Variational Theory of Hot Dense Matter
type: CreativeWork
description: We develop a variational theory of hot nuclear matter in neutron stars and supernovae. It can also be used to study charged, hot nuclear matter which may be produced in heavy-ion collisions. This theory is a generalization of the variational theory of cold nuclear and neutron star matter based on realistic models of nuclear forces and pair correlation operators. The present approach uses microcanonical ensembles and the variational principle obeyed by the free energy. We show that the correlated states of the microcanonical ensemble at a given temperature T and density rho can be orthonormalized preserving their diagonal matrix elements of the Hamiltonian. This allows for the minimization of the free energy without corrections from the nonorthogonality of the correlated basis states, similar to that of the ground state energy. Samples of the microcanonical ensemble can be used to study the response, and the neutrino luminosities and opacities of hot matter. We present methods to orthonormalize the correlated states that contribute to the response of hot matter. We apply this variational theory to symmetric nuclear matter and pure neutron matter. This extension generalizes to finite temperatures, the many body technique used in the construction of the zero temperature Akmal-Pandharipande-Ravenhall equation of state. We discuss how the formalism can be used for practical calculations of hot dense matter. Our calculations are a significant improvement over the previous calculation due to Friedman and Pandharipande. The Hamiltonian contains modern realistic two nucleon and three nucleon interactions along with relativistic boost corrections. Expectation values of various operators, including the Hamiltonian, are calculated using cluster expansion and chain summation techniques. The pair correlation operator is now calculated at every density and temperature. Neutral pion condensation along with the associated isovector spin longitudinal sum rule is analyzed. The equatio…
abstract: We develop a variational theory of hot nuclear matter in neutron stars and supernovae. It can also be used to study charged, hot nuclear matter which may be produced in heavy-ion collisions. This theory is a generalization of the variational theory of cold nuclear and neutron star matter based on realistic models of nuclear forces and pair correlation operators. The present approach uses microcanonical ensembles and the variational principle obeyed by the free energy. We show that the correlated states of the microcanonical ensemble at a given temperature T and density rho can be orthonormalized preserving their diagonal matrix elements of the Hamiltonian. This allows for the minimization of the free energy without corrections from the nonorthogonality of the correlated basis states, similar to that of the ground state energy. Samples of the microcanonical ensemble can be used to study the response, and the neutrino luminosities and opacities of hot matter. We present methods to orthonormalize the correlated states that contribute to the response of hot matter. We apply this variational theory to symmetric nuclear matter and pure neutron matter. This extension generalizes to finite temperatures, the many body technique used in the construction of the zero temperature Akmal-Pandharipande-Ravenhall equation of state. We discuss how the formalism can be used for practical calculations of hot dense matter. Our calculations are a significant improvement over the previous calculation due to Friedman and Pandharipande. The Hamiltonian contains modern realistic two nucleon and three nucleon interactions along with relativistic boost corrections. Expectation values of various operators, including the Hamiltonian, are calculated using cluster expansion and chain summation techniques. The pair correlation operator is now calculated at every density and temperature. Neutral pion condensation along with the associated isovector spin longitudinal sum rule is analyzed. The equatio…
author: Mukherjee, Abhishek
language: eng
keywords: Physics, Astronomy and Astrophysics
date published: 2015-09-25T20:03:18Z
date modified: 2026-07-22T22:26:14Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/80617