Adiabatic theorems for linear and nonlinear Hamiltonians

Abstract

Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation. It is shown that in some cases the found condition is necessary and sufficient. The adiabatic theorem is generalized for the case of nonlinear Hamiltonians.

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• Cold Bosons in Optical Lattices
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• Incoherent Landau-Zener-Stuckelberg Transitions in Single-Molecule Magnets

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• Evolutionary Processes in Quantum Decision Theory
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• Degenerate Adiabatic Perturbation Theory: Foundations and Applications
• Why the Quantitative Condition Fails to Reveal Quantum Adiabaticity
• Quantum adiabatic evolution with energy-degeneracy levels
• From power law to Anderson localization in nonlinear Schrödinger equation with nonlinear randomness
• Avoid First Order Quantum Phase Transition by Changing Problem Hamiltonians
• Hierarchical Theory of Quantum Adiabatic Evolution
• Matrix Operator Approach to the Quantum Evolution Operator and the Geometric Phase
• Periodic dynamics of fermionic superfluids in the BCS regime
• Nonequilibrium Dynamics of Ultracold Fermi Superfluids
• Adiabatic amplification of energy and magnetic moment of a charged particle after the magnetic field inversion
• Utility Rate Equations of Group Population Dynamics in Biological and Social Systems