Quantum anti-Zeno effect in artificial quantum systems

In this paper, we study a quantum anti-Zeno effect (QAZE) purely induced by repetitive measurements for an artificial atom interacting with a structured bath. This bath can be artificially realized with coupled resonators in one dimension and possesses photonic band structure like Bloch electron in a periodic potential. In the presence of repetitive measurements, the pure QAZE is discovered as the observable decay is not negligible even for the atomic energy level spacing outside of the energy band of the artificial bath. If there were no measurements, the decay would not happen outside of the band. In this sense, the enhanced decay is completely induced by measurements through the relaxation channels provided by the bath. Besides, we also discuss the controversial golden rule decay rates originated from the van Hove's singularities and the effects of the counter-rotating terms.Comment: 12 pages, 8 figure

Numerical properties of isotrivial fibrations

In this paper we investigate the numerical properties of relatively minimal isotrivial fibrations \varphi \colon X \lr C, where $X$ is a smooth, projective surface and $C$ is a curve. In particular we prove that, if $g(C) \geq 1$ and $X$ is neither ruled nor isomorphic to a quasi-bundle, then K_X^2 \leq 8 \chi(\mO_X)-2; this inequality is sharp and if equality holds then $X$ is a minimal surface of general type whose canonical model has precisely two ordinary double points as singularities. Under the further assumption that $K_X$ is ample, we obtain K_X^2 \leq 8 \chi(\mO_X)-5 and the inequality is also sharp. This improves previous results of Serrano and Tan.Comment: 30 pages. Final version, to appear in Geometriae Dedicat

Quantum Fluctuation Relations for the Lindblad Master Equation

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula

From thermal rectifiers to thermoelectric devices

We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.Comment: 42 pages, 22 figures, review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Open Quantum Random Walks

International audienceA new model of quantum random walks is introduced, on lattices as well as on nite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogue of classical Markov chains. We explore the \quantum trajectory" point of view on these quantum random walks, that is, we show that measuring the position of the particle after each time-step gives rise to a classical Markov chain, on the lattice times the state space of the particle. This quantum trajectory is a simulation of the master equation of the quantum random walk. The physical pertinence of such quantum random walks and the way they can be concretely realized is discussed. Connections and di erences with the already well-known quantum random walks, such as the Hadamard random walk, are established. We explore several examples and compute their limit behavior. We show that the typical behavior of Open Quantum Random Walks seems to be very di erent from Hadamard-type quantum random walks. Indeed, while being very quantum in their behavior, Open Quantum Random Walks tend to become more and more classical as time goes