Free Fermi Gas Research Articles

Radial Oscillations of Strange Quark Stars Admixed with Dark Matter

We investigate the equilibrium structure and radial oscillations of strange quark stars admixed with fermionic dark matter. For strange quark matter, we employ a stiff equation of state from a color-superconductivity improved bag model. For dark matter, we adopt the cold free Fermi gas model. We rederive and numerically solve the radial oscillation equations of two-fluid stars based on general relativity, in which the dark matter and strange quark matter couple through gravity and oscillate with the same frequency. Our results show that the stellar maximum mass and radius are reduced by inclusion of dark matter. As to the fundamental mode of the radial oscillations, the frequency f0 is also reduced comparing to pure strange stars, and f02 reaches the zero point at the maximum stellar mass with dM/dϵq,c=0. Therefore, the stability criteria f02>0 and dM/dϵq,c>0 are consistent in our dark matter-mixed strange quark stars with a fixed fraction of dark matter. We also find a discontinuity of f0 as functions of the stellar mass, in contrast to the continuous function in pure strange stars. And it is also accompanied with discontinuity of the oscillation amplitudes as well as a discontinuous in-phase-to-out-phase transition between oscillations of dark matter and strange quark matter.

Non-extensive statistics in Au-Au collisions

Particle production yields measured in central Au-Au collision at RHIC are obtained with free Fermi and Bose gases and also with a replacement of these statistics by non-extensive statistics. For the latter calculation, a set of different parameters was used with values of the Tsallis parameter q chosen between 1.01 and 1.25, with 1.16 generating the best agreement with experimental data, an indication that non-extensive statistics may be one of the underlying features in heavy ion-collisions.

Keldysh nonlinear sigma model for a free-fermion gas under continuous measurements

Keldysh nonlinear sigma model for a free-fermion gas under continuous measurements

A hydrodynamic approach to Stark localization

When a free Fermi gas on a lattice is subject to the action of a linear potential it does not drift away, as one would naively expect, but it remains spatially localized. Here we revisit this phenomenon, known as Stark localization, within the recently proposed framework of generalized hydrodynamics. In particular, we consider the dynamics of an initial state in the form of a domain wall and we recover known results for the particle density and the particle current, while we derive analytical predictions for relevant observables such as the entanglement entropy and the full counting statistics. Then, we extend the analysis to generic potentials, highlighting the relationship between the occurrence of localization and the presence of peculiar closed orbits in phase space, arising from the lattice dispersion relation. We also compare our analytical predictions with numerical calculations and with the available results, finding perfect agreement. This approach paves the way for an exact treatment of the interacting case known as Stark many-body localization.

An optimal upper bound for the dilute Fermi gas in three dimensions

In a system of interacting fermions, the correlation energy is defined as the difference between the energy of the ground state and the one of the free Fermi gas. We consider N interacting spin 1/2 fermions in the dilute regime, i.e., ρ≪1 where ρ is the total density of the system. We rigorously derive a first order upper bound for the correlation energy with an optimal error term of the order O(ρ7/3) in the thermodynamic limit. Moreover, we improve the lower bound estimate with respect to previous results getting an error O(ρ2+1/5).

Self-gravitating electrically charged anisotropic strange star model

The main focus of this paper is devoted to exploring the physical aspects of compact stars with the presence of electric charge under an embedded Class I approach in the arena of Bardeen geometry. We derive the embedded Class I solutions by taking spherically symmetric static spacetime with an anisotropic source of matter. We also look at the equation of state (EoS) for strange quark matter (SQM), which inspired the phenomenological MIT-Bag model as a free Fermi gas of quarks. The unknown constants are evaluated through the boundary conditions along with the Bardeen model to portray as an exterior space–time. Bardeen’s model becomes very interesting in an entertaining and unique way with great precision as it could be interpreted as the analytical solutions of some appropriate nonlinear electrodynamics associated with the gravitational field. In this concern, we thoroughly explored the dependence of several physical parameters, such as the metric potentials, energy density, pressure constituents, anisotropy, and electric charge, etc., on the chosen varied values of n. Finally, we discuss the physical viability and stability of the stellar model through various physical tests. It is important to mention here that the obtained stellar configuration is in agreement with the physical viability and stability criteria under the effect of the electric charge and anisotropic fluid source of matter.

