Breakdown of the adiabatic limit in low dimensional gapless systems

TL;DR

This paper demonstrates that the common assumption of adiabatic reversibility in low-dimensional gapless systems fails due to non-analytic and non-adiabatic regimes, especially in the thermodynamic limit, supported by numerical simulations.

Contribution

It reveals the breakdown of the adiabatic limit in low-dimensional gapless systems and identifies three generic response regimes, challenging standard assumptions.

Findings

Adiabatic limit breaks down in low-dimensional systems.

Three response regimes: mean-field, non-analytic, non-adiabatic.

Non-commuting limits of ramp speed and system size in the non-adiabatic regime.

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.