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Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

Divakaran, Uma and Dutta, Amit and Sen, Diptiman (2010) Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system. In: Physical Review B, 81 (5).

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Official URL: http://prb.aps.org/abstract/PRB/v81/i5/e054306

Abstract

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to The American Physical Society.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 24 Mar 2010 07:58
Last Modified: 19 Sep 2010 05:57
URI: http://eprints.iisc.ernet.in/id/eprint/26385

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