Strong chaos in one-dimensional quantum system

Ahmed A. Elkamshishy, Chris H. Greene

Tran Duong Anh-Tai, Mathias Mikkelsen, Thomas Busch +1 more

The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of a system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of quantum chaos in a minimal system describing one-dimensional harmonically trapped Bose-Bose mixtures by tuning the particle-particle interactions. Using an improved exact diagonalization scheme, we examine the transition from integrability to chaos when the inter-component interaction changes from weak to strong. Our study is based on the analysis of the level spacing distribution and the distribution of the matrix elements of observables in terms of the eigenstate thermalization hypothesis and their dynamics. We show that one can obtain strong signatures of chaos by increasing the inter-component interaction strength and breaking the symmetry of intra-component interactions.

A. G. Lazerson, Alexey Alexeevich Boikov

M. S. Santhanam

Patrycja Łydżba, Tomasz Sowiński

The low-energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos manifests itself in these systems. In this paper, we consider a simple but experimentally relevant one-dimensional system of a few ultracold fermions moving in a double-well potential. We analyze its many-body spectral properties, which are commonly used to trace quantum chaos. We observe some sig- natures of quantum chaos already in the system with three particles. Generally, these signatures become more pronounced when fermions are evenly added to both components. In contrast, they become suppressed when the particle imbalance is increased.

Guy Zisling, Lea Santos, Yevgeny Bar Lev

We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple system sizes which are at least three times larger than the number of particles and find that robust signatures of quantum chaos emerge for as few as 4 particles in the case of short-range interactions and as few as 3 particles for long-range interactions, and without any apparent dependence on the size of the system.