Related papers: Slow dynamics for self-adjoint semigroups and unit…
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the…
We show that peculiar collective dynamics called slow switching arises in a population of leaky integrate-and-fire oscillators with delayed, all-to-all pulse-couplings. By considering the stability of cluster states and symmetry possessed…
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
Josephson junctions constructed from superconductor-semiconductor-superconductor heterostructures have been used to realize a variety of voltage-tunable superconducting quantum devices, including qubits and parametric amplifiers. To date…
This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the…
We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition…
Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
This paper deals with semigroups of holomorphic self-maps of the upper half-plane that exhibit an extremal (i.e. the slowest possible) rate of convergence to their Denjoy--Wolff point. The main novelty lies in the parabolic case of zero…
The Computation of discrete Contractive semigroups becomes necessary when we deal with several types of evolution equations in Discretizable Hilbert spaces, in this work we study some properties of the discrete forms of the contractive…
We characterize to what extent it is possible to modify the stationary states of a quantum dynamical semigroup, that describes the irreversible evolution of a two-level system, by means of an auxiliary two-level system. We consider systems…
We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such…
We provide an analytical investigation of the entanglement dynamics for a system composed of an arbitrary number of qubits dissipating into a common environment. Specifically we consider initial states whose evolution remains confined on…
The slow dynamics of a system as it approaches a phase transition, associated with the slowing down in the decay of a correlation function, can be caused by a sharp increase in the probability of a particle's returning to its original state…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
We study certain dynamical systems which leave invariant an indefinite quadratic form via semigroups or evolution families of complex symmetric Hilbert space operators. In the setting of bounded operators we show that a…
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
To identify emerging microscopic structures in low temperature spin glasses, we study self-sustained clusters (SSC) in spin models defined on sparse random graphs. A message-passing algorithm is developed to determine the probability of…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
A numerical index is introduced for semigroups of completely positive maps of $\Cal B(H)$ which generalizes the index of E_0-semigroups. It is shown that the index of a unital completely positive semigroup agrees with the index of its…