Degeneracy Parameter Research Articles

Evolution model for substellar objects

A new model for the evolution of substellar objects is proposed, which enables computation of their internal structure and evolution in an adiabatic approximation without allowance for axial rotation, magnetic fields, and nuclear reactions. The basic set of differential equations in the model contains a new equation for the gradient of the electron degeneracy parameter and adiabatic coefficients of the new type. The results of numerical simulations of evolutionary sequences of hydrogen (X = 1), helium (Y = 1), and hydrogen-helium (X = 0.75, Y = 0.25) substellar objects with masses M < 0.08 M ⊙ during the evolutionary stage 106 yr < t < 1010 yr are reported. Luminosity-effective temperature, mass-radius, radius-time, central temperature-central density, and central temperature-age relations are analyzed for the indicated chemical composition.

Lynden-Bell and Tsallis distributions for the HMF model

Systems with long-range interactions can reach a Quasi Stationary State (QSS) as a result of a violent collisionless relaxation. If the system mixes well (ergodicity), the QSS can be predicted by the statistical theory of Lynden-Bell (1967) based on the Vlasov equation. When the initial distribution takes only two values, the Lynden-Bell distribution is similar to the Fermi-Dirac statistics. Such distributions have recently been observed in direct numerical simulations of the HMF model (Antoniazzi et al. 2006). In this paper, we determine the caloric curve corresponding to the Lynden-Bell statistics in relation with the HMF model and analyze the dynamical and thermodynamical stability of spatially homogeneous solutions by using two general criteria previously introduced in the literature. We express the critical energy and the critical temperature as a function of a degeneracy parameter fixed by the initial condition. Below these critical values, the homogeneous Lynden-Bell distribution is not a maximum entropy state but an unstable saddle point. We apply these results to the situation considered by Antoniazzi et al. For a given energy, we find a critical initial magnetization above which the homogeneous Lynden-Bell distribution ceases to be a maximum entropy state, contrary to the claim of these authors. For an energy U=0.69, this transition occurs above an initial magnetization M_{x}=0.897. In that case, the system should reach an inhomogeneous Lynden-Bell distribution (most mixed) or an incompletely mixed state (possibly fitted by a Tsallis distribution). Thus, our theoretical study proves that the dynamics is different for small and large initial magnetizations, in agreement with numerical results of Pluchino et al. (2004). This new dynamical phase transition may reconcile the two communities.

Degenerate Bose-Fermi Mixture of Metastable Atoms

We report the observation of simultaneous quantum degeneracy in a dilute gaseous Bose-Fermi mixture of metastable atoms. Sympathetic cooling of helium-3 (fermion) by helium-4 (boson), both in the lowest triplet state, allows us to produce ensembles containing more than 10(6) atoms of each isotope at temperatures below 1 microK, and achieve a fermionic degeneracy parameter of T/TF = 0.45. Because of their high internal energy, the detection of individual metastable atoms with subnanosecond time resolution is possible, permitting the study of bosonic and fermionic quantum gases with unprecedented precision. This may lead to metastable helium becoming the mainstay of quantum atom optics.

Spin-wave damping at spin-orientation phase transitions

The spectra or spin waves and their damping in the vicinity of spin-orientation phase transitions are investigated. It is shown that if the ground state is degenerate and the degeneracy is characterized by a continuous degeneracy parameter, then the spin-wave damping is not described by a Landau-Lifshitz-Gilbert relaxation term. The dissipative function is constructed for ferromagnetic crystals of different symmetry. The cases of finite and zero longitudinal magnetic susceptibility are considered. A method of finding the relaxation term in the Landau-Lifshitz equation for crystals of different symmetry is given. The spin-wave spectra and damping are calculated for ferromagnets with uniaxial and tetragonal symmetry. It is shown that the relaxation process has a two-step character. In the first step an equilibrium value of the magnetization is established on account of the exchange interaction. In the second step the spin-wave amplitude is damped as the magnetization variable precesses around its equilibrium value. The details of the Bogolyubov method of quasi-averages in application to the case of ferromagnets with a spontaneously degenerate vacuum are discussed.

