, as well as the intersite density-density interactions represented by the coupling constants 
and 
, respectively, are included in the model. Using the dynamic mean field theory (DMFT) formalism on the Bethe lattice we find rigorously the temperature dependent density of states (DOS) at half-filling. At zero temperature (
) the system is ordered to form the checkerboard pattern and the DOS has the gap 
at the Fermi level, if only 
or 
. With an increase of the DOS evolves in various ways that depend both on and . If 
or 
, two additional subbands develop inside the principal energy gap. They become wider with increasing and at a certain - and -dependent temperature 
they join with each other at 
. Since above the DOS is positive at , we interpret as the transformation temperature from insulator to metal. Having calculated the temperature dependent DOS we study thermodynamic properties of the system starting from its free energy 
and then we construct the phase diagrams in the variables and for a few values of . Our calculations give that inclusion of the intersite coupling causes the finite temperature phase diagrams become asymmetric with respect to a change of sign of . On these phase diagrams we detected stability regions of eight different kinds of ordered phases (five of them are insulating and three are conducting) and three different nonordered phases (two of them are insulating and one is conducting). Moreover, both continuous and discontinuous transitions between various phases were found.
Michael Vogl, Pontus Laurell, Aaron D. Barr, Gregory A. Fiete
2018-08-05
We present a theoretical method to generate a highly accurate {\em time-independent} Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization group-like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequency regimes that are usually inaccessible via high frequency 
expansions in the parameter 
, where 
is the upper limit for the strength of local interactions. We demonstrate our approach on both interacting and non-interacting many-body Hamiltonians where it offers an improvement over the more well-known Magnus expansion and other high frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel non-equilibrium regimes and behaviors in driven quantum many-particle systems.
Rui Zhang, Bin Wei, Dong Zhang, Jia-Ji Zhu, Kai Chang
2019-03-19
We investigate theoretically the phase transition in three dimensional cubic Ising model utilizing state-of-the-art machine learning algorithms. Supervised machine learning models show high accuracies (~99%) in phase classification and very small relative errors (
) of the energies in different spin configurations. Unsupervised machine learning models are introduced to study the spin configuration reconstructions and reductions, and the phases of reconstructed spin configurations can be accurately classified by a linear logistic algorithm. Based on the comparison between various machine learning models, we develop a few-shot strategy to predict phase transitions in larger lattices from trained sample in smaller lattices. The few-shot machine learning strategy for three dimensional(3D) Ising model enable us to study 3D ising model efficiently and provides a new integrated and highly accurate approach to other spin models.
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