Adiabatic evolution of eigenspectra of model 1-D and 2-D Hamiltonians: quantum adiabatic switching algorithm in a time-independent fourier grid Hamiltonian framework

Sarkar, Pranab ; Bhattacharyya, S. P. (1998) Adiabatic evolution of eigenspectra of model 1-D and 2-D Hamiltonians: quantum adiabatic switching algorithm in a time-independent fourier grid Hamiltonian framework International Journal of Quantum Chemistry, 67 (3). pp. 133-141. ISSN 0020-7608

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Official URL: http://www3.interscience.wiley.com/journal/29894/a...

Related URL: http://dx.doi.org/10.1002/(SICI)1097-461X(1998)67:3<133::AID-QUA1>3.0.CO;2-W

Abstract

We explore the viability of a time-independent quantum adiabatic switching algorithm in the Fourier grid Hamiltonian (FGH) framework in the presence of degeneracy, avoided crossing, and chaos. The algorithm is simple and cost effective and provides information about the full eigenspectrum of the evolving Hamiltonian. It is shown to be capable of capturing accurately the change in the pattern of level spacing distribution statistics as one switches from a nonchaotic region of parameter values into the chaotic region. The Transition turns out to be less sharp than anticipated.

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