Nonrelativistic Gas Research Articles

Relativistic theory of the viscosity of fluids across the entire energy spectrum.

The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation(deduced from a relativistic Lagrangian) and nonaffine linear response theory. The proposed relativistic theory is able to recover the viscosity of nonrelativistic classical gases, with all its key dependencies on mass, temperature, particle diameter, and Boltzmann constant, in the limit of Lorentz factor γ=1. It also unveils the relativistic enhancement mechanism of viscosity. In the limit of ultrarelativistic fluids, the theory provides an analytical formula which reproduces the cubic increase of viscosity with temperature in agreement with various estimates for hot dense matter and the quark-gluon-plasma-type fluid.

Fermi equation of state with finite temperature corrections in quantum space-times approach: Snyder model vs GUP case

We investigate the impact of the deformed phase space associated with the quantum Snyder space on microphysical systems. The general Fermi–Dirac equation of state and specific corrections to it are derived. We put emphasis on non-relativistic degenerate Fermi gas as well as on the temperature-finite corrections to it. Considering the most general one-parameter family of deformed phase spaces associated with the Snyder model allows us to study whether the modifications arising in physical effects depend on the choice of realization. It turns out that we can distinguish three different cases with radically different physical consequences.

Complex Langevin approach to interacting Bose gases

Quantitative numerical analyses of interacting dilute Bose-Einstein condensates are most often based on semiclassical approximations. Since the complex-valued field-theoretic action of the Bose gas does not offer itself to standard Monte Carlo techniques, simulations beyond their scope almost exclusively rely on quantum-mechanical techniques, which are inherently limited to small particle numbers. Here we explore an alternative approach based on a Langevin-type sampling in an extended state space, known as complex Langevin (CL) algorithm. While the use of the CL technique has a long-standing history in high-energy physics, in particular in the simulation of QCD at finite baryon density, applications to ultracold atoms are still in their infancy. Here we examine the applicability of the CL approach for a one- and two-component, three-dimensional non-relativistic Bose gas in thermal equilibrium, below and above the Bose-Einstein phase transition. By comparison with analytic descriptions at the Gaussian level, including Bogoliubov and Hartree-Fock theory, we find that the method allows computing reliably and efficiently observables in the regime of experimentally accessible parameters. Close to the transition, quantum corrections lead to a shift of the critical temperature which we reproduce within the numerical range known in the literature. With this work, we aim to provide a first test of CL as a potential out-of-the-box tool for the simulation of experimentally realistic situations, including trapping geometries and multicomponent/-species models.

The thermodynamic limit of an ideal Bose gas by asymptotic expansions and spectral ζ-functions

We analyze the thermodynamic limit—modeled as the open-trap limit of an isotropic harmonic potential—of an ideal, non-relativistic Bose gas with a special emphasis on the phenomenon of Bose–Einstein condensation. This is accomplished by the use of an asymptotic expansion of the grand potential, which is derived by ζ-regularization techniques. Herewith, we can show that the singularity structure of this expansion is directly interwoven with the phase structure of the system: In the non-condensation phase, the expansion has a form that resembles usual heat kernel expansions. By this, thermodynamic observables are directly calculable. In contrast, the expansion exhibits a singularity of infinite order above a critical density, and a renormalization of the chemical potential is needed to ensure well-defined thermodynamic observables. Furthermore, the renormalization procedure forces the system to exhibit condensation. In addition, we show that characteristic features of the thermodynamic limit, such as the critical density or the internal energy, are entirely encoded in the coefficients of the asymptotic expansion.

Thermodynamics of the Nonrelativistic Free-Electron Fermi Gas in One, Two, and Three Dimensions from the Degenerate to the Nondegenerate Temperature Regime

The thermodynamic and electronic-transport properties of trigonal EuMg2Bi2 in ab-plane magnetic fields Hx and the A-type antiferromagnetic structure have recently been reported. At a temperature of 1.8 K < TN, the Eu magnetic moments with spin S = 7/2 remain locked in the ab plane up to and above the ab-plane critical field Hxc = 27.5 kOe at which the Eu moments become parallel to Hx. Here additional measurements at low fields are reported that reveal a new spin-reorientation transition at a field Hc1 = 465 Oe where the Eu moments remain in the ab plane but become perpendicular to Hx. At higher fields, the moments cant towards the field resulting in M proportional to Hx up to Hxc. Similar results are reported from measurements of the magnetic properties of EuMg2Sb2 single crystals, where Hc1 = 220 Oe is found. Theory is formulated that models the low-field magnetic behavior of both materials, and the associated anisotropies are calculated. The ab-plane trigonal anisotropy in EuMg2Sb2 is found to be significantly smaller than in EuMg2Bi2.