Joint constraints on the lepton asymmetry of the Universe and neutrino mass from the Wilkinson Microwave Anisotropy Probe

We use the Wilkinson Microwave Anisotropy Probe (WMAP) data on the spectrum of cosmic microwave background anisotropies to put constraints on the present amount of lepton asymmetry $L$, parametrized by the dimensionless chemical potential (also called degeneracy parameter) $\ensuremath{\xi}$ and on the effective number of relativistic particle species. We assume a flat cosmological model with three thermally distributed neutrino species having all the same mass and chemical potential, plus an additional amount of effectively massless exotic particle species. The extra energy density associated to these species is parametrized through an effective number of additional species $\ensuremath{\Delta}{N}_{\mathrm{others}}^{\mathrm{eff}}$. We find that $0l|\ensuremath{\xi}|l1.1$ and correspondingly $0l|L|l0.9$ at $2\ensuremath{\sigma}$, so that WMAP data alone cannot firmly rule out scenarios with a large lepton number; moreover, a small preference for this kind of scenarios is actually found. We also discuss the effect of the asymmetry on the estimation of other parameters and, in particular, of the neutrino mass. In the case of perfect lepton symmetry, we obtain the standard results. When the amount of asymmetry is left free, we find $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}l3.6\text{ }\text{ }\mathrm{eV}$ at $2\ensuremath{\sigma}$. Finally we study how the determination of $|L|$ is affected by the assumptions on $\ensuremath{\Delta}{N}_{\mathrm{others}}^{\mathrm{eff}}$. We find that lower values of the extra energy density allow for larger values of the lepton asymmetry, effectively ruling out, at $2\ensuremath{\sigma}$ level, lepton symmetric models with $\ensuremath{\Delta}{N}_{\mathrm{others}}^{\mathrm{eff}}\ensuremath{\simeq}0$.

Lepton asymmetry and primordial nucleosynthesis in the era of precision cosmology

We calculate and display the primordial light-element abundances as a function of a neutrino degeneracy parameter $\ensuremath{\xi}$ common to all flavors. It is the only unknown parameter characterizing the thermal medium at the primordial nucleosynthesis epoch. The observed primordial helium abundance ${Y}_{\mathrm{p}}$ is the most sensitive cosmic ``leptometer.'' Adopting the conservative ${Y}_{\mathrm{p}}$ error analysis of Olive and Skillman implies $\ensuremath{-}0.04\ensuremath{\lesssim}\ensuremath{\xi}\ensuremath{\lesssim}0.07$ whereas the errors stated by Izotov and Thuan imply $\ensuremath{\xi}=0.0245\ifmmode\pm\else\textpm\fi{}0.0092$ ($1\ensuremath{\sigma}$). Improved determinations of the baryon abundance have no significant impact on this situation. A determination of ${Y}_{\mathrm{p}}$ that reliably distinguishes between a vanishing or nonvanishing $\ensuremath{\xi}$ is a crucial test of the cosmological standard assumption that sphaleron effects equilibrate the cosmic lepton and baryon asymmetries.

Constraining the Spectrum of Supernova Neutrinos fromν-Process Induced Light Element Synthesis

We constrain energy spectra of supernova neutrinos through the avoidance of an overproduction of the 11B abundance during Galactic chemical evolution. In supernova nucleosynthesis calculations with a parametrized neutrino spectrum as a function of temperature of nu(mu,tau) and nu(mu,tau) and total neutrino energy, we find a strong neutrino temperature dependence of the 11B yield. When the yield is combined with observed abundances, the acceptable range of the nu(mu,tau) and nu(mu,tau) temperature is found to be 4.8 to 6.6 MeV. Nonzero neutrino chemical potentials would reduce this temperature range by about 10% for a degeneracy parameter eta(nu) = mu(nu)/kT(nu) smaller than 3.

