Related papers: Unstable Systems in Relativistic Quantum Field The…
A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types…
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
We consider the problem of propagation of an unstable particle in the framework of Quantum Field Theory. Using unitarity, we show that a real renormalization constant free of threshold singularities naturally arises.
We discuss relaxation in bosonic and fermionic many-particle systems. For integrable systems, the time evolution can cause a dephasing effect, leading for finite subsystems to certain steady states. We give an explicit derivation of those…
A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic…
The nonlinear evolution of a unstable electrostatic wave is considered for a multi-species Vlasov plasma. From the singularity structure of the associated amplitude expansions, the asymptotic features of the electric field and distribution…
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs…
We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by constructing classical lattice-gas models…
We analyze the survival probability of unstable particles in the context of quantum field theory. After introducing the spectral function of resonances, we show that deviations from the exponential decay law occur at short times after the…
Integrability in quantum theory has been defined in more than one ways. Recently, Braak suggested a new definition that a quantum system is integrable if the number of parameters required to specify the eigenstates and the number degrees of…
The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved that there are situations when biologically unstable…
The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds…
In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…
In the paper we consider the problem of the rigorous description of the kinetic evolution in the presence of initial correlations of quantum large particle systems. One of the developed approaches consists in the description of the…