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We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…
In this work we present the results of a numerical and semiclassical analysis of high lying states in a Hamiltonian system, whose classical mechanics is of a generic, mixed type, where the energy surface is split into regions of regular and…
In this paper we develop the topics of Quantum Recurrences and of Quantum Fidelity which have attracted great interest in recent years. The return probability is given by the square modulus of the overlap between a given initial wavepacket…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We study properties of moving relativistic quantum unstable systems. We show that in contrast to the properties of classical particles and quantum stable objects the velocity of moving freely relativistic quantum unstable systems can not be…
We show that the mechanism of quantum freeze of fidelity decay for perturbations with zero time-average, recently discovered for a specific case of integrable dynamics [New J. Phys. 5 (2003) 109], can be generalized to arbitrary quantum…
We consider a quantum system of non-interacting fermions at temperature T, in the framework of linear response theory. We show that semiclassical theory is an appropriate framework to describe some of their thermodynamic properties, in…
We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic…
We present a detailed discussion of some features of quantum mechanical metastability. We analyze the nature of decaying (quasistationary) states and the regime of validity of the exponencial law, as well as decays at finite temperature. We…
Building on a model recently proposed by F. Calogero, we postulate the existence of a coherent, long--range universal tremor affecting any stable and confined classical dynamical system. Deriving the characteristic fluctuative unit of…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
We study in detail the time behavior of classical fidelity for chaotic systems. We show in particular that the asymptotic decay, depending on system dynamical properties, can be either exponential, with a rate determined by the gap in the…
States supported by chaotic open quantum systems fall into two categories: a majority showing instantaneous ballistic decay, and a set of quantum resonances of classically vanishing support in phase space. We present a theory describing…
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial…
We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit…
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…
The stability of nuclei is discussed with respect to the width of the Gaussian wave packets within Quantum Molecular Dynamics model. A detailed study is carried out by taking different equations of state (i.e., static soft and hard and the…
Within the framework of the hypothesis offered by authors about a complex-valued nature of physical quantities the stability of basic equations of the classical physics concerning complex-valued perturbations of parameters and boundary…
We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "normal form" coordinate system near such Turing patterns…
Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain…