Fausto Borgonovi

Quantum chaos and thermalization in isolated systems of interacting particles

This review is devoted to the problem of thermalization in a small isolated conglomerate of interacting constituents. A variety of physically important systems of intensive current interest belong to this category: complex atoms, molecules (including biological molecules), nuclei, small devices of condensed matter and quantum optics on nano- and micro-scale, cold atoms in optical lattices, ion traps. Physical implementations of quantum computers, where there are many interacting qubits, also fall into this group. Statistical regularities come into play through inter-particle interactions, which have two fundamental components: mean field, that along with external conditions, forms the regular component of the dynamics, and residual interactions responsible for the complex structure of the actual stationary states. At sufficiently high level density, the stationary states become exceedingly complicated superpositions of simple quasiparticle excitations. At this stage, regularities typical of quantum chaos emerge and bring in signatures of thermalization. We describe all the stages and the results of the processes leading to thermalization, using analytical and massive numerical examples for realistic atomic, nuclear, and spin systems, as well as for models with random parameters. The structure of stationary states, strength functions of simple configurations, and concepts of entropy and temperature in application to isolated mesoscopic systems are discussed in detail. We conclude with a schematic discussion of the time evolution of such systems to equilibrium.

Diffusion and Localization in Chaotic Billiards

We study analytically and numerically the classical diffusive process which takes place in a chaotic billiard. This allows to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described by Random Matrix Theory. In particular the phenomenon of quantum dynamical localization should be observable in real experiments.

Onset of chaos and relaxation in isolated systems of interacting spins: Energy shell approach

We study the onset of chaos and statistical relaxation in two isolated dynamical quantum systems of interacting spins 1/2, one of which is integrable and the other chaotic. Our approach to identifying the emergence of chaos is based on the level of delocalization of the eigenstates with respect to the energy shell, the latter being determined by the interaction strength between particles or quasiparticles. We also discuss how the onset of chaos may be anticipated by a careful analysis of the Hamiltonian matrices, even before diagonalization. We find that despite differences between the two models, their relaxation processes following a quench are very similar and can be described analytically with a theory previously developed for systems with two-body random interactions. Our results imply that global features of statistical relaxation depend on the degree of spread of the eigenstates within the energy shell and may happen to both integrable and nonintegrable systems.

Superradiance Transition in Photosynthetic Light-Harvesting Complexes

We investigate the role of long-lasting quantum coherence in the efficiency of energy transport at room temperature in Fenna-Matthews-Olson photosynthetic complexes. The excitation energy transfer due to coupling of the light-harvesting complex to the reaction center (“sink”) is analyzed using an effective non-Hermitian Hamiltonian. We show that, as the coupling to the reaction center is varied, maximal efficiency in energy transport is achieved in the vicinity of the superradiance transition, characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. Our results demonstrate that the presence of the sink (which provides a quasi-continuum in the energy spectrum) is the dominant effect in the energy transfer which takes place even in the absence of a thermal bath. This approach allows one to study the effects of finite temperature and the effects of any coupling scheme to the reaction center. Moreover, taking into account a realistic electric dipole ...

Magnetic resonance force microscopy and a single-spin measurement

Spin Dynamics -- Quasiclassical Description Spin Dynamics -- Quantum Description Mechanical Vibrations of the Cantilever Single-Spin Detection in Magnetic Force Microscopy (MFM) Transient Process in MFM -- The Exact Solution of the Master Equation Periodic Spin Reversals in Magnetic Resonance Force Microscopy (MRFM) Driven by -Pulses Oscillating Adiabatic Spin Reversals Driven by the Frequency Modulated rf Field Oscillating Cantilever-Driven Adiabatic Reversals (OSCAR) Technique in MRFM CT-Spin Dynamics in the OSCAR Technique Magnetic Noise and Spin Relaxation in OSCAR MRFM MRFM Applications: Measurement of an Entangled Spin State and Quantum Computation MRFM Techniques and Spin Diffusion.

CHAOS AND THERMALIZATION IN A DYNAMICAL MODEL OF TWO INTERACTING PARTICLES

A quantum dynamical model of two interacting spins, with chaotic and regular components, is investigated using a finite two-particles symmetrized basis. Chaotic eigenstates give rise to an equilibrium occupation number distribution in close agreement with the Bose-Einstein distribution despite the small number of particles (

Avoiding quantum chaos in quantum computation.

n=2

Cooperative robustness to static disorder: Superradiance and localization in a nanoscale ring to model light-harvesting systems found in nature

). However, the corresponding temperature differs from that derived from the standard Canonical Ensemble. On the other side, an acceptable agreement with the latter is restored by artificially randomizing the model. Different definitions of temperature are then discussed and compared .Abstract The thermal properties of a quantum dynamical model of two interacting spins, with chaotic and regular components, are investigated using a finite two-particles symmetrized basis. Chaotic eigenstates give rise to an equilibrium occupation number distribution in close agreement with the Bose-Einstein distribution despite the small number of particles ( n = 2). However, the corresponding temperature differs from that derived from the standard canonical ensemble. On the other side, an acceptable agreement with the latter is restored by artificially randomizing the model. Different definitions of temperature are then discussed and compared.

Focusing in multiwell potentials: Applications to ion channels

We study a one-dimensional chain of nuclear

Delocalization border and onset of chaos in a model of quantum computation

1/2-