2010 **Abstract:** 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 th…

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“…This prediction was recently confirmed in cold-atom experiments with accelerated optical lattices (Zenesini, Lignier, Tayebirad et al, 2009). An analogous mechanism also explains the amount of energy injected into a system upon crossing a quantum-critical point or parameter changes in a gapless phase (Dziarmaga, 2010), as obtained from adiabatic perturbation theory (Grandi and Polkovnikov, 2010). In these cases the excitation energy typically behaves as ΔEðτÞ ∼ τ −η for large ramp times τ → ∞, with the positive exponent η depending on the details of the system and the ramp protocol.…”

confidence: 93%

“…This prediction was recently confirmed in cold-atom experiments with accelerated optical lattices (Zenesini, Lignier, Tayebirad et al, 2009). An analogous mechanism also explains the amount of energy injected into a system upon crossing a quantum-critical point or parameter changes in a gapless phase (Dziarmaga, 2010), as obtained from adiabatic perturbation theory (Grandi and Polkovnikov, 2010). In these cases the excitation energy typically behaves as ΔEðτÞ ∼ τ −η for large ramp times τ → ∞, with the positive exponent η depending on the details of the system and the ramp protocol.…”

confidence: 93%

“…As shown in Refs. [26,37], this response is closely related to the geometrical properties of the ground state via 1 2 sin…”

confidence: 99%

“…The quantities considered so far could have in principle been obtained by using adiabatic perturbation theory [31], since our perturbative results capture only the lowest order correction in J z /J to the above physical quantities. Therefore, we now focus on the spin flip correlation function S + S − , which contains the bosonic fields in the exponent and demonstrates the non-perturbative nature of bosonization: the present approach yields to first correction in J z to the exponent of the spin-flip correlation function.…”

mentioning

confidence: 99%