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We propose conditions for the emergence of Turing patterns in a domain that changes in size by homogeneous growth/shrinkage. These conditions to determine the bifurcation are based on considering the geometric change of a potential function…
We study double-barrier interfaces separating regions of asymptotically subsonic and supersonic flow of Bose condensed atoms. These setups contain at least one black hole sonic horizon from which the analog of Hawking radiation should be…
The influence of multiplicative white noise on the resonance capture of strongly nonlinear oscillatory systems under chirped-frequency excitations is investigated. It is assumed that the intensity of the perturbation decays polynomially…
We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of ``noise''…
We derive self-consistent expressions of current and noise for single-electron transistors driven by time-dependent perturbations. We take into account effects of the electrical environment, higher-order co-tunneling, and time-dependent…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…
Transient electron dynamics and the Fano resonance formation over time in transport through a two quantum dot system in a T-shape geometry (2QD-T) are analysed for free electrons. Time evolution of the transport characteristics are…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
Theoretical research on electronic properties in mesoscopic condensed matter systems has focused primarily on the electron charge freedom degrees, while its corresponding spin freedom degrees have not yet received the same attention.…
In this paper we demonstrate that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir. Our results follows from a generalization of the Born-Markov approximation, which relies in…
Our main goal in this paper is to extend to any system of coupled quadratic Hamiltonians some properties known for systems of quantum harmonic oscillators related with the Brownian Quantum Motion model. In a first part we get a rather…
We study the dynamics of shear-band formation and evolution using a simple rheological model. The description couples the local structure and viscosity to the applied shear stress. We consider in detail the Couette geometry, where the model…
We have studied the rich dynamics of a damped particle inside an external double-well potential under the influence of state-dependent time-delayed feedback. In certain regions of the parameter space, we observe multistability with the…
The tunneling through an opaque barrier with a strong oscillating component is investigated. It is shown, that in the strong perturbations regime (in contrast to the weak one), higher perturbations rate does not necessarily improve the…
By using an exact solution to the time-dependent Schr\"{o}dinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source…
We study the time evolution of bosonic systems where multiple driven bosonic modes of light interact with multiple mechanical resonators through arbitrary, time-dependent, optomechanical-like interactions. We find the analytical expression…
We study the interplay between structural and conductivity (composite) disorder and the collective electrical response in random networks models. Translating the problem of time-dependent electrical response (resonance and transient…
The resonance states and the decay dynamics of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation are studied for a simple, however flexible model system, the double delta-shell potential. This model allows analytical solutions and…
We develop the concept of scattering matrix and we use it to perform stable numerical calculations of resonant tunneling of electrons through a multiple potential barrier in a semiconductor heterostructure. Electrons move in two external…