CHARGED PION CONDENSATION PHENOMENON OF DENSE BARYONIC MATTER INDUCED BY FINITE VOLUME: THE NJL₂ MODEL CONSIDERATION

Abstract

The properties of two-flavored massless Nambu-Jona-Lasinio model in (1+1)-dimensional R 1 × S 1 spacetime with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials µI , µ. The consideration is performed in the large Nc limit, where Nc is the number of colored quarks. It is shown that at L = ∞ (L is the length of the circumference S 1 ) the pion condensation (PC) phase with zero quark number density is realized at arbitrary nonzero µI and for rather small values of µ. However, at arbitrary finite values of L the phase portrait of the model contains the PC phase with nonzero quark number density (in the case of periodic boundary conditions for quark fields). Hence, finite sizes of the system can serve as a factor promoting the appearance of the PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of L.

Charged Pion Condensation in Dense Quark Matter: Nambu–Jona-Lasinio Model Study

“…In the previous Section 2 (see 2.4) it was shown that charged PC does not take place in neutral quark matter with isospin asymmetry. But recently there have been found conditions that can be realized in real physical situations and can lead to the appearance of charged PC in dense quark matter [34,[37][38][39][40][41]. Some of these conditions are elaborated in the framework of the (3+1)-dimensional NJL model discussed in the previous section [40,41].…”

“…In this mini-review we discuss the present status of the charged PC phase in dense quark matter and, especially, pay attention to the factors promoting the emergence of charged PC phenomenon in dense quark matter. Namely, in the paper [34] it was found that this phase might be realized in dense baryonic system that has finite size. It was also demonstrated in [37] that in dense baryonic matter spatially inhomogeneous charged PC might appear, and more recently it was found in [38][39][40][41][42] that chiral imbalance is another interesting factor that can induce a charged PC phase.…”

The Zeeman effect in a modified Gross—Neveu model in (2 + 1)-dimensional space—time with compactification

“…THE PHASE STRUCTURE OF THE MODEL WITH ACCOUNT FOR THE CHEMICAL POTENTIAL AND TEMPERATURE If the term that is independent of σ is written out explicitly in (8), the effective potential can be rewrit ten as (9) Using the formula , ln which can be found, for example, in [19], after some simplifications, the effective potential can be rewritten as (11) where (12) (13) (14) here, Li are special functions polylogarithms [20], =…”

“…Thus, a Lagrangian similar to the (1 + 1) dimensional Gross-Neveu model occurs in the study of one dimensional polymers, such as polyacet ylene [3,4], and a Lagrangian similar to the (2 + 1) dimensional Gross-Neveu model occurs in the study of two dimensional polymers (such as graphene, see, for example, [5]). Thus, the Gross-Neveu model that is used for the description of such systems with account for the influences of such parameters as tem perature, chemical potential, and external fields [5][6][7][8][9] is of special interest.…”

“…In this study, we do not consider the Aharonov-Bohm effect that is caused by the magnetic field; the influence of this effect without account for the Zee man effect was considered in [8,9,12]. The simulta neous accounting for the Zeeman and Aharonov-Bohm effects is a subject for future studies.…”