Nonzero Chemical Potential Research Articles

Different Aspects of Entropic Cosmology

We provide a short review of the recent developments in entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change in entropy of the apparent horizon during the cosmic evolution of the universe; in particular, it is expressed by TdS=−d(ρV)+WdV (where W is the work density and other quantities have their usual meanings). In this way, the first law actually links various theories of gravity with the entropy of the apparent horizon. This leads to a natural question—“What is the form of the horizon entropy corresponding to a general modified theory of gravity?”. The second law of horizon thermodynamics states that the change in total entropy (the sum of horizon entropy + matter fields’ entropy) with respect to cosmic time must be positive, where the matter fields behave like an open system characterised by a non-zero chemical potential. The second law of horizon thermodynamics importantly provides model-independent constraints on entropic parameters. Finally, we discuss the standpoint of entropic cosmology on inflation (or bounce), reheating and primordial gravitational waves from the perspective of a generalised entropy function.

Revisiting the spatially inhomogeneous condensates in the (1+1) -dimensional chiral Gross–Neveu model via the bosonic two-point function in the infinite-N limit

This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the (1+1) -dimensional chiral Gross–Neveu (GN) model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results (Schön and Thies 2000 At The Frontier of Particle Physics: Handbook of QCD, Boris Ioffe Festschrift vol 3 (World Scentific) ch 33, pp 1945–2032; Boehmer et al 2008 Phys. Rev. D 78 065043; Boehmer and Thies 2009 Phys. Rev. D 80 125038; Thies 2018 Phys. Rev. D 98 096019; Thies 2022 Phys. Rev. D 105 116003). The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-N limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic 1-particle irreducible two-point vertex function of the chiral GN model and the spinodal line of the GN model.

Squeezing effect on D+∕D− with nonzero chemical potential

The medium mass modification may lead to a squeezing effect. In the baryonic medium, the mass of D meson was expected to reduce and the in-medium masses of [Formula: see text] and [Formula: see text] may show a splitting effect, and the chemical potential of D meson may be not zero. We study the squeezing effect on the yield ratio [Formula: see text] with nonzero chemical potential. Due to the in-medium mass splitting, the squeezing effect on the momentum distributions of [Formula: see text] and [Formula: see text] are different. Without the squeezing effect, the yield ratio [Formula: see text] remains constant as the transverse momentum increases. The yield ratio [Formula: see text] is affected by the squeezing effect, resulting in a dependence on transverse momentum. An increase in transverse momentum leads to a decrease in the yield ratio, especially when there is a high chemical potential. Additionally, the in-medium mass splitting amplifies this phenomenon. The yield ratio [Formula: see text] with nonzero chemical potential approaches 1 when there is a large average in-medium mass reduction, which becomes more evident at higher transverse momentum. The study of the squeezing effect on the yield ratio [Formula: see text] with nonzero chemical potential may be meaningful for the CBM and PANDA experiments of the FAIR project at GSI.

Torsional constitutive relations at finite temperature

The general form of the linear torsional constitutive relations at finite temperature of the chiral current, energy-momentum tensor, and spin energy potential are computed for a chiral fermion fluid minimally coupled to geometric torsion and with nonzero chiral chemical potential. The corresponding transport coefficients are explicitly calculated in terms of the energy and number densities evaluated at vanishing torsion. A microscopic calculation of these constitutive relations in some particular backgrounds is also presented, confirming the general structure found.

Chemical potential (in)dependence of hadron scatterings in the hadronic phase of QCD-like theories and its applications

We formulate a method for calculating the hadron-hadron scattering amplitudes at nonzero chemical potential (μ) in the hadronic phase at zero temperature, where the baryon number symmetry remains to be violated. Although it is widely believed that the physical quantities do not change even if we turn on a small μ at zero temperature, the shape of correlation functions for a single hadron depends on μ. Then, the dispersion relation of the single hadron is modified to E(p, μ) = p2+m2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{{\ extbf{p}}^2+{m}^2} $$\\end{document} – μnO. Here, m and nO denote the hadron mass at μ = 0 and the quantum number, respectively. From this relation, it is possible that the effective mass of the hadron depends on μ. We extend the HAL QCD method at μ = 0 to the case of μ ≠ 0, which allows us to extract the scattering phase shifts via the interaction potential. We have found that the interaction potential can depend on μ only through the effective mass while the scattering phase shifts, obtained by solving the Schrödinger equation with the interaction potential, are independent of μ. We also numerically analyze the S-wave scatterings of two pions with isospin I = 2 and two scalar diquarks within the framework of QC2D at nonzero quark chemical potential. While the lattice is not exactly set to zero temperature, the μ-independence can be observed. Furthermore, we improve the results for the S-wave scatterings of two hadrons obtained above by taking the μ-independence for granted. Thanks to the asymmetric property of the correlation functions for diquarks at μ ≠ 0, we can access a long-τ regime and can reduce the systematic error coming from inelastic contributions.

