Nose has derived a set of dynamical equations that can be shown to give canonically distributed positions and momenta provided the phase space average can be taken into the trajectory average, i.e., the system is ergodic [S. Nose, J. Chem. Phys. 81, 511 (1984), W. G. Hoover, Phys. Rev. A 31, 1695 (1985)]. Unfortunately, the Nose–Hoover dynamics is not ergodic for small or stiff systems. Here a modification of the dynamics is proposed which includes not a single thermostat variable but a chain of variables, Nose–Hoover chains. The ‘‘new’’ dynamics gives the canonical distribution where the simple formalism fails. In addition, the new method is easier to use than an extension [D. Kusnezov, A. Bulgac, and W. Bauer, Ann. Phys. 204, 155 (1990)] which also gives the canonical distribution for stiff cases.

/pdf/nose-hoover-chains-the-canonical-ensemble-via-continuous-x9g8wtwvs8.pdf

Nosé-Hoover chains : the canonical ensemble via continuous dynamics

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

Nuclear collisions can compress nuclear matter to densities achieved within neutron stars and within core-collapse supernovae. These dense states of matter exist momentarily before expanding. We analyzed the flow of matter to extract pressures in excess of 10 34 pascals, the highest recorded under laboratory-controlled conditions. Using these analyses, we rule out strongly repulsive nuclear equations of state from relativistic mean field theory and weakly repulsive equations of state with phase transitions at densities less than three times that of stable nuclei, but not equations of state softened at higher densities because of a transformation to quark matter.

https://science.sciencemag.org/content/sci/298/5598/1592.full.pdf

Determination of the equation of state of dense matter.

Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions

“Quantum” molecular dynamics—a dynamical microscopic n-body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions

In nuclear collisions induced by stable or radioactive neutron-rich nuclei a transient state of nuclear matter with an appreciable isospin asymmetry as well as thermal and compressional excitation can be created. This offers the possibility to study the properties of nuclear matter in the region between symmetric nuclear matter and pure neutron matter. In this review, we discuss recent theoretical studies of the equation of state of isospin-asymmetric nuclear matter and its relations to the properties of neutron stars and radioactive nuclei. Chemical and mechanical instabilities as well as the liquid-gas phase transition in asymmetric nuclear matter are investigated. The in-medium nucleon-nucleon cross sections at different isospin states are reviewed as they affect significantly the dynamics of heavy ion collisions induced by radioactive beams. We then discuss an isospin-dependent transport model, which includes different mean-field potentials and cross sections for the proton and neutron, and its applic...

http://cds.cern.ch/record/329650/files/9707014.pdf

Isospin Physics in Heavy-Ion Collisions at Intermediate Energies

Canonical ensembles from chaos

The disappearance of collective flow in nucleus-nucleus collisions occurs at an incident energy ([ital E][sub bal]) where the attractive scattering dominant at low energies balances the repulsive scattering dominant at high energies. We have performed the first systematic study of the entrance-channel mass dependence of the disappearance of flow and hence [ital E][sub bal]. The new data presented for the C+C, Ne+Al, Ar+Sc, and Kr+Nb systems show that [ital E][sub bal] scales as [ital A][sup [minus]1/3] where [ital A] is the mass of the combined system. Boltzmann-Uehling-Uehlenbeck model calculations show trends which are in qualitative agreement with these new results.

Wolfgang Bauer

Papers

Isospin Physics in Heavy-Ion Collisions at Intermediate Energies

Canonical ensembles from chaos

Mass dependence of the disappearance of flow in nuclear collisions.

Hadronic Interferometry in Heavy-Ion Collisions

New approach to fragmentation reactions: The nuclear lattice model☆