Related papers: Nonlinear level crossing models
We study the propagation of wave packets for a one-dimensional system of two coupled Schr\"odinger equations with a cubic nonlinearity, in the semi-classical limit. Couplings are induced by the nonlinearity and by the potential, whose…
We develop a general theory of Landau-Zener (LZ) tunneling in a two-level system with amplitude-dependent, sign-reversible nonlinear coupling, distinguishing it fundamentally from conventional on-site nonlinearity. Through a combination of…
We consider nonadiabatic systems in which the classical Born-Oppenheimer approximation breaks down. We present a general theory that accurately captures the full transmitted wavepacket after multiple transitions through either a single or…
We obtain the exact expression for the matrix of nonadiabatic transition probabilities in the model of three interacting states with a time-dependent Hamiltonian. Unlike other known solvable Landau-Zener-like problems, our solution is…
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 study Landau-Zener interband transitions for a non-symmetric optical lattice in the presence of an external force. We show that gain and losses of the light beam, as well as the relative occupation probabilities of the bands involved in…
We study the Landau-Zener-Stueckelberg (LZS) effect for a two-level system with a time-dependent nonlinear bias field (the sweep function) W(t). Our main concern is to investigate the influence of the nonlinearity of W(t) on the probability…
We analyze the crossing of a quantum critical point based on exact results for the transverse XY model. In dependence of the change rate of the driving field, the evolution of the ground state is studied while the transverse magnetic field…
We study the transitions between neighboring energy levels in a quasi-one-dimensional semiconductor quantum dot with two interacting electrons in it, when it is subject to a linearly time-dependent electric field. We analyze the…
When the level separation of a qubit is modulated periodically across an avoided crossing, tunneling to the excited state - and consequently Landau-Zener-St\"uckelberg interference - can occur. The types of modulation studied so far…
The approach by Ettore Majorana for non-adiabatic transitions between two quasi-crossing levels is revisited. We rederive the transition probability, known as the Landau-Zener-St\"{u}ckelberg-Majorana formula, and introduce Majorana's…
During the adiabatic time evolution levels crossing violates the adiabaticity and makes transitions between levels possible. Conventionally only two energy levels cross simultaneously. The transition probabilities for this case were found…
We present a comprehensive analysis of the Landau-Zener tunnelling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunnelling probability in the adiabatic limit (i.e., very slowly…
We investigate coherent and incoherent tunneling phenomena in conditions of crossing diabatic potentials. We consider a model of two crossing parabolic diabatic potentials with an independent of coordinates constant adiabatic coupling. As a…
Nonlinear mixed effects models represent a powerful tool to simultaneously analyze data from several individuals. In this study a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to…
The present work focuses on the calculation of a non-adiabatic transition probability between two states which may or may not cross with each other and are coupled to each other by a moving $\delta$ function potential. Here, the time…
We present a rigorous analysis of the Landau-Zener linear-in-time term crossing problem for quadratic-nonlinear systems relevant to the coherent association of ultracold atoms in degenerate quantum gases. Our treatment is based on an exact…
The nonadiabatic transition probabilities in the two-level systems are calculated analytically by using the monodromy matrix determining the global feature of the underlying differential equation. We study the time-dependent 2x2 Hamiltonian…
We investigate the Landau-Zener transition in two- and three- level systems subject to a classical Gaussian noise. Two complementary limits of the noise being fast and slow compared to characteristic Landau-Zener tunnel times are discussed.…
The Kronig-Penney model is used to Study the effect of nonlinear interaction on the transmissive properties of both ordered and disordered chains. In the ordered case, the nonlinearity can either localize or delocalize the electronic states…