Approaching PetaVolts per Meter Plasmonics Using Structured Semiconductors

A newly uncovered class of plasmons in the strongly excited limit opens access to unprecedented Petavolts per meter electromagnetic fields with wide-ranging, transformative impact. Unlike conventional plasmons, such plasmons are constituted by non-perturbative, large-amplitude oscillations of the ultradense, delocalized free electron Fermi gas inherent in conductive media. Here structured semiconductors doped to have an appropriate conduction electron density are introduced to tune the properties of the Fermi gas for matched excitation of large-amplitude plasmons using readily available electron beams which enables immediate experimental validation. Specifically, an electrostatic, surface “crunch-in” plasmon is collisionlessly excited by the beam launched inside a tube. Strong excitation due to matching results in relativistic oscillations of the electron gas and unravels unique phenomena. Relativistically induced ballistic electron transport comes about due to relativistic multifold increase in the mean free path and also leads to unconventional heat deposition beyond Ohm’s law. This explains the absence of observed damage or solid-plasma formation in past experiments on conductive samples interacting with electron bunches shorter than 10−13 seconds. Furthermore, relativistic momentum leads to copious tunneling of electron gas across the surface, which then crunches inside the tube. Relativistic effects along with large, localized electron density variations underlying these modes necessitate kinetic approach to theoretical and computational modeling. Kinetic model presented here demonstrates experimental viability of observing tens of gigavolts per meter plasmonic fields excited by matching readily available electron beams to plasmons in semiconductors with 1018cm−3 free electron density, and paves the way for Petavolts per meter plasmonics.

Rényi entropy and negativity for massless Dirac fermions at conformal interfaces and junctions

We investigate the ground state of a (1+1)-dimensional conformal field theory (CFT) built with M species of massless free Dirac fermions coupled at one boundary point via a conformal junction/interface. Each CFT represents a wire of finite length L. We develop a systematic strategy to compute the Rényi entropies for a generic bipartition between the wires and the entanglement negativity between two non-complementary sets of wires. Both these entanglement measures turn out to grow logarithmically with L with an exactly calculated universal prefactor depending on the details of the junction and of the bipartition. These analytic predictions are tested numerically for junctions of free Fermi gases, finding perfect agreement.

Mobile impurity in a one-dimensional gas at finite temperatures

We consider the McGuire model of a one-dimensional gas of free fermions interacting with a single impurity. We compute the static one-body function and momentum distribution of the impurity at finite temperatures. The results involve averages over Fredholm determinants that we further analyse using the effective form factors approach. With this approach, we derive the large-distance behaviour of the one-body function, which takes the form of an averaged exponential decay. This method allows us to study an experimentally important regime of small momenta of the impurity's momentum distribution. We also consider the one-body function at short distances and compute finite temperature Tan's contact.

Investigating effects of relativistic kinematics, dimensionality, interactions, and short-range correlations on the ratio of quartic over quadratic nuclear symmetry energies

While ample evidence for the so-called empirical parabolic law of the equation of state (EOS) of isospin asymmetric nuclear matter (ANM) has been obtained in many studies within both nonrelativistic and relativistic nuclear many-body theories using various interactions, it has been unclear if there is any fundamental physics reason for the small quartic symmetry energy compared to the quadratic one even as the ANM approaches pure neutron matter. Within both relativistic and nonrelativistic free Fermi gas (FFG) models in coordinate spaces of arbitrary dimension $d$ with and without considering short-range correlations (SRCs) as well as nonlinear relativistic mean field models, we study effects of relativistic kinematics, dimensionality, interactions, and SRC on the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ of quartic over quadratic symmetry energies in ANM EOSs. We found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ in the FFG model depends strongly on the dimension $d$. While it is very small already in the normal three-dimensional space, it could be even smaller in spaces with reduced dimensions for subsystems of particles in heavy-ion reactions and/or whole neutron stars due to constraints, collectivities, and/or symmetries. We also found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ could theoretically become very large only at the ultrarelativistic limit far above the density reachable in neutron stars. However, nuclear interaction directly and/or indirectly through SRC-induced high-momentum nucleons affects significantly the density dependence of $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ compared to the relativistic FFG model prediction. The SRCs affect significantly not only the kinetic energy of symmetric nuclear matter but also the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ while the relativistic corrections are found negligible. Although we found no fundamental physics reason for the $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ to be very small especially at high densities, the results may help better understand the EOS of dense neutron-rich matter.