Stability analysis of nonthermal fixed points in longitudinally expanding kinetic theory

We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of nonthermal fixed points in a non-Abelian plasma. We construct a perturbative expansion of the Fokker-Planck collision kernel in an adiabatic approximation and show that the (next-to-)leading order solutions reproduce the known nonthermal fixed point scaling exponents. Working at next-to-leading order, we derive the stability equations for scaling exponents and find the relaxation rate to the nonthermal fixed point. This approach provides the basis for an understanding of the prescaling phenomena observed in QCD kinetic theory and nonrelativistic Bose gas systems.

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.

A General Framework for the Kinetic Modelling of Polyatomic Gases

A general framework for the kinetic modelling of non-relativistic polyatomic gases is proposed, where each particle is characterized both by its velocity and by its internal state, and the Boltzmann collision operator involves suitably weighted integrals over the space of internal states. The description of the internal structure of a molecule is kept highly general, and this allows classical and semi-classical models, such as the monoatomic gas description, the continuous internal energy structure, and the description with discrete internal energy levels, to fit our framework. We prove the H-Theorem for the proposed kinetic equation of Boltzmann type in this general setting, and characterize the equilibrium Maxwellian distribution and the thermodynamic number of degrees of freedom. Euler equations are derived, as zero-order approximation in a suitable asymptotic expansion. In addition, within this general framework it is possible to build up new models, highly desirable for physical applications, where rotation and vibration are precisely described. Examples of models for the Hydrogen Fluoride gas are shown. A link between state-based and energy-based points of view is presented.

Erratum: Fractional dark energy: Phantom behavior and negative absolute temperature [Phys. Rev. D 104 , 103508 (2021)

The fractional dark energy (FDE) model describes the accelerated expansion of the Universe through a nonrelativistic gas of particles with a noncanonical kinetic term. This term is proportional to the absolute value of the three-momentum to the power of $3w$, where $w$ is simply the dark energy equation of state parameter, and the corresponding energy leads to an energy density that mimics the cosmological constant. In this paper we expand the fractional dark energy model considering a non-zero chemical potential and we show that it may thermodynamically describe a phantom regime. The Planck constraints on the equation of state parameter put upper limits on the allowed value of the ratio of the chemical potential to the temperature. In the second part, we investigate the system of fractional dark energy particles with negative absolute temperatures (NAT). NAT are possible in quantum systems and in cosmology, if there exists an upper bound on the energy. This maximum energy is one ingredient of the FDE model and indicates a connection between FDE and NAT, if FDE is composed of fermions. In this scenario, the equation of state parameter is equal to minus one and, using cosmological observations, we find that the transition from positive to negative temperatures is allowed at any redshift larger than one.

Fermionic King model: critical masses resulting from the competition of quantum and evaporation effects

We study the influence of evaporation (the escape of constituents) on the thermodynamics of a self-gravitating non-relativistic gas of fermions in the framework of Newtonian gravitation. For this purpose, it is reconsidered as the so-called fermionic King model introduced by Ruffini and Stella in the context of dark matter halos problems (1983 Astron. Astrophys. 119 3). As the usual King model, the present model predicts density profiles that drop to zero at a certain finite radius R, which is referred to as the tidal radius. Our interest is focused on the thermodynamics of this model at constant total mass M and constant tidal radius R. A special interest is devoted to study the incidence of mass on the collective phenomena of gravitational collapse and evaporation disruption. The underlying physics is driven by the Fermi mass M F ∼ ℏ 6/G 3 m 8 R 3, which corresponds to the total mass of a self-gravitating degenerate Fermi gas of non-relativistic point particles with mass m, whose linear size is equal to the tidal radius R of evaporation. Numerical calculations predict three critical values for the total mass, M 1 > M 2 > M 3, which hallmark the thermodynamic stability. The lower bound is a critical value of the total mass below the which the system gravitation is unable to confine its constituents, so that the system with total mass M < M 3 undergoes an evaporation disruption. The other bounds, M 2 ≃ 90.9M F and M 1 ≃ 8.9 × 106 M F, are critical values that hallmark the continuous (or discontinuous) character of the microcanonical phase transition associated with gravothermal collapse and the presence of states with negative heat capacities.

On the hydrogen atom in the holographic universe

We investigate the holographic bound utilizing a homogeneous, isotropic, and non-relativistic neutral hydrogen gas present in the de Sitter space. Concretely, we propose to employ de Sitter holography intertwined with quantum deformation of the hydrogen atom using the framework of quantum groups. Particularly, the quantum algebra is used to construct a finite-dimensional Hilbert space of the hydrogen atom. As a consequence of the quantum deformation of the hydrogen atom, we demonstrate that the Rydberg constant is dependent on the de Sitter radius, L Λ. This feature is then extended to obtain a finite-dimensional Hilbert space for the full set of all hydrogen atoms in the de Sitter universe. We then show that the dimension of the latter Hilbert space satisfies the holographic bound. We further show that the mass of a hydrogen atom , the total number of hydrogen atoms at the Universe, N, and the retrieved dimension of the Hilbert space of neutral hydrogen gas, , are related to the de Sitter entropy, , the Planck mass, , the electron mass, , and the proton mass , by , and , respectively.

