## Arts & Sciences Electronic Theses and Dissertations

Summer 8-15-2017

#### Author's School

Graduate School of Arts and Sciences

Physics

#### Degree Name

Doctor of Philosophy (PhD)

Dissertation

#### Abstract

Understanding the behavior of matter at ultra-high density such as neutron stars require the knowledge of ground state properties of Quantum chromodynamics (QCD) at finite chemical potential. However, this task has turned out to be very difficult because of two main reasons: 1) QCD may still be strongly coupled at those regimes making perturbative calculations unreliable and 2) QCD at finite density suffers from the sign problem that makes the use of lattice simulation problematic and it even affects phenomenological models. In the first part of this thesis, we show that the sign problem in analytical calculations of finite density models can be solved by considering the \textit{CK}-symmetric, where \textit{C} is charge conjugation and \textit{K} is complex conjugation, complex saddle points of the effective action. We then explore the properties and consequences of such complex saddle points at non-zero temperature and density. Due to \textit{CK} symmetry, the mass matrix eigenvalues in these models are not always real but can be complex, which results in damped oscillation of the density-density correlation function, a new feature of finite density models. To address the generality of such behavior, we next consider a lattice model of QCD with static quarks at strong-coupling. Computation of the mass spectrum confirms the existence of complex eigenvalues in much of temperature-chemical potential plane. This provides an independent confirmation of our results obtained using phenomenological models of QCD.

The existence of regions in parameter space where density-density correlation function exhibit damped oscillation is one of the hallmarks of typical liquid-gas system. The formalism developed to tackle the sign problem in QCD models actually gives a simple understanding for the existence of such behavior in liquid-gas system. To this end, we develop a generic field theoretic model for the treatment of liquid-gas phase transition. An effective field theory at finite density derived from a fundamental four dimensional field theory turns out to be complex but \textit{CK} symmetric. The existence of \textit{CK} symmetry results in complex mass eigenvalues, which in turn leads to damped oscillatory behavior of the density-density correlation function.

In the last part of this thesis, we study the effect of large amplitude density oscillations on the transport properties of superfluid nuclear matter. In nuclear matter at neutron-star densities and temperature, Cooper pairing leads to the formations of a gap in the nucleon excitation spectra resulting in exponentially strong Boltzmann suppression of many transport coefficients. Previous calculations have shown evidence that density oscillations of sufficiently large amplitude can overcome this suppression for flavor-changing $\beta$ processes via the mechanism of gap-bridging". We address the simplifications made in that initial work, and show that gap bridging can counteract Boltzmann suppression of neutrino emissivity for the realistic case of modified Urca processes in matter with $^3P_2$ neutron pairing.

English (en)

#### Chair and Committee

Michael C. Ogilvie

#### Committee Members

Mark G. Alford, Claude Bernard, Bhupal Dev, Renato Feres,