Exploring physical features of anisotropic quark stars in Brans-Dicke theory with a massive scalar field via embedding approach * *Supported by the Postdoctoral Fellowship at Zhejiang Normal University (ZC304022919)

The main aim of this study is to explore the existence and salient features of spherically symmetric relativistic quark stars in the background of massive Brans-Dicke gravity. The exact solutions to the modified Einstein field equations are derived for specific forms of coupling and scalar field functions using the equation of state relating to the strange quark matter that stimulates the phenomenological MIT-Bag model as a free Fermi gas of quarks. We use a well-behaved function along with the Karmarkar condition for class-one embedding as well as junction conditions to determine the unknown metric tensors. The radii of strange compact stars viz., PSR J1416-2230, PSR J1903+327, 4U 1820-30, CenX-3, and EXO1785-248, are predicted via their observed mass for different values of the massive Brans-Dicke parameters. We explore the influences of the mass of scalar field , coupling parameter , and bag constant on state determinants and perform several tests on the viability and stability of the constructed stellar model. Conclusively, we find that our stellar system is physically viable and stable as it satisfies all the energy conditions and necessary stability criteria under the influence of a gravitational scalar field.

Improved treatment of dark matter capture in neutron stars III: nucleon and exotic targets

We consider the capture of dark matter (DM) in neutron stars via scattering on hadronic targets, including neutrons, protons and hyperons. We extend previous analyses by including momentum dependent form factors, which account for hadronic structure, and incorporating the effect of baryon strong interactions in the dense neutron star interior, rather than modelling the baryons as a free Fermi gas. The combination of these effects suppresses the DM capture rate over a wide mass range, thus increasing the cross section for which the capture rate saturates the geometric limit. In addition, variation in the capture rate associated with the choice of neutron star equation of state is reduced.For proton targets, the use of the interacting baryon approach to obtain the correct Fermi energy is essential for an accurate evaluation of the capture rate in the Pauli-blocked regime. For heavy neutron stars, which are expected to contain exotic matter, we identify cases where DM scattering on hyperons contributes significantly to the total capture rate. Despite smaller neutron star capture rates, compared to existing analyses, we find that the projected DM-nucleon scattering sensitivity greatly exceeds that of nuclear recoil experiments for a wide DM mass range.

Effects of Magnetic Fields in Hot White Dwarfs

Abstract In this work, we study the effects of magnetic fields on hot white dwarfs. We model their interior as a nuclei lattice surrounded by a relativistic free Fermi gas of electrons, accounting for effects from temperature, Landau levels, and anomalous magnetic moment. We find that, at low densities (corresponding to the outer regions of star), both temperature and magnetic field effects play an important role in the calculation of microscopic thermodynamical quantities. To study macroscopic stellar structures within a general-relativistic approach, we numerically solve the coupled Einstein–Maxwell equations for fixed entropy per particle configurations and discuss how temperature affects stellar magnetic field profiles, masses, and radii.

Quantum many-body calculations using body-centered cubic lattices

It is often computationally advantageous to model space as a discrete set of points forming a lattice grid. This technique is particularly useful for computationally difficult problems such as quantum many-body systems. For reasons of simplicity and familiarity, nearly all quantum many-body calculations have been performed on simple cubic lattices. Since the removal of lattice artifacts is often an important concern, it would be useful to perform calculations using more than one lattice geometry. In this work we show how to perform quantum many-body calculations using auxiliary-field Monte Carlo simulations on a three-dimensional body-centered cubic (BCC) lattice. As a benchmark test we compute the ground state energy of 33 spin-up and 33 spin-down fermions in the unitary limit, which is an idealized limit where the interaction range is zero and scattering length is infinite. As a fraction of the free Fermi gas energy $E_{\rm FG}$, we find that the ground state energy is $E_0/E_{\rm FG}= 0.369(2), 0.371(2),$ using two different definitions of the finite-system energy ratio. This is in excellent agreement with recent results obtained on a cubic lattice \cite{He:2019ipt}. We find that the computational effort and performance on a BCC lattice is approximately the same as that for a cubic lattice with the same number of lattice points. We discuss how the lattice simulations with different geometries can be used to constrain the size lattice artifacts in simulations of continuum quantum many-body systems.

