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

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.

6 pages including 3 figures; significantly expanded -- this is the published version

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Cited by in corpus (8)

• Nonequilibrium dynamics of closed interacting quantum systems
• Space-time renormalization in phase transition dynamics
• Dynamics of a quantum phase transition in the 1D Bose-Hubbard model: excitations and correlations induced by a quench
• Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching
• Near-adiabatic parameter changes in correlated systems: Influence of the ramp protocol on the excitation energy
• Testing quantum adiabaticity with quench echo
• Driven one-dimensional noisy Kitaev chain
• Quenching across quantum critical points in periodic systems: dependence of scaling laws on periodicity