We calculate the response of a two-level system to a monochromatic excitation in the framework of a nonlinear homogeneous dissipative generalization of the Schrödinger equation. Non-Lorentzian dependences of the real and imaginary parts of the dynamical response function on the frequency are...

We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator, which enables us to construct the kinetic equations in scaling limits in the presence of correlations of particle states at initial time,...

We systematically investigate slowly moving matter-wave gap soliton propagation in weak random optical lattices. With the weak randomness, an effective-particle theory is constructed to show that the motion of a gap soliton is similar to a particle moving in random potentials. Based on the...

We present one-dimensional (1D) stability analysis of a recently proposed method to filter and control localized states of the Bose–Einstein condensate (BEC), based on novel trapping techniques that allow one to conceive methods to select a particular BEC shape by controlling and manipulating...

The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a function of temperature. The family of classical paths,...

Two-dimensional stability of a controlled Bose-Einstein condensation state, in the form of a nonlinear Schrödinger soliton [JETP Lett. <Emphasis Type="Bold">80 535 (2004)], is studied for the condensations with both repulsive and attractive inter-atom interactions. The Gross-Pitaevski equation is solved numerically,...</emphasis>