Related papers: Resonance in a driven two-level system: analytical…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
We present multiplicity results for the periodic and Neumann-type boundary value problems associated with coupled Hamiltonian systems. For the periodic problem, we couple a system having twist condition with another one whose nonlinearity…
This paper studies the 1-loop approximation for a massless spin-1/2 field on a flat four-dimensional Euclidean background bounded by two concentric 3-spheres, when non-local boundary conditions of the spectral type are imposed. The use of…
We consider a linear Schr\"odinger equation with a small nonlinear perturbation in $R^3$. Assume that the linear Hamiltonian has exactly two bound states and its eigenvalues satisfy some resonance condition. We prove that if the initial…
A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal…
To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion,…
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter $\lambda(t) =…
We develop a two-timing perturbation analysis to investigate the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations…
Using kinetic equation in the relaxation approximation (RTA), we investigate a flow generated by an infinite plate oscillating with frequency $\omega$. Geometrical simplicity of the problem allows a solution in the entire range of…
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for…
We study time dependent solutions in cubic open string field theory which are expected to describe the configuration of the rolling tachyon. We consider the truncated system consisting of component fields of level zero and two, which are…
This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by…
A two-dimensional model of an electron moving under the influence of an attractive zero-range potential as well as external magnetic and electric fields is analyzed. We prove by numerical investigations that there are formed such resonances…
Resonance, defined as the oscillation of a system when the temporal frequency of an external stimulus matches a natural frequency of the system, is important in both fundamental physics and applied disciplines. However, the spatial…
We present rigorous results for quantum systems with both bound and continuum states subjected to an arbitrary strength time-periodic field. We prove that the wave function takes the form of a sum of time-periodic resonant states with…
Self-propelled particles that are subject to noise are a well-established generic model system for active matter. A homogeneous alignment field can be used to orient the direction of the self-propulsion velocity and to model systems like…
We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and…
A spin-rotation symmetry in spin-orbit coupled two-dimensional electron systems gives rise to a long-lived spin excitation that is robust against short-range impurity scattering. The influence of a constant in-plane electric field on this…