It is demonstrated that an isolated generic quantum many-body system does relax to a state well described by the standard statistical mechanical prescription The thermalization happens at the level of individual eigenstates, allowing the computation of thermal averages from knowledge of any eigenstate in the microcanonical energy window An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive Recently, meaningful experimental studies1,2 of the problem have become possible, stimulating theoretical interest3,4,5,6,7 In generic isolated systems, non-equilibrium dynamics is expected8,9 to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible10 For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete11 Some recent studies4,5 even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems Here we demonstrate that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch12 and Srednicki13 A striking consequence of this eigenstate-thermalization scenario, confirmed for our system, is that knowledge of a single many-body eigenstate is sufficient to compute thermal averages—any eigenstate in the microcanonical energy window will do, because they all give the same result

Thermalization and its mechanism for generic isolated quantum systems

The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications.

Self-consistent mean-field models for nuclear structure

Random-matrix theories in quantum physics : common concepts

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.

Random Matrix Theories in Quantum Physics: Common Concepts

Table of experimental nuclear ground state charge radii: An update

The root-mean-square radius for neutrons in nuclei is investigated in the Skyrme Hartree-Fock model. The main source of theoretical variation comes from the exchange part of the density-dependent interaction which can be related to a basic property of the neutron equation of state. A precise measurement of the neutron radius in ${}^{208}\mathrm{Pb}$ would place an important new constraint on the equation of state for neutron matter. The Friedman-Pandharipande neutron equation of state would lead to a very precise value of $0.16\ifmmode\pm\else\textpm\fi{}0.02\mathrm{fm}$ for the difference between the neutron and the proton root-mean-square radius in ${}^{208}\mathrm{Pb}$.

https://people.nscl.msu.edu/~brown/brown-all-papers/261-2000-PhysRevLett.85.5296.pdf

Neutron radii in nuclei and the neutron equation of state

I talk about appearance of new magic numbers and disappearance of some existing usual magic numbers in exotic nuclei far from the s-stability line. This is a very intriguing problem, and its mechanism is related to basic properties of nucleon-nucleon interaction in a very robust way. Several exotic features of nuclei far from stability will be mentioned in a unified way in relation to this interaction.

https://people.nscl.msu.edu/~brown/brown-all-papers/274-2001-PhysRevLett.87.082502.pdf

Magic numbers in exotic nuclei and spin-isospin properties of the NN interaction.

We derive new Hamiltonians for the sd shell, USDA and USDB, based on a renormalized G matrix with linear combinations of two-body matrix elements adjusted to fit a complete set of data for experimental binding energies and excitation energies for the sd-shell nuclei. These Hamiltonians provide a new level of precision for realistic sd-shell wave functions for applications to nuclear structure and nuclear astrophysics.

https://people.nscl.msu.edu/~brown/brown-all-papers/377-2006-PhysRevC.74.034315-usdab.pdf

New USD Hamiltonians for the sd shell

A new set of Skyrme parameters is obtained from a fit to the binding energies, rms charge radii, and single-particle energies of both normal and exotic spherical nuclei. Nuclear matter and neutron matter properties are used to put constraints on the parameters which are not well determined from the nuclear data. Special problems with the Nolen-Schiffer anomaly and the spin-orbit interaction are discussed. @S0556-2813 ~98!02107-4#

B. Alex Brown

Papers

Neutron radii in nuclei and the neutron equation of state

Magic numbers in exotic nuclei and spin-isospin properties of the NN interaction.

New USD Hamiltonians for the sd shell

New Skyrme interaction for normal and exotic nuclei

The nuclear shell model as a testing ground for many-body quantum chaos