Bunching, antibunching, and the Poisson limit of Bose-Einstein processes at low-degeneracy parameters

Random point processes are often classified as bunched, unbunched, or antibunched, depending on the value assumed by their variance-to-mean ratio (the Fano factor); in the low-degeneracy limit, the Fano factor of a Bose-Einstein process approaches the Poisson value of unity. This fact probably added strength to the conjecture that in the limit of zero degeneracy a Bose-Einstein process reduces to a memoryless Poisson process. After considering some statistics related both to counting and to arrival times, we have experimentally verified that a Bose-Einstein process retains its correlation properties down to values of the degeneracy parameter of the order of 0.01. It also follows that the two most common definitions of photon bunching, the one based on the Fano factor and the one based on the correlation function, are not equivalent at low degeneracy levels.

Stopping of relativistic electrons in a partially degenerate electron fluid

The stopping mechanisms of relativistic electron beams in superdense and partially degenerate electron fluid targets are investigated in the framework of the fast ignitor concept for inertial confinement fusion. In order to comply with specific demands in this area, we focus attention on the target partial degeneracy parameter theta= T(e) / T(f) , in terms of the thermal to Fermi temperature ratio. The target electron fluid is thus modeled very accurately with a random phase approximation dielectric function. The stopping results are shown to be very weakly theta dependent. However, a quantum target description is needed to recover their correct increasing trend with increasing projectile energy. The ranges and effective penetration depths in precompressed thermonuclear fuels are shown to be nearly a factor of 2 shorter than earlier classical estimates in the same conditions. The overall conclusions pertaining to the feasibility of fast ignition thus remain unchanged.

Galvanomagnetic and thermoelectric properties of p-Bi2−x SbxTe3−y Sey solid solutions at low temperatures (&lt;220 K)

The galvanomagnetic and thermoelectric properties of p-Bi2−xSbxTe3−ySey solid solutions (x≤1.2, y≤0.09) are studied for various carrier concentrations. The degeneracy parameter βd governing the scattering processes in solid solutions was calculated in terms of the many-valley energy spectrum model. The data on the degeneracy parameter and the Seebeck coefficient α were used to calculate the effective scattering parameter reff and the reduced Fermi level η. The parameter reff was found to depend on the carrier concentration in the materials studied. The temperature dependences of the effective density-of-states mass m/m0 and mobility μ0 in samples with various carrier concentrations were determined.

Local “Mean Field” Theory of Hydraulically Controlled Strait Flow

Abstract The free discharge of a layer of bottom water in a wide strait (e.g., the Denmark Strait) differs from the classical control problem because of the strong geostrophic turbulence. As a consequence, the cross-stream (x) variation of the time-averaged downstream velocity υ(x) is “underdetermined” and depends on more parameters than available conditions. To resolve this “degeneracy” the classical control condition is generalized; the result requires the discharge Q to be extremized with respect to the degeneracy parameters and with respect to the constraints. One of these constraints is that a branch point or a local stationary wave can be supported at some section of the long channel. By either maximizing Q or by requiring a stationary wave, useful approximations are obtained. Future work should consider the joint variational problem. Specific calculations are made for nonuniform potential vorticity in a rectangular channel and also for variable cross-stream bottom topography. In the latter case, th...

WMAP, neutrino degeneracy, and non-Gaussianity constraints on isocurvature perturbations in the curvaton model of inflation

In the curvaton model of inflation, where a second scalar field, the "curvaton", is responsible for the observed inhomogeneity, a non-zero neutrino degeneracy may lead to a characteristic pattern of isocurvature perturbations in the neutrino, cold dark matter and baryon components. We find the current data can only place upper limits on the level of isocurvature perturbations. These can be translated into upper limits on the neutrino degeneracy parameter. In the case that lepton number is created before curvaton decay, we find that the limit on the neutrino degeneracy parameter is comparable with that obtained from Big-bang nucleosynthesis. For the case that lepton number is created by curvaton decay we find that the absolute value of the non-Gaussianity parameter, |f_nl|, must be less than 10 (95% confidence interval).