Effects of modified dispersion relations on free Fermi gas: Equations of state and applications in astrophysics

Deformed dispersion relations are considered in the study of equations of state of Fermi gas with applications to compact objects. Different choices of deformed energy relations are used in the formulation of our model. As a first test, we consider a relativistic star with a simple internal structure. The mass-radius diagrams obtained suggest a positive influence of deformed Fermi gas, depending of the functions employed. In addition, we comment on how realistic equations of state, in which interactions between nucleons are taken into account, can be addressed.

Fermi polaron in low-density spin-polarized neutron matter

We study the properties of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons. In particular, we analyze its energy ($E_\downarrow$), effective mass ($m^*_\downarrow$) and quasiparticle residue ($Z_\downarrow$). Results are compared with those of state-of-the-art quantum Monte Carlo calculations of the attractive Fermi polaron realized in ultracold atomic gases experiments, and with those of previous studies of the neutron polaron. Calculations are performed within the Brueckner--Hartree--Fock approach using the chiral two-body nucleon-nucleon interaction of Entem and Machleidt at N$^3$LO with a 500 MeV cut-off and the Argonne V18 phenomenological potential. Only contributions from the $^1S_0$ partial wave, which is the dominant one in the low-density region considered, are included. Contributions from three-nucleon forces are expected to be irrelevant at these densities and, therefore, are neglected in the calculation. Our results show that for Fermi momenta between $\sim 0.25$ and $\sim 0.45$ fm$^{-1}$ the energy, effective mass and quasiparticle residue of the impurity vary only slightly, respectively, in the ranges $-0.604\,E_F < E_\downarrow < -0.635\,E_F $, $1.300\,m < m^*_\downarrow < 1.085\, m$ and $0.741 <Z_\downarrow< 0.836$ in the case of the chiral interaction, and $-0.621\,E_F < E_\downarrow < -0.643\,E_F $, $1.310\,m < m^*_\downarrow < 1.089\, m$ and $0.739 <Z_\downarrow< 0.832$ when using the Argonne V18 potential. These results are compatible with those derived from ultracold atoms and show that a spin-down neutron impurity in a free Fermi gas of spin-up neutrons with a Fermi momentum in the range $0.25\lesssim k_F \lesssim 0.45$ fm$^{-1}$ exhibits properties very similar to those of an attractive Fermi polaron in the unitary limit.

Low-Density Neutron Matter and the Unitary Limit

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

Numerical continuum tensor networks in two dimensions

We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of fermionic projected entangled pair states obtained via a tensor network formulation of multi-grid, and another based on the combination of the fermionic projected entangled pair state with layers of isometric coarse-graining transformations. We first benchmark our approach on the two-dimensional free Fermi gas then proceed to study the two-dimensional interacting Fermi gas with an attractive interaction in the unitary limit, using tensor networks on grids with up to 1000 sites.

Dark matter admixed neutron stars

Neutron stars could contain a mixture of ordinary nuclear matter and dark matter, such that dark matter could influence observable properties of the star, such as its mass and radius. We study these dark matter admixed neutron stars for two choices of dark matter: a free Fermi gas and mirror dark matter. In addition to solving the multi-fluid Tolman-Oppenheimer-Volkoff equations for static solutions and presenting mass-radius diagrams, we focus on two computations that are lacking in the literature. The first is a rigorous determination of stability over the whole of parameter space, which we do using two different methods. The first method is based on harmonic time-dependent perturbations to the static solutions and on solving for the radial oscillation frequency. The second method, which is less well-known, conveniently makes use of unperturbed, static solutions only. The second computation is of the radial oscillation frequency, for fundamental modes, over large swaths of parameter space.

Stability of the Enhanced Area Law of the Entanglement Entropy

We consider a multi-dimensional continuum Schrödinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper bound and a lower bound on the bipartite entanglement entropy of the ground state of the corresponding quasi-free Fermi gas. The bounds prove that the scaling behaviour of the entanglement entropy remains a logarithmically enhanced area law as in the unperturbed case of the free Fermi gas. The central idea for the upper bound is to use a limiting absorption principle for such kinds of Schrödinger operators.