A Langevin canonical framework for a chiral two--level system coupled to a bath of harmonic oscillators is developed within a coupling scheme different to the well known spin-boson model. Thermal equilibrium values are reached at asymptotic times by solving the corresponding set of non--linear coupled equations in a Markovian regime. In particular, phase difference thermal values (or, equivalently, the so--called coherence factor) and heat capacity through energy fluctuations are obtained and discussed in terms of tunneling rates and asymmetries.
We derive a simple formula for the fluctuations of the time average around the thermal mean for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, et al. in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large non-ergodic fluctuations and show how they are related to a super-aging correlation function.
A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields. An exact hierarchical equations of motion formalism is constructed on the basis of calculus-on-path-integral algorithm, via the auxiliary influence generating functionals related to the interaction bath correlation functions in a parametrization expansion form. The corresponding continued-fraction Greens functions formalism for quantum dissipation is also presented. Proposed further is the principle of residue correction, not just for truncating the infinite hierarchy, but also for incorporating the small residue dissipation that may arise from the practical difference between the true and the parametrized bath correlation functions. The final residue-corrected hierarchical equations of motion can therefore be used practically for the evaluation of arbitrary dissipative quantum systems.
Stochastically switching force terms appear frequently in models of biological systems under the action of active agents such as proteins. The interaction of switching force and Brownian motion can create an effective thermal equilibrium even though the system does not obey a potential function. In order to extend the field of energy landscape analysis to understand stability and transitions in switching systems, we derive the quasipotential that defines this effective equilibrium for a general overdamped Langevin system with a force switching according to a continuous-time Markov chain process. Combined with the string method for computing most-probable transition paths, we apply our method to an idealized system and show the appearance of previously unreported numerical challenges. We present modifications to the algorithms to overcome these challenges, and show validity by demonstrating agreement between our computed quasipotential barrier and asymptotic Monte Carlo transition times in the system.
Heat engines used to output useful work have important practical significance, which, in general, operate between heat baths of infinite size and constant temperature. In this paper we study the efficiency of a heat engine operating between two finite-size heat sources with initial temperature differences. The total output work of such heat engine is limited due to the finite heat capacity of the sources. We investigate the effects of different heat capacity characteristics of the sources on the heat engines efficiency at maximum work (EMW) in the quasi-static limit. In addition, we study the efficiency of the engine working in finite-time with maximum power of each cycle is achieved and find the efficiency follows a simple universality as $eta=eta_{mathrm{C}}/4+Oleft(eta_{mathrm{C}}^{2}right)$. Remarkably, when the heat capacity of the heat source is negative, such as the black holes, we show that the heat engine efficiency during the operation can surpass the Carnot efficiency determined by the initial temperature of the heat sources. It is further argued that the heat engine between two black holes with vanishing initial temperature difference can be driven by the energy fluctuation. The corresponding EMW is proved to be $eta_{mathrm{EMW}}=2-sqrt{2}$, which is two time of the maximum energy release rate $mu=left(2-sqrt{2}right)/2approx0.29$ of two black hole emerging process obtained by S. W. Hawking.
We investigate the principal chiral model between two and four dimensions by means of a non perturbative Wilson-like renormalization group equation. We are thus able to follow the evolution of the effective coupling constants within this whole range of dimensions without having recourse to any kind of small parameter expansion. This allows us to identify its three dimensional critical physics and to solve the long-standing discrepancy between the different perturbative approaches that characterizes the class of models to which the principal chiral model belongs.
H. C. Pe~nate-Rodriguez
,A. Dorta-Urra
,P. Bargue~no
.
(2013)
.
"A Langevin canonical approach to the dynamics of chiral two level systems. Thermal averages and heat capacity"
.
Salvador Miret-Artes
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