Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0711.2806

Perturbative Treatment of Symmetry Breaking Within Random Matrix Theory

J. X. de Carvalho·M. S. Hussein·M. P. Pato·A. J. Sargeant
View original source ↗Read source document ↗Export metadata ↓

Abstract

We discuss the applicability, within the Random Matrix Theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both twofold and threefold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequecies is considered to be missing in the sample. Our findings are relevant to isospin violation study in nuclei.

Explore related subjects

nucl-thquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. X. de Carvalho, M. S. Hussein, M. P. Pato, A. J. Sargeant. 2008-03-15. Perturbative Treatment of Symmetry Breaking Within Random Matrix Theory. https://doi.org/10.1016/j.physleta.2008.05.035

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Chiral Symmetry and Its Restoration in QCD

Chiral symmetry is an approximate symmetry of QCD in the light-quark sector. Its spontaneous breaking in the QCD vacuum explains why the pion is anomalously light and why it plays a central role in nuclear physics, including the tensor component of the nuclear force and the saturation properties of nuclei. This article introduces chirality through the Dirac equation and shows how a fermion mass mixes left- and right-handed components, in close analogy with the Bogoliubov--Valatin theory of superconductivity. We then explain spontaneous symmetry breaking, the Nambu--Goldstone theorem, and the role of the chiral condensate as an order parameter. The axial $U(1)_A$ anomaly and its consequences, especially for the $η'$ meson, are discussed. Chiral effective models, including Nambu--Jona-Lasinio-type models, linear sigma models with anomaly terms, and parity-doublet models for baryons, are reviewed as tools for describing hadron properties and the equation of state of dense matter. Finally, we discuss how chiral symmetry may be partially restored at finite temperature and/or baryon density, and summarize experimental probes such as deeply bound pionic atoms, dilepton production in relativistic heavy-ion collisions, $η'$-mesic nuclei, and baryonic observables.

nucl-th↗
arXiv2026

Time-evolution formalism in the complex scaling method: Application to the two-proton decay of $^{6}$Be

We apply our complex-scaled time-evolution operator to the two-proton decay of $^{6}$Be. The nucleus is described as an $α+p+p$ three-body system with explicit Jacobi-coordinate rearrangement and the realistic Argonne $v8'$ NN interaction for the proton-proton subsystem. Starting from a confined initial wave packet, the decay dynamics are described by expansion over the complex-scaled eigenstates of the final Hamiltonian. The decay width extracted from the late-time survival probability agrees closely with that obtained from the CSM resonance pole. The time-dependent densities in different Jacobi coordinates reveal complementary aspects of the evolving three-body geometry, while the spin-singlet component remains dominant during the decay. In particular, the correlated two-proton configuration persists even in the presence of the strong short-range repulsion of the realistic NN interaction. These results demonstrate the applicability of the complex-scaled time-evolution framework to explicit three-body decay dynamics and provide a consistent description of the decay width, spatial evolution, and spin correlations of $^{6}$Be.

nucl-th↗
arXiv2026

Spin-One Secondary Pairing in Two-Flavor Color Superconductivity: Spinful Relativistic Superfluidity and Anomaly Matching

We study secondary pairing in the two-flavor color-superconducting (2SC) phase, where the residual ungapped quarks form a same-chirality $J^P=1^+$ condensate driven by an attractive instanton-induced interaction. We determine its symmetry realization, quasiparticle structure, anomaly matching, and low-energy effective theory. The pairing gap is necessarily nodal; in particular, the complex axial state has two point nodes and realizes a spinful relativistic superfluid. This state preserves the full chiral symmetry ${\rm SU}(2)_{\rm L}\times{\rm SU}(2)_{\rm R}$ while breaking the modified baryon-number symmetry ${\rm U}(1)_{\tilde{\rm B}}$ and spatial rotations, with rotations about the nodal axis locked to the condensate phase. This locking gives rise to a Berry term, the Mermin-Ho relation, and a type-B orientational Nambu-Goldstone mode in addition to the superfluid phonon. We also show how anomaly matching is reorganized by secondary pairing: the perturbative mixed ${\rm SU}(2)_{\rm L,R}^2{\rm U}(1)_{\tilde{\rm B}}$ anomaly is realized by a Wess-Zumino coupling of the superfluid phonon, whereas the ${\rm SU}(2)_{\rm L}$ and ${\rm SU}(2)_{\rm R}$ Witten anomalies are carried by the point-node Bogoliubov-de Gennes flavor doublets. The resulting theory provides a concrete dense-QCD realization of a spinful relativistic superfluid with nodal fermions required by anomaly matching.

nucl-th↗