Related papers: Bifurcation in kinetic equation for interacting Fe…
Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by sudden parameter changes. We discuss the characterization of such dynamical phase transitions based on the statistics of produced…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
The one-dimensional kinetic equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and frequency of collisions affine depending on the module of molecular velocity is constructed. Laws of preservation of number of…
Ground state energies and superfluid gaps are calculated for degenerate Fermi systems interacting via long attractive scattering lengths such as cold atomic gases, neutron and nuclear matter. In the intermediate region of densities, where…
The phenomenon of Fermi acceleration is addressed for a dissipative bouncing ball model with external stochastic perturbation. It is shown that the introduction of energy dissipation (inelastic collisions of the particle with the moving…
The objective of this paper is to investigate the stability of limit cycles of a mathematical model with a distributed delay which describes the interaction between p53 and mdm2. Choosing the delay as a bifurcation parameter we study the…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
This chapter presents a dynamical systems point of view of the study of systems with delays. The focus is on how advanced tools from bifurcation theory, as implemented for example in the package DDE-BIFTOOL, can be applied to the study of…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
The Kramers problem for quantum fermi-gases with specular - diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers problem the new generalised method of a source of the decision of the boundary problems…
A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention…
We study generic features of open quantum systems embedded into a continuum of scattering wavefunctions and compare them with results discussed in optics. A dynamical phase transition may appear at high level density in a many-level system…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
We investigate the emergence of sustained spatio-temporal behaviors in reaction-phase separation systems. We focus on binary systems, in which either one or both species can phase separate, and we discuss the stability of the homogeneous…
We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic…
Heavy ion collisions in the Fermi energy regime may simultaneously show features of direct and dissipative processes. To investigate this behavior in detail, we study isotope and velocity distributions of projectile-like fragments in the…
Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic…
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…