Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-06-30
Prog. Theor. Phys. 126 (2011), 577-595
Physics
Condensed Matter
Strongly Correlated Electrons
To be published in Prog. Theor. Phys. (Kyoto)
Scientific paper
10.1143/PTP.126.577
A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the oscillating Schwinger Hamiltonian to establish the relationship between the internal (due to time-dependent eigenfunctions) and external (due to time-dependent Hamiltonian) time scales. We prove that this relationship needs to be taken as an independent quantum adiabatic approximation criterion. We give four examples, including logical expositions based on the spin-1/2 two-level system to address the gapped and gapless (due to energy level crossings) systems, as well as to understand how does this theorem allows one to study dynamical systems such as chemical reactions.
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