Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system
| Autor: | Zihad Qureshi, Joseph J. Betouras, Peter Mason, Johnny Zhong, Mumnuna A. Qureshi, Alexandre M. Zagoskin |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Physics
education.field_of_study Quantum Physics Quantum decoherence Statistical Mechanics (cond-mat.stat-mech) Population FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas Adiabatic theorem symbols.namesake Classical mechanics Quantum state Magnus expansion 0103 physical sciences symbols Quantum system 010306 general physics education Adiabatic process Hamiltonian (quantum mechanics) Quantum Physics (quant-ph) Condensed Matter - Statistical Mechanics |
| Popis: | We consider the evolution of a quantum state of a Hamiltonian which is parametrically perturbed via a term proportional to the adiabatic parameter \lambda (t). Starting with the Pechukas-Yukawa mapping of the energy eigenvalues evolution on a generalised Calogero-Sutherland model of 1D classical gas, we consider the adiabatic approximation with two different expansions of the quantum state in powers of d\lambda/dt and compare them with a direct numerical simulation. We show that one of these expansions (Magnus series) is especially convenient for the description of non-adiabatic evolution of the system. Applying the expansion to the exact cover 3-satisfability problem, we obtain the occupation dynamics which provides insight on the population of states. Comment: 12 pages, 6 figures |
| Databáze: | OpenAIRE |
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