The Quest for Solvable Multistate Landau-Zener Models

Abstract

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 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. In addition, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.

26 pages, 12 figures

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Cited by in corpus (22)

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• Integrable time-dependent quantum Hamiltonians
• Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets
• Low-frequency spectroscopy for quantum multi-level systems
• Multistate Landau-Zener models with all levels crossing at one point
• Three-Level Landau-Zener Dynamics
• Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory
• Landau-Zener transitions and Adiabatic impulse approximation in an array of two Rydberg atoms with time-dependent detuning
• Suppression of multiphoton resonances in driven quantum systems via pulse shape optimization
• Generalized Adiabatic Impulse Approximation
• A large class of solvable multistate Landau-Zener models and quantum integrability
• Dynamic spin localization and gamma-magnets
• Loss of adiabaticity with increasing tunneling gap in non-integrable multistate Landau-Zener models
• Integrable multistate Landau-Zener models with parallel energy levels
• Nonlinear multi-state tunneling dynamics in a spinor Bose-Einstein condensate
• Solution to a class of multistate Landau-Zener model beyond integrability conditions
• Diabatic quantum and classical annealing of the Sherrington-Kirkpatrick model
• Effect of decay of the final states on the probabilities of the Landau-Zener transitions in multistate non-integrable models
• Landau-Zener transitions through a pair of higher order exceptional points
• Weyl's Relations, Integrable Matrix Models and Quantum Computation
• Graph-theoretical search for integrable multistate Landau-Zener models
• Exact solutions for the time-evolution of quantum spin systems under arbitrary waveforms using algebraic graph theory