It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

http://absimage.aps.org/image/DAMOP06/MWS_DAMOP06-2006-000603.pdf

A quantum Newton's cradle

The last decade has witnessed both quantitative and qualitative progresses in Shell Model studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using the Lanczos tridiagonal construction, whose formal and numerical aspects we will analyze. Besides, many new approximation methods have been developed in order to overcome the dimensionality limitations. Furthermore, new effective nucleon-nucleon interactions have been constructed that contain both two and three-body contributions. The former are derived from realistic potentials (i.e., consistent with two nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. In the present review we will concentrate on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the Shell Model to describe simultaneously all the manifestations of the nuclear dynamics either of single particle or collective nature. We will also treat in some detail the problems associated with rotational motion, the origin of quenching of the Gamow Teller transitions, the double beta-decays, the effect of isospin non conserving nuclear forces, and the specificities of the very neutron rich nuclei. Many other calculations--that appear to have ``merely'' spectroscopic interest--are touched upon briefly, although we are fully aware that much of the credibility of the Shell Model rests on them.

The shell model as a unified view of nuclear structure

We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.

https://iopscience.iop.org/article/10.1088/0034-4885/79/5/056001/pdf

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.

Energy levels of light nuclei A=8,9,10

Energy levels of A = 21−44 nuclei (V)

It is shown that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum behavior of such a signal for different systems suggests the following conjecture: The energy spectra of chaotic quantum systems are characterized by 1/f noise.

/pdf/quantum-chaos-and-1-f-noise-392xmwatux.pdf

Quantum chaos and 1/f noise.

Many-body quantum chaos: Recent developments and applications to nuclei

Binding energies and other global properties of nuclei in the middle of the $\mathrm{pf}$ shell, such as $M1,E2,$ and Gamow-Teller sum rules, have been obtained using a new shell model code (NATHAN) written in quasispin formalism and using a $j\ensuremath{-}j$-coupled basis. An extensive comparison is made with the recently available shell model Monte Carlo results using the effective interaction KB3. The binding energies for nearly all the ${1f}_{7/2}$ nuclei are compared with the measured (and extrapolated) results.

Full 0ħω shell model calculation of the binding energies of the 1 f 7 / 2 nuclei

The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest-neighbor spacing distribution P(s) and the spectral rigidity given by the Delta(3)(L) statistic. It is shown that some standard unfolding procedures, such as local unfolding and Gaussian broadening, lead to a spurious saturation of Delta(3)(L) that spoils the relationship of this statistic with the regular or chaotic motion of the system. This effect can also be misinterpreted as Berry's saturation.

/pdf/misleading-signatures-of-quantum-chaos-3p2i6etbwf.pdf

Misleading signatures of quantum chaos.

In this paper we extend the shell model calculations previously made for the very neutron-rich nuclei with $Zg~14$ to Al, Mg, Na, Ne, F, and O, using the same valence space and effective interaction. Predictions are made for the neutron separation energies and for the location of the neutron drip line. We find that the isotopes of Ne, Na, and Mg are deformed for $Ng~22.$ In ${}^{40}\mathrm{Mg},$ which is at the edge of the drip line, the $N=28$ shell closure does not stand. By enlarging the valence space to include intruder states we are able to account for the vanishing of the $N=20$ neutron shell closure in a small region around ${}^{31}\mathrm{Na}$ that we delineate. The dominance of the intruders explains the collective features experimentally found in this region.

J. Retamosa

Papers

Quantum chaos and 1/f noise.

Many-body quantum chaos: Recent developments and applications to nuclei

Full 0ħω shell model calculation of the binding energies of the 1 f 7 / 2 nuclei

Misleading signatures of quantum chaos.

Shell model study of the neutron rich isotopes from oxygen to silicon