Giulio Casati

Relevance of classical chaos in quantum mechanics: The hydrogen atom in a monochromatic field

Abstract We present analytical and numerical results on the mechanism of excitation and ionization of hydrogen atoms under microwave fields. In particular we predict the existence of a critical value of the microwave field, the quantum delocalization border , above which the quantum packet delocalizes and strong excitation and ionization takes place. Below the quantum border, the packet is localized even though the corresponding classical system can be chaotic and obeys a diffusion equation. Our studies reveal some other unexpected new features of quantum dynamics which also could be observed in laboratory experiments and provides a quantum theory for subthreshold ionization.

Thermodynamic bounds on efficiency for systems with broken time-reversal symmetry.

We show that for systems with broken time-reversal symmetry the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a figure of merit and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the so-called strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, always within linear response, it is allowed to have Carnot efficiency and nonzero power simultaneously .

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

In recent years, the study of heat to work conversion has been re-invigorated by nanotechnology. Steady-state devices do this conversion without any macroscopic moving parts, through steady-state flows of microscopic particles such as electrons, photons, phonons, etc. This review aims to introduce some of the theories used to describe these steady-state flows in a variety of mesoscopic or nanoscale systems. These theories are introduced in the context of idealized machines which convert heat into electrical power (heat-engines) or convert electrical power into a heat flow (refrigerators). In this sense, the machines could be categorized as thermoelectrics, although this should be understood to include photovoltaics when the heat source is the sun. As quantum mechanics is important for most such machines, they fall into the field of quantum thermodynamics. In many cases, the machines we consider have few degrees of freedom, however the reservoirs of heat and work that they interact with are assumed to be macroscopic. This review discusses different theories which can take into account different aspects of mesoscopic and nanoscale physics, such as coherent quantum transport, magnetic-field induced effects (including topological ones such as the quantum Hall effect), and single electron charging effects. It discusses the efficiency of thermoelectric conversion, and the thermoelectric figure of merit. More specifically, the theories presented are (i) linear response theory with or without magnetic fields, (ii) Landauer scattering theory in the linear response regime and far from equilibrium, (iii) Green-Kubo formula for strongly interacting systems within the linear response regime, (iv) rate equation analysis for small quantum machines with or without ..... (SEE THE PDF FOR THE REST OF THIS ABSTRACT)

Thermalization and ergodicity in one-dimensional many-body open quantum systems

Using an approach based on the time-dependent density-matrix renormalization-group method, we study the thermalization in spin chains locally coupled to an external bath. Our results provide evidence that quantum chaotic systems do thermalize, that is, they exhibit relaxation to an invariant ergodic state which, in the bulk, is well approximated by the grand canonical state. Moreover, the resulting ergodic state in the bulk does not depend on the details of the baths. On the other hand, for integrable systems we found that the invariant state in general depends on the bath and is different from the grand canonical state.

One-Dimensional Self-Organization and Nonequilibrium Phase Transition in a Hamiltonian System

Self-organization and nonequilibrium phase transitions are well known to occur in two- and three-dimensional dissipative systems. Here, instead, we provide numerical evidence that these phenomena also occur in a one-dimensional Hamiltonian system. To this end, we calculate the heat conductivity by coupling the two ends of our system to two heat baths at different temperatures. It is found that when the temperature difference is smaller than a critical value, the heat conductivity increases with the system size in power law with an exponent considerably smaller than 1. However, as the temperature difference exceeds the critical value, the systems behavior undergoes a transition and the heat conductivity tends to diverge linearly with the system size. Correspondingly, an ordered structure emerges. These findings suggest a new direction for exploring the transport problems in one dimension.

Violation of Bell inequalities in larger Hilbert spaces: robustness and challenges

We explore the challenges posed by the violation of Bell-like inequalities by

From Thermal Rectifiers to Thermoelectric Devices

d

Quantum limitations of chaos and subthreshold ionization in hydrogen atom

-dimensional systems exposed to imperfect state-preparation and measurement settings. We address, in particular, the limit of high-dimensional systems, naturally arising when exploring the quantum-to-classical transition. We show that, although suitable Bell inequalities can be violated, in principle, for any dimension of given subsystems, it is in practice increasingly challenging to detect such violations, even if the system is prepared in a maximally entangled state. We characterize the effects of random perturbations on the state or on the measurement settings, also quantifying the efforts needed to certify the possible violations in case of complete ignorance on the system state at hand.

Principles of Quantum Computation And Information: Basic Tools And Special Topics

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.

Asymptotic decay of the classical Loschmidt echo in chaotic systems

The problem, whether any such effects survive also in Quantum Mechanics is an important one, expecially in connection with studies on microwave ionization of Rydberg atoms. Previous works [1-8] have shown, that strong ionization and excitation can take place even for frequencies well below the one photon ionization threshold. There are strong indications that this quantum phenomenon is connected with the appearance of chaotic motion in the corresponding classical system; indeed, in the classical model of a Hydrogen atom under an external periodic field, a stochastic transition takes place, leading to unlimited diffusion in phase space and eventually to ionization [2,3].