Non-Fermi-liquid specific heat of normal degenerate quark matter

Abstract

We compute the low-temperature behavior of the specific heat of normal (non-color-superconducting) degenerate quark matter as well as that of an ultradegenerate electron gas. Long-range magnetic interactions lead to non-Fermi-liquid behavior with an anomalous leading T lnT ÿ1 term. Depending on the thermodynamic potential used as a starting point, this effect appears as a consequence of the logarithmic singularity in the fermion self-energy at the Fermi surface or directly as a contribution from the only weakly screened quasistatic magnetic gauge bosons. We show that a calculation of Boyanovsky and de Vega claiming the absence of a leading T lnT ÿ1 term missed it by omitting vector boson contributions to the internal energy. Using a formulation which collects all nonanalytic contributions in bosonic ring diagrams, we systematically calculate corrections beyond the well-known leading-log approximation. The higher-order terms of the low-temperature expansion turn out to also involve fractional powers T 32n=3 and we explicitly determine their coefficients up to and including order T 7=3 as well as the subsequent logarithmically enhanced term T 3 lnc=T. We derive also a harddense-loop resummed expression which contains the infinite series of anomalous terms to leading order in the coupling and which we evaluate numerically. At low temperatures, the resulting deviation of the specific heat from its value in naive perturbation theory is significant in the case of strongly coupled normal quark matter and thus of potential relevance for the cooling rates of (proto)neutron stars with a quark matter component.

Cool Quark Matter

“…with δ ≈ −0.8563832 [10]. Some higher order terms to the former expansion can be obtained from [27,28].…”

“…At lower temperatures, in particular when T becomes of order m E ∼ gµ B , an increasing set of low-lying Matsubara modes, however, needs to be resummed. This poses a problem, which has been tackled in the regime T ∼ g x µ B , x > 1, by the Hard Dense Loop (HDL) approach, revealing non-Fermi liquid behavior [25][26][27][28].…”

Unconventional behavior of Dirac fermions in three-dimensional gauge theory

“…Note that this logarithmic expression does not contradict our results. Actually, the power-law specific heat presented here amounts to a summation of all powers of lnT [56,57,60,68].…”

Non-Fermi liquid behavior of thermal relaxation time in degenerate electron plasma

“…The other quantity which we require for the estimation of relaxation time is the specific heat. It has already been derived in the context of degenerate quark matter in [9,10]. For the degenerate electron gas it can be written as,…”

“…This can be attributed to the absence of static screening of the magnetic photon [8]. Several investigations have been performed in recent years where incorporation of such corrections have been seen to have serious implications on various physical quantities like pressure, entropy, viscosity or quantities like drag and diffusion coefficients [9][10][11][12]. Non-Fermi liquid behavior for the neutrino emissivity or the neutrino mean free path have also been studied extensively [13][14][15].…”