Measuring neutrino mass and asymmetry with matter pairwise velocities

ABSTRACT Neutrinos are believed to be the most abundant fermions in the Universe, but their masses are unknown, except for being non-zero but much smaller than other fermions. Cosmological relic neutrinos could also have non-zero chemical potentials (or asymmetries). Using neutrino-involved N-body simulations, we investigate the neutrino effects on the matter pairwise velocity, which itself is an interesting probe of cosmology. We find that for light-halo ([1011, 1013] M⊙) mean pairwise velocity, in the transition range ([4, 15] Mpc), the effects of neutrino masses overwhelm the effects of neutrino asymmetries, while in the two-halo-group range ([25, 50] Mpc), for both light and heavy haloes ([1013, 1015] M⊙), the effects of neutrino asymmetries dominate, making it possible to disentangle the two effects. We provide fitting formulae to quantify the effects of neutrino mass and asymmetry on halo–halo pairwise velocities.

QCD material parameters at zero and non-zero chemical potential from the lattice

Using an eighth-order Taylor expansion in baryon chemical potential, we recently obtained the (2+1)-flavor QCD equation of state (EoS) at nonzero conserved charge chemical potentials from the lattice. We focused on strangeness-neutral, isospin-symmetric QCD matter, which closely resembles the situation encountered in heavy-ion collision experiments. Using this EoS, we present here results on various QCD material parameters; in particular we compute the specific heat, speed of sound, and compressibility along appropriate lines of constant physics. We show that in the entire range relevant for the beam energy scan at RHIC, the specific heat, speed of sound, and compressibility show no indication for an approach to critical behavior that one would expect close to a possibly existing critical endpoint.

Dual simulation of a Polyakov loop model at finite baryon density: Correlations and screening masses

Computations of screening masses in finite-temperature QCD at finite density are plagued by the sign problem and have been performed so far with an imaginary chemical potential. Here, we use a dual formulation of a Polyakov-loop model which allows the determination of screening masses at real baryon chemical potential. This is a second paper in a series devoted to a detailed study of dual Polyakov-loop models at finite density. While the first paper was mainly devoted to establishing the phase diagram of the model, here we compute correlation functions of the Polyakov loops and the second-moment correlation length at non-zero chemical potential. This enables us to evaluate numerically the screening masses from correlations of the real and imaginary parts of the Polyakov loops. We also compute these masses in the mean-field approximation and compare with numerical results. In addition, we provide a quantitative improvement of the general phase diagram presented in the first paper.

Nonrelativistic Dirac fermions on the torus

Two dimensional conformal field theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes these theories away from criticality, where many of their aspects are still poorly understood. In this note we make a step towards filling this gap, by analyzing the theory of a Dirac fermion on the torus, deformed by a mass term and a chemical potential for the particle number symmetry. The theory breaks conformal and Lorentz invariance, and we study its spectrum and partition function. We also focus on two limits that are interesting on their own right: a massless relativistic fermion with nonzero chemical potential (a simple model for CFTs at finite density), and nonrelativistic Schrodinger fermions (of relevance in condensed matter systems). Taking inspiration from recent developments in massive modular forms, we obtain a representation of the torus free energy based on Fourier-transforming over a twisted boundary condition. This dual representation fullfills many properties analogous to modular invariance in CFTs. In particular, we use this result to derive Cardy-like formulas for the high energy density of states of these theories.

Properties of kaon at non-zero temperature and baryon chemical potential

Properties of kaon at non-zero temperature and baryon chemical potential

Thermodynamics of the electron–positron plasma at very high temperatures and sources of annihilation γ-quanta in our Galaxy

Thermodynamic properties and equations of state of the electron–positron plasma (or gas) at high and very high temperatures (T≥170 keV) are derived and investigated. We have derived a number of simple analytical formulas for the Fermi–Dirac distribution functions, which can be applied to various Fermi gases and plasmas in different cases. Almost all these formulas are represented in the form of series expansions. The coefficients in these expansions are relatively simple functions of the μT ratio, where T is the temperature and μ is the chemical potential of this Fermi system. Our approach works well for high-temperature electron–positron plasmas, which are in thermal equilibrium with the photon gas of annihilation γ-quanta, and for the model gas of fermions, where there is no radiation at all. The first case corresponds to the ultra-relativistic limit for high-temperature electron–positron plasma, while the second case represents a model Fermi gas of particles, which has some non-zero chemical potential. By investigating sources of annihilation γ-quanta in our Galaxy, we have arrived to a remarkable conclusion about the high-temperature limit in our regular (photon) optics.