Statistical mechanics and phase diagrams of rotating self-gravitating fermions

We compute statistical equilibrium states of rotating self-gravitating systems enclosed within a box by maximizing the Fermi-Dirac entropy at fixed mass, energy and angular momentum. We increase the rotation up to the Keplerian limit and describe the flattening of the configuration until mass shedding occurs. At the maximum rotation, the system develops a cusp at the equator. We draw the equilibrium phase diagram of the rotating self-gravitating Fermi gas and discuss the structure of the caloric curve as a function of degeneracy parameter and angular velocity. We argue that systems described by the Fermi-Dirac distribution in phase space do not bifurcate to non-axisymmetric structures, in continuity with the case of polytropes with index n>0.808 (the Fermi gas at T=0 corresponds to n=3/2). This contrasts with the study of Votyakov et al. (2002) who consider a Fermi-Dirac distribution in configuration space and find ``double star'' structures (their model at T=0 corresponds to n=0). We also discuss the influence of rotation on the onset of the gravothermal catastrophe for globular clusters. On general grounds, we complete previous investigations concerning the nature of phase transitions in self-gravitating systems. We emphasize the inequivalence of statistical ensembles regarding the formation of binaries (or low-mass condensates) in the microcanonical ensemble and Dirac peaks (or massive condensates) in the canonical ensemble. We also describe an hysteretic cycle between the gaseous phase and the condensed phase that are connected by a ``collapse'' or an ``explosion''. This notion of hysteresis in self-gravitating systems is new.

Sphaleron relaxation temperatures

The transition of sphaleron processes from non-equilibrium to thermal equilibrium in the early Universe is examined in detail.The relations between the damping rates and frequencies of the weak and QCD sphaleron degeneracy parameters are determined in general form and the respective relaxation temperatures are calculated in specific scenarios.It is pointed out that the gauge coupling constants running with energy produces strong and weak sphaleron rates closer to each other at very high temperatures and makes them larger in supersymmetric models than in the standard model case.

Comments on the evolution of strongly degenerate neutrinos in the early universe

We reconsider the evolution of strongly degenerate neutrinos in the early universe. Our chief concern is the validity of the entropy conservation after the neutrino annihilation process has frozen out (so that the establishment of chemical equilibrium is not trivial). We argue that the entropy indeed conserves because elastic scattering keeps the neutrino and antineutrino distribution functions in the equilibrium form and the sum of their chemical potential keeps zero even after the neutrino annihilation freeze-out. We also simulate the evolution of the degenerate neutrino spectrum to support the argument. We conclude that the change in the neutrino degeneracy parameter when the relativistic degrees of freedom in the universe decreases is calculated using the entropy conservation and the lepton number conservation without worrying about at what temperature the neutrino annihilation process freezes out.

NEUTRINO-INDUCED NEUTRAL-CURRENT REACTION CROSS SECTIONS FOR r-PROCESS NUCLEI

Neutrino-induced reactions play an important role during and after the r-process, if the latter occurs in an environment with extreme neutrino fluxes such as the neutrino-driven wind model or neutron star mergers. Recently we have evaluated the charged-current neutrino–nucleus cross sections relevant for r-process simulations. We extend our approach here to the neutral-current cross sections. Our tabulation considers neutron-rich nuclei with neutron numbers N=41–135 and charge numbers Z=21–82 and lists total as well as partial neutron spallation cross sections. The calculations have been performed within the random phase approximation considering multipole transitions with J≤3 and both parities. The supernova neutrino spectrum is described by a Fermi–Dirac distribution with various temperature parameters between T=2.8 MeV and T=10 MeV and with the degeneracy parameters α=0 and α=3.

