Related papers: Multiparticle Landau-Zener problem
The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians. Within the multistate Landau-Zener (MLZ) theory, however, there has been a successful alternative approach to…
We discuss a class of models that generalize the two-state Landau-Zener (LZ) Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great…
We determine transition probabilities in two exactly solvable multistate Landau-Zener (LZ) models and discuss applications of our results to the theory of dynamic passage through a phase transition in the dissipationless quantum mechanical…
We discuss solvable multistate Landau-Zener (MLZ) models whose Hamiltonians have commuting partner operators with $\sim 1/\tau$-time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the…
The exact analytical solution of the degenerate Landau-Zener model, wherein two bands of degenerate energies cross in time, is presented. The solution is derived by using the Morris-Shore transformation, which reduces the fully coupled…
The transition dynamics of two-state systems with time-dependent energy levels, first considered by Landau, Zener, Majorana, and St\"uckelberg, is one of the basic models in quantum physics and has been used to describe various physical…
Three analytic solutions to the Schr\"{o}dinger equation for the time-dependent Landau-Zener Hamiltonian are presented. They correspond to specific finite-time driving paths in a bounded parameter space of a two-level system. Two of these…
We study a class of multistate Landau-Zener model which cannot be solved by integrability conditions or other standard techniques. By analyzing analytical constraints on its scattering matrix and performing fitting to results from numerical…
The Landau-Zener problem, where a minimum energy separation is passed with constant rate in a two-state quantum-mechanical system, is an excellent model quantum system for a computational project. It requires a low-level computational…
Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient…
We formulate and approximately solve a specific many-body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving…
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…
We identify a nontrivial 4-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two…
We discuss common properties and reasons for integrability in the class of multistate Landau-Zener (MLZ) models with all diabatic levels crossing at one point. Exploring the Stokes phenomenon, we show that each previously solved model has a…
We introduce the isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian (with only 1-electron interactions). This suggests that all methods developed for the former can be employed for the latter,…
I present a simple algorithm based on a type of partial reverse-engineering that generates an unlimited number of exact analytical solutions to the Schrodinger equation for a general time-dependent two-level Hamiltonian. I demonstrate this…
Exactly solvable multistate Landau-Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy the integrability conditions with…
We consider the Landau-Zener problem for a multilevel quantum system that is coupled to an external environment. In particular, we consider a number of cases of three-level systems coupled to a harmonic oscillator that represents the…
The degenerate Landau-Zener-Majorana-St\"uckelberg model consists of two degenerate energy levels whose energies vary with time and in the presence of an interaction which couples the states of the two levels. In the adiabatic limit, it…
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…