相关论文: Landau-Zener Problem for Trilinear Hamiltonians

The Landau-Zener formula describes the diabatic transition probability of a two-level system under linear driving. Its rigorous derivation typically relies on sophisticated mathematical tools, such as special functions, Laplace transforms,…

We consider the nonlinear scattering and transmission of an atom laser, or Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The nonlinearity inherent in this problem leads to several new physical features beyond the…

We study the influence of a fast noise on Landau-Zener transitions. We demonstrate that a fast colored noise much weaker than the conventional white noise can produce transitions itself or can change substantially the Landau-Zener…

In circular accelerators, crossing the linear coupling resonance induces the exchange of the transverse emittances, provided the process is adiabatic. This has been considered in some previous works, where the description of the phenomenon…

It has recently been discovered that for certain rates of mode-exchange collisions analytic solutions can be found for a Hamiltonian describing the two-mode Bose-Einstein condensate. We proceed to study the behavior of the system using…

We study the flow of a spinor (F=1) Bose-Einstein condensate in the presence of an obstacle. We consider the cases of ferromagnetic and polar spin-dependent interactions and find that the system demonstrates two speeds of sound that are…

We discuss the dynamics of a Bose-Einstein condensate of atoms which is suddenly coupled to a condensate of molecules by an optical or magnetic Feshbach resonance. Three limiting regimes are found and can be understood from the transient…

Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…

We present a theory of resonances for a class of non-autonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of…

Parametric resonance can produce particles from oscillating scalar field, where an exponential growth of the particle number density can be developed. While it has been noticed that stimulated decay in Boltzmann equations exhibits similar…

We revisit the adiabatic criterion in stimulated Raman adiabatic passage for the three-level $\Lambda$-system, and compare the situation with and without nonlinearity. In linear systems, the adiabatic condition is derived with the help of…

The Landau problem for inhomogeneous magnetic fields is examined in a very general context and several interesting analogies with the Nielsen-Olesen vortices are established. Firstly we show that the Landau problem with non-homogeneous…

We examine one important (and overlooked in all previous investigations) aspect of well - known crossing diabatic potentials or Landau - Zener (LZ) problem. We derive the semiclassical quantization rules for the crossing diabatic potentials…

We investigate the many-body Landau-Zener (LZ) process in a two-site Bose-Hubbard model driven by a time-periodic field. We find that the driving field may induce sideband transitions in addition to the main LZ transitions. These…

In this paper, we analyze the adiabatic crossing of a resonance for Hamiltonian systems when a double-resonance condition is satisfied by the linear frequency at an elliptic fixed point. We discuss in detail the phase-space structure on a…

A disordered version of the one dimensional asymmetric exclusion model where the particle hopping rates are quenched random variables is studied. The steady state is solved exactly by use of a matrix product. It is shown how the phenomenon…

We consider the propagation of a dark soliton in a quasi 1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary…

The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues. The conditions in Williams [14] are rather restrictive, and…

We provide a classification of the possible flow of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single…

A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser (a laser with self-similar propagation of ultrashort pulses), is used as a variational wave function to solve the Gross-Pitaevskii…