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Wojciech De Roeck

Publications and source records attributed to Wojciech De Roeck.

65 records · Page 4Linked to original sources
arXiv2011

Diffusive behavior from a quantum master equation

We study a general class of translation invariant quantum Markov evolutions for a particle on $\bbZ^d$. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and exponentially fast relaxation of the momentum distribution. It is shown that the particle position diffuses in the long time limit. This generalizes standard results about central limit theorems for classical (non-quantum) Markov processes.

math-ph↗
arXiv2007

Fluctuations of Quantum Currents and Unravelings of Master Equations

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system.

cond-mat.stat-mech↗
arXiv2007

Large deviation generating function for energy transport in the Pauli-Fierz model

We consider a finite quantum system coupled to quasifree thermal reservoirs at different temperatures. Under the assumptions of small coupling and exponential decay of the reservoir correlation function, the large deviation generating function of energy transport into the reservoirs is shown to be analytic on a bounded set. Our method is different from the spectral deformation technique which was employed recently in the study of spin-boson-like models. As a corollary, we derive the Gallavotti-Cohen fluctuation relation for the entropy production and a central limit theorem for energy transport.

math-ph↗
arXiv2007

Extended Weak Coupling Limit for Pauli-Fierz Operators

We consider the weak coupling limit for a quantum system consisting of a small subsystem and reservoirs. It is known rigorously since [Dav74] that the Heisenberg evolution restricted to the small system converges in an appropriate sense to a Markovian semigroup. In the nineties, Accardi, Frigerio and Lu [AFL90] initiated an investigation of the convergence of the unreduced unitary evolution to a singular unitary evolution generated by a quantum Langevin equation. We present a version of this convergence which is both simpler and stronger than the formulations which we know. Our main result says that in an appropriately understood weak coupling limit the interaction of the small system with environment can be expressed in terms of the so-called quantum white noise.

math-ph↗
arXiv2007

Symmetries of the ratchet current

Recent advances in nonequilibrium statistical mechanics shed new light on the ratchet effect. The ratchet motion can thus be understood in terms of symmetry (breaking) considerations. We introduce an additional symmetry operation besides time-reversal, that effectively reverses the nonequilibrium driving. That operation of field-reversal combined with time-reversal decomposes the nonequilibrium action so to clarify under what circumstances the ratchet current is a second order effect around equilibrium, what is the direction of the ratchet current and what are possibly the symmetries in its fluctuations.

cond-mat.stat-mech↗
arXiv2007

Quantum fluctuation theorem: Can we go from micro to meso?

Quantum extensions of the Gallavotti-Cohen fluctuation theorem (FT) for the entropy production have been discussed by several authors. There is a practical gap between microscopic forms of FT and mesoscopic (i.e. not purely Hamiltonian) forms for open systems. In a microscopic setup, it is easy to state and to prove FT. In a mesoscopic setup, it is difficult to identify fluctuations of the entropy production. (This difficulty is absent in the classical case.) We discuss a particular mesoscopic model: a Lindblad master equation, in which we state FT and, more importantly, connect it rigorously with the underlying microscopic FT. We also remark that FT is satisfied by the Lesovik-Levitov formula for statistics of charge transport.

cond-mat.stat-mech↗
arXiv2006

Extended Weak Coupling Limit for Friedrichs Hamiltonians

We study a class of self-adjoint operators defined on the direct sum of two Hilbert spaces: a finite dimensional one called sometimes a ``small subsystem'' and an infinite dimensional one -- a ``reservoir''. The operator, which we call a ``Friedrichs Hamiltonian'', has a small coupling constant in front of its off-diagonal term. It is well known that under some conditions in the weak coupling limit the appropriately rescaled evolution in the interaction picture converges to a contractive semigroup when restricted to the subsystem. We show that in this model, the properly renormalized and rescaled evolution converges on the whole space to a new unitary evolution, which is a dilation of the above mentioned semigroup. Similar results have been studied before \cite{AFL} in more complicated models and they are usually referred to as "stochastic Limit".

math-ph↗
arXiv2006

Steady state fluctuations of the dissipated heat for a quantum stochastic model

We introduce a quantum stochastic dynamics for heat conduction. A multi-level subsystem is coupled to reservoirs at different temperatures. Energy quanta are detected in the reservoirs allowing the study of steady state fluctuations of the entropy dissipation. Our main result states a symmetry in its large deviation rate function.

cond-mat.stat-mech↗
arXiv2003

A quantum version of free energy - irreversible work relations

We give a quantum version of the Jarzynski relation between the distribution of work done over a certain time-interval on a system and the difference of equilibrium free energies. The main new ingredient is the identification of work depending on the quantum history of the system and the proper definition of various quantum ensembles over which the averages should be made. We also discuss a number of different regimes that have been considered by other authors and which are unified in the present set-up. In all cases, and quantum or classical, it is a general relation between heat and time-reversal that makes the Jarzynski relation so universally valid.

cond-mat↗
arXiv2002

Photon fields in a fluctuating spacetime

We present a model of interacting quantum fields, formulated in a non-perturbative manner. One of the fields is treated semi-classically, the other is the photon field. The model has an interpretation of an electromagnetic field in a fluctuating spacetime. The model is equivalent with the quantization of electromagnetism proposed recently by Czachor. Interesting features are that standard photon theory is recovered as a limiting case, and that localized field operators for the electromagnetic field exist as unbounded operators in Hilbert space.

hep-th↗