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Title: Four-state nonstationary models in multistate Landau-Zener theory

Abstract

A dynamic four-state system is considered within the context of multistate Landau-Zener theory. It is shown that the theory accounts very well for the time-dependent state populations and final transition probabilities even in cases when multiple crossings appear in close vicinity of each other. This is also true for multiple paths systems when the phases are appropriately accounted for. It is found that transitions may take place also between diabatic states that do not couple directly and that the dynamics of such crossings may be accurately described within the multichannel Landau-Zener theory.

Authors:
;  [1]; ;  [2]
  1. V. Fock Institute of Physics, St. Petersburg State University, 198504 St. Petersburg (Russian Federation)
  2. Department of Physics and Technology, University of Bergen, N-5007 Bergen (Norway)
Publication Date:
OSTI Identifier:
20976640
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevB.75.014441; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LIFETIME; POTENTIAL ENERGY; QUANTUM MECHANICS; SURFACES; TIME DEPENDENCE

Citation Formats

Ostrovsky, V. N., Volkov, M. V., Hansen, J. P., and Selstoe, S. Four-state nonstationary models in multistate Landau-Zener theory. United States: N. p., 2007. Web. doi:10.1103/PHYSREVB.75.014441.
Ostrovsky, V. N., Volkov, M. V., Hansen, J. P., & Selstoe, S. Four-state nonstationary models in multistate Landau-Zener theory. United States. doi:10.1103/PHYSREVB.75.014441.
Ostrovsky, V. N., Volkov, M. V., Hansen, J. P., and Selstoe, S. Mon . "Four-state nonstationary models in multistate Landau-Zener theory". United States. doi:10.1103/PHYSREVB.75.014441.
@article{osti_20976640,
title = {Four-state nonstationary models in multistate Landau-Zener theory},
author = {Ostrovsky, V. N. and Volkov, M. V. and Hansen, J. P. and Selstoe, S.},
abstractNote = {A dynamic four-state system is considered within the context of multistate Landau-Zener theory. It is shown that the theory accounts very well for the time-dependent state populations and final transition probabilities even in cases when multiple crossings appear in close vicinity of each other. This is also true for multiple paths systems when the phases are appropriately accounted for. It is found that transitions may take place also between diabatic states that do not couple directly and that the dynamics of such crossings may be accurately described within the multichannel Landau-Zener theory.},
doi = {10.1103/PHYSREVB.75.014441},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 1,
volume = 75,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. Expressions for some state-to-state transition probabilities are derived in degenerate cases.
  • Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. Additionally, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.
    Cited by 3
  • Cited by 1
  • Within this paper, we discuss common properties and reasons for integrability in the class of multistate Landau-Zener models with all diabatic levels crossing at one point. Exploring the Stokes phenomenon, we show that each previously solved model has a dual one, whose scattering matrix can be also obtained analytically. For applications, we demonstrate how our results can be used to study conversion of molecular into atomic Bose condensates during passage through the Feshbach resonance, and provide purely algebraic solutions of the bowtie and special cases of the driven Tavis-Cummings model.
    Cited by 1