Integrating by parts at finite density

Both nonzero temperature and chemical potentials break the Lorentz symmetry present in vacuum quantum field theory by singling out the rest frame of the heat bath. This leads to complications in the application of thermal perturbation theory, including the appearance of novel infrared divergences in loop integrals and an apparent absence of four-dimensional integration-by-parts (IBP) identities, vital for high-order computations. Here, we propose a new strategy that enables the use of IBP techniques in the evaluation of Feynman integrals, in particular vacuum or bubble diagrams, in the limit of vanishing temperature T but nonzero chemical potentials μ. The central elements of the new setup include a contour representation for the temporal momentum integral, the use of a small but nonzero T as an IR regulator, and the systematic application of both temporal and spatial differential operators in the generation of linear relations among the loop integrals of interest. The relations we derive contain novel inhomogeneous terms featuring differentiated Fermi-Dirac distribution functions, which severely complicate calculations at nonzero temperature, but are shown to reduce to solvable lower-dimensional objects as T tends to zero. Pedagogical example computations are kept at the one- and two-loop levels, but the application of the new method to higher-order calculations is discussed in some detail.

Bose-Einstein condensation of photons in microcavity plasmas.

Bose-Einstein condensation of a finite number of photons propagating inside a plasma-filled microcavity is investigated. The nonzero chemical potential is provided by the electrons, which induces a finite photon mass and allows condensation to occur. We derive an equationthat models the evolution of the photon-mode occupancies, with Compton scattering taken into account as the mechanism of thermalization. The kinetic evolution of the photon spectrum is solved numerically, and we find evidence of condensation down to nanosecond timescales for typical microplasma conditions, n_{e}∼10^{14}-10^{15}cm^{-3}. The critical temperature scales almost linearly with the number of photons, and we find high condensate fractions at microcavity-plasma temperatures, for experimentally achievable cavity lengths (100-500µm) and photon numbers (10^{10}-10^{12}).

Effects of the QCD critical point on the spectra and flow coefficients of hadrons

The space-time evolution of the hot and dense fireball of quarks and gluons produced in ultrarelativistic heavy-ion collisions at nonzero baryonic chemical potential and temperature has been studied by using relativistic dissipative hydrodynamics. For this purpose, a numerical code has been developed to solve the relativistic viscous causal hydrodynamics in ($3+1$) dimensions with the inclusion of QCD critical point ($CP$) through the equation of state and scaling behavior of transport coefficients. We compute the transverse momentum spectra, directed and elliptic flow coefficients of pions and protons to comprehend the effect of $CP$ on these observables. It is found that the integration over the entire space-time history of the fireball largely obliterates the effects of $CP$ on the spectra and flow coefficients for the event averaged initial conditions considered here.

Meson excitation time as a probe of holographic critical point

We study the time evolution of expectation value of Wilson loop as a non-local observable in a strongly coupled field theory with a critical point at finite temperature and nonzero chemical potential, which is dual to an asymptotically AdS charged black hole via gauge/gravity duality. Due to inject of energy into the plasma, the temperature and a chemical potential increase to finite values and the plasma experiences an out-of-equilibrium process. By defining meson excitation time t_{ex} as a time at which the meson falls into the final excited state, we investigate the behavior of t_{ex} near the critical point as the system evolves towards the critical point. We observe that by increasing the interquark distance the dynamical critical exponent increases smoothly. Also, we obtain for slow quenches different values of the dynamical critical exponent, although for fast quenches our result for the dynamical critical exponent is in agreement with the one that is reported for studying the quasi-normal modes. Consequently, this indicates that in this model for fast quenches and small values of interquark distances the gauge invariant Wilson loop is a good non-local observable to probe the critical point.