Fractional dark energy: Phantom behavior and negative absolute temperature

The fractional dark energy (FDE) model describes the accelerated expansion of the Universe through a nonrelativistic gas of particles with a noncanonical kinetic term. This term is proportional to the absolute value of the three-momentum to the power of $3w$, where $w$ is simply the dark energy equation of state parameter, and the corresponding energy leads to an energy density that mimics the cosmological constant. In this paper we expand the fractional dark energy model considering a nonzero chemical potential and we show that it may thermodynamically describe a phantom regime. The Planck constraints on the equation of state parameter put upper limits on the allowed value of the ratio of the chemical potential to the temperature. In the second part, we investigate the system of fractional dark energy particles with negative absolute temperatures (NAT). NAT are possible in quantum systems and in cosmology, if there exists an upper bound on the energy. This maximum energy is one ingredient of the FDE model and indicates a connection between FDE and NAT, if FDE is composed of fermions. In this scenario, the equation of state parameter is equal to minus one and, using cosmological observations, we find that the transition from positive to negative temperatures is allowed at any redshift larger than one.

Quantum magnetotransport oscillations in graphene nanoribbons coupled to superconductors

Magnetotransport properties of zigzag and armchair graphene nanoribbons that are in contact with superconductors are investigated using a tight-binding model. The cyclotron orbital motion together with the quantum interference under the coexistence of Andreev and normal reflections gives rise to a number of oscillations in characteristic magnetic-field regimes when the superconducting coupling is weak. The oscillations become irregular and/or suppressed as the coupling is made strong. The period of the oscillations differs from that when a nonrelativistic two-dimensional electron gas is employed rather than the graphene sheet. The modifications of the oscillations are attributed to the phase shift associated with the reflection from the graphene–superconductor interface. The presence of a magnetic field suppresses the quantum blocking of Andreev transmission, which occurs for the edge mode of zigzag nanoribbons, in the same way regardless of it being induced by the Andreev retro- or specular reflection.

Fractional dark energy

In this paper we introduce the fractional dark energy model, in which the accelerated expansion of the Universe is driven by a nonrelativistic gas (composed by either fermions or bosons) with a noncanonical kinetic term. The kinetic energy is inversely proportional to the cube of the absolute value of the momentum for a fluid with an equation of state parameter equal to minus one, and whose corresponding energy density mimics the one of the cosmological constant. In the general case, the dark energy equation of state parameter (times three) is precisely the exponent of the momentum in the kinetic term. We show that this inverse momentum operator appears in fractional quantum mechanics and it is the inverse of the Riesz fractional derivative. The observed vacuum energy can be obtained through the integral of the Fermi-Dirac (or Bose-Einstein) distribution and the lowest allowed energy of the particles. Finally, a possible thermal production and fate of fractional dark energy is investigated.

Effusion of Gas Through a Small Hole

A vessel containing a classical non-relativistic ideal gas is studied, which has a small hole. Gas effuses through this hole, but the hole is so tiny that the gas inside the vessel remains homogeneous. The density and the temperature of the gas inside the vessel are obtained as functions of time.

Photoinduced electronic and spin properties of two-dimensional electron gases with Rashba spin-orbit coupling under perpendicular magnetic fields

We theoretically investigate photoinduced phenomena induced by time-periodic driving fields in two-dimensional electron gases under perpendicular magnetic fields with Rashba spin-orbit coupling. Using perturbation theory, we provide analytical results for the Floquet-Landau energy spectrum appearing due to THz radiation. By employing the resulting photo-modulated states, we compute the dynamical evolution of the spin polarization function for an initially prepared coherent state. We find that the interplay of the magnetic field, Rashba spin-orbit interaction and THz radiation can lead to inversion of the spin polarization. The dynamics also induces fractional revivals and non-trivial beating patterns in the autocorrelation function due to interference of the photo-modulated quantum states. We also calculate the transverse photo-assisted conductivity in the linear response regime using Kubo formalism and analyze the impact of the radiation field and Rashba spin-orbit interaction. In the static limit, we find that our results reduce to well-known expressions of the conductivity in non-relativistic and quasi-relativistic (topological insulator surfaces) two-dimensional electron gas thoroughly described in the literature. We discuss the possible experimental detection of our theoretical prediction and their relevance for spin-orbit physics at high magnetic fields.

