Landau-Zener Transitions in Chains

Abstract

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 regime. In particular, we show that statistics of particles in a new phase demonstrate scaling behavior. Our results also reveal a symmetry that we claim is a property of a large class of multistate LZ models, whose explicit solutions are not presently known. We support our arguments by direct numerical simulations.

8 pages, 7 figures

References in corpus (13)

• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Dynamics of a quantum phase transition in a ferromagnetic Bose-Einstein condensate
• Coherent destruction of tunneling, dynamic localization and the Landau-Zener formula
• Coherent Particle Transfer in an On-Demand Single-Electron Source
• Non-adiabacity and large flucutations in a many particle Landau Zener problem
• Many body generalization of the Landau Zener problem
• Fast quantum noise in Landau-Zener transition
• Tailoring the correlation and anti-correlation behavior of path-entangled photons in Glauber-Fock oscillator lattices
• Dynamics of a many-particle Landau-Zener model: inverse sweep
• Comment on "Exact results for survival probability in the multistate Landau-Zener model"
• Counterintuitive transitions between crossing energy levels
• Production efficiency of Feshbach molecules in fermion systems
• Molecular production at a wide Feshbach resonance in Fermi-gas of cooled atoms

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• Landau-Zener dynamics of a nanoresonator containing a tunneling spin
• Landau-Majorana-Stuckelberg-Zener dynamics driven by coupling for two interacting qutrit systems
• Coupling-assisted Landau-Majorana-Stuckelberg-Zener transition in two-interacting-qubit systems
• Generalized Adiabatic Impulse Approximation
• Nonadiabatic transitions in exactly solvable quantum mechanical multichannel model: role of level curvature and counterintuitive behavior
• Coherent reaction between molecular and atomic Bose-Einstein condensates: integrable model
• Dynamics of a two-state system through a real level crossing
• Mott-insulator state of cold atoms in tilted optical lattices: doublon dynamics and multi-level Landau-Zener tunneling
• Integrable multistate Landau-Zener models with parallel energy levels
• Steepest Entropy Ascent for Two-State Systems with Slowly Varying Hamiltonians
• Adiabatic preparation of a cold exciton condensate
• Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance
• The model of a level crossing with a Coulomb band: exact probabilities of nonadiabatic transitions
• Exact transition probabilities in the three-state Landau-Zener-Coulomb model
• Intermittent emission of particles from a Bose-Einstein condensate in a one-dimensional lattice
• Analytic approach to the Landau-Zener problem in bounded parameter space
• Electric circuit analog of Landau-Zener tunneling using time-varying elements
• Multiple-time-scale Landau-Zener transitions in many-body systems
• Graph-theoretical search for integrable multistate Landau-Zener models
• Integrability in the multistate Landau-Zener model with time-quadratic commuting operators