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EPJ Web of Conferences
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We discuss an innovative method for the description of inhomogeneous phases designed to improve the standard Ginzburg-Landau expansion. The method is characterized by two key ingredients. The first one is a moving average of the order parameter designed to account for the long-wavelength modulations of the condensate. The second one is a sum of the high frequency modes, to improve the description of the phase transition to the restored phase. The method is applied to compare the free energies of 1D and 2D inhomogeneous structures arising in the chirally symmetric broken phase.
Physical Review D
We develop an innovative technique for studying inhomogeneous phases with a spontaneous broken symmetry. The method relies on the knowledge of the exact form of the free energy in the homogeneous phase and on a specific gradient expansion of the order parameter. We apply this method to quark matter at vanishing temperature and large chemical potential, which is expected to be relevant for astrophysical considerations. The method is remarkably reliable and fast as compared to performing the full numerical diagonalization of the quark Hamiltonian in momentum space, and is designed to improve the standard Ginzburg-Landau expansion close to the phase transition points. For definiteness we focus on inhomogeneous chiral symmetry breaking, accurately reproducing known results for 1D and 2D modulations and examining novel crystalline structures, as well. Consistently with previous results, we find that the energetically favored modulation is the so-called 1D real kink crystal. We propose a qualitative description of the pairing mechanism to motivate this result.
Physical Review B, 1995
A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter.
Acta Crystallographica Section A Foundations of Crystallography, 1987
The structural description, symmetry and diffraction properties of incommensurate modulated phases are revised using a real-space framework. The superspace formalism usually employed is reformulated using a practical description where no multidimensional geometrical constructions are needed. The incommensurate structural distortion is described in terms
Physics Letters B, 2015
We analyze the presence of inhomogeneous phases in the QCD phase diagram within the framework of nonlocal chiral quark models. We concentrate in particular in the positions of the tricritical (TCP) and Lifshitz (LP) points, which are studied in a general context using a generalized Ginzburg-Landau approach. We find that for all the phenomenologically acceptable model parametrizations considered the TCP is located at a higher temperature and a lower chemical potential in comparison with the LP. Consequently, these models seem to favor a scenario in which the onset of the first order transition between homogeneous phases is not covered by an inhomogeneous, energetically favored phase. The behavior of strongly interacting matter under extreme conditions of temperature and/or density has been extensively studied along the last decades. However, after a considerable amount of theoretical and experimental work, the phase diagram of Quantum Chromodynamics (QCD) still remains poorly understood. For instance, qualitative features such as the precise nature of the chiral phase transition at low temperatures, or even the existence of a critical point, have not been firmly established yet. From the theoretical point of view, one of the main reasons for this state of affairs is that the ab-initio lattice QCD approach has difficulties to deal with the region of medium/low temperatures and moderately high densities, owing to the so-called "sign problem". Thus, most of the present knowledge about the behavior of strongly interacting matter arises from the study of effective models, which offer the possibility to get predictions of the transition features at regions that are not accesible through lattice techniques. In this context, in the last years some works have considered that the chiral symmetry restoration al low temperatures could be driven by the formation of non-uniform phases [1]. One particularly interesting result suggests that the expected critical endpoint of the first order chiral phase transition might be replaced by a so-called Lifshitz
EPJ Web of Conferences, 2018
We study the dynamics of the formation of inhomogeneous chirally broken phases in the final stages of a heavy-ion collision, with particular interest on the time scales involved in the formation process. The study is conducted within the framework of a Ginzburg-Landau time evolution, driven by a free energy functional motivated by the Nambu-Jona-Lasinio model. Expansion of the medium is modeled by one-dimensional Bjorken flow and its effect on the formation of inhomogeneous condensates is investigated. We also use a free energy functional from a nonlocal Nambu-Jona-Lasinio model which predicts metastable phases that lead to long-lived inhomogeneous condensates before reaching an equilibrium phase with homogeneous condensates.
Nuclear and Particle Physics Proceedings, 2016
A significant fraction of the current efforts in the QCD research community is focused on characterizing the phases of strong-interaction matter that occur at finite densities and temperatures. So far, most of the experimental probes have been limited to the relatively narrow window of the QCD phase diagram characterized by high temperatures and low chemical potentials, explored in high-energy ion collision experiments at RHIC and LHC. More recently, some new insight on the finite chemical potential region has been obtained by the energy-beam scan program at RHIC, aimed at possibly determining the existence of a critical point in the QCD phase transition. On the theoretical side, studies of strong interactions are also limited by the reliability of available methods. While the zero density, finite temperature region or the zero temperature, superdense region can be investigated with the help of well-established approaches like lattice and weakly coupled QCD respectively, the study of the intermediate densities and temperatures region has to rely on effective models and nonperturbative methods, some of which are still being developed. In the past few years, a growing number of compelling arguments, backed up by model calculations, pointed out that the intermediate-density region of the QCD phase diagram may be characterized by the formation of inhomogeneous condensates which spontaneously break some of the spatial symmetries of the theory. In the following we provide a brief recapitulation of these arguments and describe some recent results in a 3+1-dimensional QCD-inspired NJL model with quark-hole condensation in the form of a plane wave in the scalar and tensor channels. This model exhibits particular features in close analogy to its 1+1-dimensional counterpart, most notably an asymmetric spectral density and the arising of an anomalous contribution to the free energy.
Physics of Atomic Nuclei, 2012
We investigate inhomogeneous chiral symmetry breaking phases in the phase diagram of the two-avor Nambu-Jona-Lasinio model, concentrating on phases with one-dimensional modulations. It is found that the rst-order transition line in the phase diagram of homogeneous phases gets completely covered by an inhomogeneous phase which is bordered by second-order transition lines. The inhomogeneous phase turns out to be remarkably stable when vector interactions are included.
Low Temperature Physics, 2003
Two-dimensional (2D) excitation-emission spectra of biphenyl doped with free-base chlorin were measured at 5 K under various pressures up to 350 MPa. Besides the features related to zero-phonon lines and their phonon sidebands, a broad spectral band amounting to 80% of the total intensity at 5 K was revealed in the 2D spectra. The obtained inhomogeneous distribution function shows drastic changes with increasing pressure-the triplet structure observable at normal pressure in the incommensurate phase ICIII of biphenyl converges to a singlet in the high-pressure commensurate phase CI. These observations are assumed to reflect specific for incommensurate phases relaxation after an optical excitation of probe molecules and interaction of them with the incommensurate modulation wave.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2011
We propose a modified Gaussian ansatz to study binary condensates, trapped in harmonic and optical lattice potentials, both in miscible and immiscible domains. The ansatz is an apt one as it leads to the smooth transition from miscible to immiscible domains without any a priori assumptions. In optical lattice potentials, we analyze the squeezing of the density profiles due to the increase in the depth of the optical lattice potential. For this we develop a model with three potential wells, and define the relationship between the lattice depth and profile of the condensate.
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