Anisotropic stars with a modified polytropic equation of state

In this article, we have presented the anisotropic stars by taking a modified polytropic equation of state (pr = k ρ1+1/n − α, where k and α are constants) in the framework of the Korkina-Orlyanskii spacetime. In this study, we have discussed four different models as: (A) n = 1 (Bose–Einstein Condensate (BEC) neutron liquid), (B) n = 2, (C) n = 3/2 (Non-relativistic neutron gas, (D) n = 3 (Ultra relativistic Fermi-gas). Moreover, we have tested several physical properties for each model. To compare the stiffness of these four models, we have plotted the M − R curves, M − I curves and compression modulus. As per the M − R curves, the equation of state can hold maximum mass when the polytropic index in 2 and minimum mass when n = 1 (BEC neutron liquid). Further, the ultra relativistic Fermi gas (n = 3) can also hold more Mmax than its non-relativistic counter part (n = 3/2). These results are further supported by the compression modulus. Lastly, to show its physical validity we have fitted six well known compact stars in M − R curve within their observational error bars.

Simplified calculations of plasma oscillations with non-extensive statistics

We use the exponential parametrization of the nonextensive distribution to calculate the dielectric constant in an electron gas obeying the nonextensive statistics. As we show, the exponential parametrization allows us to make such calculations in a straightforward way, bypassing the use of intricate formulas obtained from integral tables and/or numerical methods. For illustrative purposes, we apply first the method to the calculation of the permittivity and the corresponding dispersion relation in the ultrarelativistic limit of the electron gas, and verify that it reproduces in a simple way the results that had been obtained previously by other authors using the standard parametrization of the nonextensive distribution. In the same spirit we revisit the calculation of the same quantities for a non-relativistic gas, in the high frequency limit, which has been previously carried out, first by Lima, Silva and Santos, and subsequently revised by Chen and Li. Our own results agree with those obtained by Chen and Li. For completeness, we also apply the method the low frequency limit in the non-relativistic case, which has been previously considered by Dai, Chen and Li in the context of the stream plasma instability. We discuss some features of the results obtained in each case and their interpretation of terms of generalized nonextensive quantities, such as the Debye length $\lambda_{D}^{(q)}$, the plasma frequency $\omega_{p}^{(q)}$ and the ultra-relativistic frequency $\Omega^{(q)}_{e,rel}$. In the limit $q \rightarrow 1$ such quantities reduce to their classical value and the classical result of the dispersion relations are reproduced.

Exact analytic solution of an unsolvable class of first Lane–Emden equation for polytropic gas sphere

This article provides for the first time a general analytical solution to the Lane-Emden equation of the first kind. So far only three known analytical solutions are found in the literature, for the following values of n: 0, 1 and 5. A common feature these three solutions share is their boundary conditions: θ(ξ)∣ξ=0=1 and dθ(ξ)dξ∣ξ=0=0. If a third boundary condition d2θ(ξ)dξ2∣ξ=0,= −1 is used, only the solution for n=1 is able to meet all three. In order to address this difference, our solution aims to be more inclusive and takes into account θ(ξ)=1ξ and the constant solution. By keeping τ in parametric form, we found out that θ(ξ(τ))=1ξ(τ)→1 when ξ → 0. Thus proving that 1ξ→1 in the origin. It is worth noting that upon integrating the Lane-Emden equation, we came across five parameters. Three of them depend on the three boundary conditions used and two can be adjusted numerically.In order to demonstrate the validity of our solution, we tested it on six cases of interest to the scientific community related to studies on real stars and exoplanets. The adiabatic exponents are n=1.5,n=2,n=2.592, n=3,n=3.23 and n ≃ 5 contained in the intervals 1 < n < 5 and 5 ≲ n < 9. It is worth noting that four of these cases are of particular importance; n=1.5, which corresponds to an adiabatic star supported by the pressure of non-relativistic gas; n=3, which corresponds to an adiabatic star supported by the pressure of an ultra-relativistic gas. Finally, n=2.592 and n=3.23, which correspond to exoplanets. The obtained solution of the Lane–Emden equation of the first kind proves valid for any value of n.

Equation of state of the free electron gas in a magnetic field at arbitrary degeneracy

We study the equation of state of the non-relativistic free-electron gas in a constant magnetic field at arbitrary degeneracy based on the seminal work of Biswas et al. [Phys. Plasmas 20, 052503 (2013)]. The approach naturally unifies the Pauli paramagnetism, the Landau diamagnetism, and the de Haas–van Alphen effect. We consider the magnetization and the susceptibility as well as various thermodynamic quantities. In particular, the specific heats at constant volume and constant pressure are calculated, from which the adiabatic index is obtained. Weak and strong field limits are examined in detail. It is shown that the various quantities of interest saturate at strong magnetic field. Results are consistent with previous calculations performed at zero magnetic field. The polylogarithms are more adapted than the Fermi–Dirac integrals to describe the present system. The de Haas–van Alphen effect is not restricted to the magnetization and susceptibility but can be seen for other thermodynamic quantities.