Tunable and giant spatial Goos–Hänchen shifts in a parity-time symmetric Cantor photonic crystals incorporated with a centered graphene layer

In this study, we present the spectral features of a one-dimensional parity-time symmetric layered structure was composed of two quasi-photonic crystals which submit to the Cantor sequence and a graphene layer is embedded in the center of the quasi-crystals. Exceptional points, reflection and transmission spectra and the spatial Goos-Hänchen (GH) shifts are investigated at two distinct terahertz regions in the presence and absence of the graphene layer and compared them. The effect of the modification of imaginary part of refractive index of constituting gain and loss media are also examined. Our results show that, the proposed structure display giant enhanced GS shifts which are tunable with the chemical potential of embedded graphene layer, while GH shifts are weak in the absence of graphene layer. Results display different value and sign of GH shifts for the zero and nonzero chemical potentials. Very extreme GH shifts are obtained by judicious choice of chemical potential and imaginary value of the refractive index of constituting materials. Our results display that not only the photonic bandgap edge modes, but also bandgap modes can support giant GH shifts at Terahertz frequencies. Functionally, these types of structures are very desirable for designing optoelectronic devices that can be adjusted by the amount of chemical potential.

Lattice QCD equation of state at finite chemical potential from an alternative resummation: Strangeness neutrality and beyond

In this contribution we present a resummation of the Quantum Chromodynamics (QCD) equation of state from lattice simulations at imaginary chemical potentials. We generalize the scheme introduced in a previous work [1], to the case of non-zero strangeness chemical potential. We present continuum extrapolated results for thermodynamic observables in the temperature range 130MeV ≤ T ≤ 280 MeV, for chemical potentials up to μB/T = 3:5, along the strangeness neutral line. Furthermore, we relax the constraint of strangeness neutrality, by extrapolating to small values of the strangeness-to-baryon-number ratio R = nS / nB.

Effective Lagrangian at nonzero isospin chemical potential

We revisit the most general effective Lagrangian within chiral perturbation theory at nonzero isospin chemical potential ${\ensuremath{\mu}}_{I}$ up to $\mathcal{O}({p}^{4})$. In addition to the contributions already considered in the literature, we discuss the effects of new terms allowed by the symmetries derived within the external source method including spurion fields, as well as linear-field corrections relevant to $\mathcal{O}({p}^{4})$. We study the influence of those new contributions to the free energy density at zero temperature and observables derived from it, such as the pion and quark condensates and the isospin density. Corrections are shown to be compatible with lattice results, which favor nonzero values for the low-energy constants (LECs) multiplying the new $\mathcal{O}({p}^{2})$ and $\mathcal{O}({p}^{4})$ field operators in the Lagrangian. In particular, the $\mathcal{O}({p}^{4})$ LECs are renormalized to render the free energy density finite. Constraints on the LECs arise from preserving the physical condition ${n}_{I}({\ensuremath{\mu}}_{I}<{\ensuremath{\mu}}_{c})=0$, while ${\ensuremath{\mu}}_{c}={M}_{\ensuremath{\pi}}$ still holds to leading order and can be maintained to next-to-leading order through an additional constraint requiring the new LECs.

Grassmann higher-order tensor renormalization group approach for two-dimensional strong-coupling QCD

We present a tensor-network approach for two-dimensional strong-coupling QCD with staggered quarks at nonzero chemical potential. After integrating out the gauge fields at infinite coupling, the partition function can be written as a full contraction of a tensor network consisting of coupled local numeric and Grassmann tensors. To evaluate the partition function and to compute observables, we develop a Grassmann higher-order tensor renormalization group method, specifically tailored for this model. During the coarsening procedure, the blocking of adjacent Grassmann tensors is performed analytically, and the total number of Grassmann variables in the tensor network is reduced by a factor of two at each coarsening step. The coarse-site numeric tensors are truncated using higher-order singular value decompositions. The method is validated by comparing the partition function, the chiral condensate and the baryon density computed with the tensor method with exact analytical results on small lattices up to volumes of 4×4. For larger volumes, we present first tensor results for the chiral condensate as a function of the mass and volume, and observe that the chiral symmetry is not broken dynamically in two dimensions. We also present tensor results for the number density as a function of the chemical potential, which hint at a first-order phase transition.

Non-perturbative renormalization of the QCD flavour-singlet local vector current

We compute non-perturbatively the renormalization constant of the flavour-singlet local vector current ZV in lattice QCD with 3 massless flavours. Gluons are discretized by the Wilson plaquette action while quarks by the O(a)-improved Wilson–Dirac operator. The constant ZV is fixed by comparing the expectation values (1-point functions) of the conserved and local vector currents at finite temperature in the presence of shifted boundary conditions and at non-zero imaginary chemical potential. Monte Carlo simulations with a moderate computational cost allow us to obtain ZV with an accuracy of about 8‰ for values of the inverse bare coupling constant β=6/g02 in the range 5.3≤β≤11.5.