Breakdown of the adiabatic limit in low dimensional gapless systems

Abstract

It is generally believed that a generic system can be reversibly transformed from one state into another by sufficiently slow change of parameters. A standard argument favoring this assertion is based on a possibility to expand the energy or the entropy of the system into the Taylor series in the ramp speed. Here we show that this argumentation is only valid in high enough dimensions and can break down in low-dimensional gapless systems. We identify three generic regimes of a system response to a slow ramp: (A) mean-field, (B) non-analytic, and (C) non-adiabatic. In the last regime the limits of the ramp speed going to zero and the system size going to infinity do not commute and the adiabatic process does not exist in the thermodynamic limit. We support our results by numerical simulations. Our findings can be relevant to condensed-matter, atomic physics, quantum computing, quantum optics, cosmology and others.

11 pages, 5 figures, to appear in Nature Physics (originally submitted version)

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Universal adiabatic dynamics across a quantum critical point
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation
• Many body generalization of the Landau Zener problem
• Evolution of the macroscopically entangled states in optical lattices
• Robustness of adiabatic passage trough a quantum phase transition
• Production efficiency of Feshbach molecules in fermion systems
• Inconsistencies of the Adiabatic Theorem and the Berry Phase

Cited by in corpus (3)

• Optimal non-linear passage through a quantum critical point
• Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field
• Microscopic expression for the heat in the adiabatic basis