We investigate a particle confined within a double-well potential, its behavior described by a one-dimensional nonlinear Schrödinger equation. Transitions between the two lowest self-trapped states of this system are studied, in the two-mode approximation, under the influence of the external time-dependent perturbation. If the perturbation is harmonic in time, with the frequency omega, then tra...

The parametric resonance of the axial vibrations of a cantilever pipe conveying harmonically perturbed two-phase flow is investigated using the method of multiple scale perturbation. The nonlinear coupled and uncoupled planar dynamics of the pipe are examined for a scenario when the axial vibration is parametrically excited by the pulsating frequencies of the two phases conveyed by the pipe. Aw...

We propose discrete TBA equations for models with discrete spectrum. We illustrate our construction on the Calogero-Moser model and determine the discrete 2-body TBA function which yields the exact N -body CalogeroMoser thermodynamics. We apply this algorithm to the Lieb-Liniger model in a harmonic well, a model which is relevant for the microscopic description of harmonically trapped Bose-Eins...

A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady state solution of the equation for the density matrix in th...

We rigorously define the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive δ′-interaction, of strength β, centred at 0 (the bottom of the confining parabolic potential), by explicitly providing its resolvent. Our approach is based on a ‘coupling constant renormalization’, related to a technique originated in quantum field theory and implemented in the rigorous mathe...

We show that noncollinear high harmonic generation (HHG) can be fully understood in terms of nonlinear optical wave mixing. We demonstrate this by superposing on the fundamental ω1 field its second harmonic ω2 of variable intensity in a noncollinear geometry. It allows us to identify, by momentum conservation, each field's contribution (n1,n2) to the extreme ultraviolet emission at frequency Ω ...

Time-resolved variations of the ion velocity distribution function (IVDF) are measured in the cylindrical Hall thruster using a novel heterodyne method based on the laser-induced fluorescence technique. This method consists in inducing modulations of the discharge plasma at frequencies that enable the coupling to the breathing mode. Using a harmonic decomposition of the IVDF, one can extract ea...

We consider a simple harmonic oscillator subject to time-dependent, spatially homogeneous perturbation and show that it is canonically equivalent non-perturbed oscillator. The canonical transformation relates both systems can be implemented as unitary mapping the perturbed system onto each other. This allows us explicitly compute time dependence of states system, in particular phase affects all...