Validity of Quantum Adiabatic Theorem

Abstract

The consistency of quantum adiabatic theorem has been doubted recently. It is shown in the present paper that the difference between the adiabatic solution and the exact solution to the Schrodinger equation with a slowly changing driving Hamiltonian is small; while the difference between their time derivatives is not small. This explains why substituting the adiabatic solution back into Schrodinger equation leads to "inconsisitency" of the adiabatic theorem. Physics is determined completely by the state vector, and not by its time drivative. Therefore the quantum adiabatic theorem is physically correct.

Reference [6] has been published as "Phys. Rev. Lett. 93, 160408(2004)" recently. It was quoted as "quant-ph/0404022 v6"

References in corpus (2)

• Robustness of adiabatic quantum computation
• Inconsistency in the application of the adiabatic theorem

Cited by in corpus (32)

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• Adiabatic theorems for linear and nonlinear Hamiltonians
• Validity of adiabaticity in Cavity QED
• Manipulating phonons of a trapped-ion system using optical tweezers
• Generalized Geometrical Phase in the Case of Continuous Spectra
• Perturbative Analysis of Possible Failures in the Traditional Adiabatic Conditions
• An Amelioration for the Sign Problem: Adiabatic Quantum Monte Carlo
• The adiabatic theorem in the presence of noise
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• Why the Quantitative Condition Fails to Reveal Quantum Adiabaticity
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• Optimizing adiabaticity in quantum mechanics
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• The relationship between minimum gap and success probability in adiabatic quantum computing
• Consistency between adiabatic and nonadiabatic geometric phases for nonselfadjoint hamiltonians
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• Intrinsic Dynamical Fluctuation Assisted Symmetry Breaking in Adiabatic Following
• Matrix Operator Approach to the Quantum Evolution Operator and the Geometric Phase
• Necessity of integral formalism
• Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach
• General conditions for a quantum adiabatic evolution
• Geometric Floquet Condition for Quantum Adiabaticity
• Optimal control of population transfer in multi-level systems by dynamical quantum geometric tensor