Nonergodic metallic and insulating phases of Josephson junction chains.

Strictly speaking, the laws of the conventional statistical physics, based on the equipartition postulate [Gibbs J W (1902) Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics] and ergodicity hypothesis [Boltzmann L (1964) Lectures on Gas Theory], apply only in the presence of a heat bath. Until recently this restriction was believed to be not important for real physical systems because a weak coupling to the bath was assumed to be sufficient. However, this belief was not examined seriously until recently when the progress in both quantum gases and solid-state coherent quantum devices allowed one to study the systems with dramatically reduced coupling to the bath. To describe such systems properly one should revisit the very foundations of statistical mechanics. We examine this general problem for the case of the Josephson junction chain that can be implemented in the laboratory and show that it displays a novel high-temperature nonergodic phase with finite resistance. With further increase of the temperature the system undergoes a transition to the fully localized state characterized by infinite resistance and exponentially long relaxation.