Related papers: Multiparticle Landau-Zener problem
We generalize the Brundobler-Elser hypothesis in the multistate Landau-Zener problem to the case when instead of a state with the highest slope of the diabatic energy level there is a band of states with an arbitrary number of parallel…
Analytical solutions to the time-dependent Schrodinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited…
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…
We discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insights obtained from an analysis of the classical mechanics of the process, we confine each electron to move along the lines…
Two-level system strongly coupled to a single resonator mode (harmonic oscillator) is a paradigmatic model in many subfields of physics. We study theoretically the Landau-Zener transition in this model. Analytical solution for the…
We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellipsoid, hyperboloid and paraboloid. We start form the two-center MICZ-Kepler system Hamiltonian and then making the reduction into the various…
Two problems incorporating a set of horizontal linear potentials crossed by a sloped linear potential are analytically solved and compared with numerical results: (a) the case where boundary conditions are specified at the ends of a finite…
Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schr\"odinger equation. This equation is equivalent to a high-dimensional Helmholtz equation and it has solutions that are outgoing waves,…
It is shown fields that cannot be represented over one complex plane can be further decomposed for representation over multiple complex planes. This finding is demonstrated here by solving of the Schr\"{o}dinger equation for the hydrogen…
We present experimental results on the preparation of a desired quantum state in a two-level system with the maximum possible fidelity using driving protocols ranging from generalizations of the linear Landau-Zener protocol to…
A semiclassical (SC) approach is developed for nonequilibrium quantum transport in molecular junctions. Following the early work of Miller and White [J. Chem. Phys. 84, 5059 (1986)], the many-electron Hamiltonian in second quantization is…
Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schr\"{o}dinger equation is applied for a solution of a two--dimensional (2D) problem for two particles interacting via Kratzer,…
An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of…
A comprehensive theory of the Landau-Zener transition in quadratic nonlinear two-state systems is developed. A compact analytic formula involving elementary functions only is derived for the final transition probability. The formula…
We study Landau-Zener transitions between two states with the addition of a shared discretized continuum. The continuum allows for population decay from the initial state as well as indirect transitions between the two states. The…
In this paper, we present quantum algorithms for a class of highly-oscillatory transport equations, which arise in semiclassical computation of surface hopping problems and other related non-adiabatic quantum dynamics, based on the…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
We consider the self-dual Chern-Simons-Schr\"odinger model in two spatial dimensions. This problem is $L^2$-critical. Under equivariant setting, global wellposedness and scattering were proved in [Liu-Smith, 2016] for solution with initial…
We present a method for efficiently finding solutions of L\"uscher's quantisation condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such…
We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final…