Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-10-12
"Quantum Quenching, Annealing and Computation", Eds. A. Das, A. Chandra and B. K. Chakrabarti, Lect. Notes in Phys., vol. 802
Physics
Condensed Matter
Statistical Mechanics
20 pages, 3 figures, contribution to "Quantum Quenching, Annealing and Computation", Eds. A. Das, A. Chandra and B. K. Chakrab
Scientific paper
We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian. We first consider a two-level system and give an elementary derivation of the asymptotics of the transition probability when the tuning parameter slowly changes in the finite range. Then we apply this perturbation theory to many-particle systems with low energy spectrum characterized by quasiparticle excitations. Within this approach we derive the scaling of various quantities such as the density of generated defects, entropy and energy. We discuss the applications of this approach to a specific situation where the system crosses a quantum critical point. We also show the connection between adiabatic and sudden quenches near a quantum phase transitions and discuss the effects of quasiparticle statistics on slow and sudden quenches at finite temperatures.
Grandi Claudia de
Polkovnikov Anatoli
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