27 research outputs found
Part III, Free Actions of Compact Quantum Groups on C*-Algebras
We study and classify free actions of compact quantum groups on unital
C*-algebras in terms of generalized factor systems. Moreover, we use these
factor systems to show that all finite coverings of irrational rotation
C*-algebras are cleft
On the efficiency of heat engines at the micro-scale and below
We investigate the thermodynamic efficiency of sub-micro-scale heat engines
operating under the conditions described by over-damped stochastic
thermodynamics. We prove that at maximum power the efficiency obeys for
constant isotropic mobility the universal law
where is the efficiency of an ideal Carnot cycle. The corresponding
power optimizing protocol is specified by the solution of an optimal mass
transport problem. Such solution can be determined explicitly using well known
Monge--Amp\`ere--Kantorovich reconstruction algorithms. Furthermore, we show
that the same law describes the efficiency of heat engines operating at maximum
work over short time periods. Finally, we illustrate the straightforward
extension of these results to cases when the mobility is anisotropic and
temperature dependent.Comment: 5 pages; revised version including the derivation of the efficiency
and of the corresponding optimal protocols in the presence of anisotropic
temperature dependent mobilit
An Application of Pontryagin’s Principle to Brownian Particle Engineered Equilibration
We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the optimal control equations steering in finite-time the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that it occurs at minimum entropy if the set of admissible controls is restricted by certain bounds on the time derivatives of the protocols. We apply our equations to the engineered equilibration of an optical trap considered in a recent proof of principle experiment. We also analyze an elementary model of nucleation previously considered by Landauer to discuss the thermodynamic cost of one bit of information erasure. We expect our model to be a useful benchmark for experiment design as it exhibits the same integrability properties of well-known models of optimal mass transport by a compressible velocity field
Ergodic Properties of Quantum Birth and Death Chains
We study a class of quantum Markov processes that, on the one hand, is
inspired by the micromaser experiment in quantum optics and, on the other hand,
by classical birth and death processes. We prove some general geometric
properties and irreducibility for non-degenerated parameters. Furthermore, we
analyze ergodic properties of the corresponding transition operators. For
homogeneous birth and death rates we show how these can be fully determined by
explicit calculation. As for classical birth and death chains we obtain a rich
yet simple class of quantum Markov chains on an infinite space, which allow
only local transitions while having divers ergodic properties.Comment: 26 pages, 7 figure
Part II, Free actions of compact groups on C*-algebras
We study a simple class of free actions of non-Abelian groups on unital C* -algebras, namely cleft actions. These are characterized by the fact that the associated noncommutative vector bundles are trivial. In particular, we provide a complete classification theory for these actions and describe its relations to classical principal bundles.Peer reviewe
Part I, Free actions of compact Abelian groups on C*-algebras
We study free actions of compact groups on unital C*-algebras. In particular, we provide a complete classification theory of these actions for compact Abelian groups and explain its relation to the classification of classical principal bundles.Peer reviewe
Model for calorimetric measurements in an open quantum system
We investigate the experimental setup proposed in [New J. Phys., 15, 115006 (2013)] for calorimetric measurements of thermodynamic indicators in an open quantum system. As theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak coupling assumptions, the evolution of the qubit-calorimeter system can be described by a generalized quantum jump process including as dynamical variable the temperature of the calorimeter. We study the jump process by numeric and analytic methods. Asymptotically with the duration of the drive, the qubit-calorimeter attains a steady state. In this same limit, we use multiscale perturbation theory to derive a Fokker--Planck equation governing the calorimeter temperature distribution. We inquire the properties of the temperature probability distribution close and at the steady state. In particular, we predict the behavior of measurable statistical indicators versus the qubit-calorimeter coupling constant.Peer reviewe