Big bang nucleosynthesis with Gaussian inhomogeneous neutrino degeneracy

We consider the effect of inhomogeneous neutrino degeneracy on big bang nucleosynthesis for the case where the distribution of neutrino chemical potentials is given by a Gaussian. The chemical potential fluctuations are taken to be isocurvature, so that only inhomogeneities in the electron chemical potential are relevant. Then the final element abundances are a function only of the baryon-photon ratio $\ensuremath{\eta},$ the effective number of additional neutrinos $\ensuremath{\Delta}{N}_{\ensuremath{\nu}},$ the mean electron neutrino degeneracy parameter $\overline{\ensuremath{\xi}},$ and the rms fluctuation of the degeneracy parameter, ${\ensuremath{\sigma}}_{\ensuremath{\xi}}.$ We find that for fixed $\ensuremath{\eta},$ $\ensuremath{\Delta}{N}_{\ensuremath{\nu}},$ and $\overline{\ensuremath{\xi}},$ the abundances of ${}^{4}\mathrm{He},$ D, and ${}^{7}\mathrm{Li}$ are, in general, increasing functions of ${\ensuremath{\sigma}}_{\ensuremath{\xi}}.$ Hence, the effect of adding a Gaussian distribution for the electron neutrino degeneracy parameter is to decrease the allowed range for $\ensuremath{\eta}.$ We show that this result can be generalized to a wide variety of distributions for $\ensuremath{\xi}.$

Constraints on neutrino degeneracy from the cosmic microwave background and primordial nucleosynthesis

We reanalyze the cosmological constraints on the existence of a net universal lepton asymmetry and neutrino degeneracy based upon the latest high resolution CMB sky maps from BOOMERANG, DASI, and MAXIMA-1. We generate likelihood functions by marginalizing over $({\ensuremath{\Omega}}_{\mathrm{b}}{h}^{2},{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}},{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}},{\ensuremath{\Omega}}_{\ensuremath{\Lambda}},h,n)$ plus the calibration uncertainties. We consider flat ${\ensuremath{\Omega}}_{M}+{\ensuremath{\Omega}}_{\ensuremath{\Lambda}}=1$ cosmological models with two identical degenerate neutrino species, ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}}\ensuremath{\equiv}|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}|=|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\tau}}}|$ and a small ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}}.$ We assign weak top-hat priors on the electron-neutrino degeneracy parameter ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}}$ and ${\ensuremath{\Omega}}_{b}{h}^{2}$ based upon allowed values consistent with the nucleosynthesis constraints as a function of ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}}.$ The change in the background neutrino temperature with degeneracy is also explicitly included, and Gaussian priors for $h=0.72\ifmmode\pm\else\textpm\fi{}0.08$ and the experimental calibration uncertainties are adopted. The marginalized likelihood functions show a slight $(0.5\ensuremath{\sigma})$ preference for neutrino degeneracy. Optimum values with two equally degenerate \ensuremath{\mu} and \ensuremath{\tau} neutrinos imply ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}}{=1.0}_{\ensuremath{-}1.0(0.5\ensuremath{\sigma})}^{+0.8(1\ensuremath{\sigma})},$ from which we deduce ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}}{=0.09}_{\ensuremath{-}0.09}^{+0.15},$ and ${\ensuremath{\Omega}}_{b}{h}^{2}{=0.021}_{\ensuremath{-}0.002}^{+0.06}.$ The $2\ensuremath{\sigma}$ upper limit becomes ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}}&lt;~2.1,$ which implies ${\ensuremath{\xi}}_{{\ensuremath{\nu}}_{e}}&lt;~0.30,$ and ${\ensuremath{\Omega}}_{b}{h}^{2}&lt;~0.030.$ For only a single large-degeneracy species the optimal value is $|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}|$ or $|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\tau}}}|=1.4$ with a $2\ensuremath{\sigma}$ upper limit of $|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\mu}}}|$ or $|{\ensuremath{\xi}}_{{\ensuremath{\nu}}_{\ensuremath{\tau}}}|&lt;~2.5.$

Phase transitions in self-gravitating systems: self-gravitating fermions and hard-sphere models.

We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of self-gravitating fermions and hard-sphere models. Depending on the values of the parameters, three kinds of phase transitions (of zero, first, and second order) are evidenced. They separate a "gaseous" phase with a smoothly varying distribution of matter from a "condensed" phase with a core-halo structure. We propose a simple analytical model to describe these phase transitions. We determine the value of energy (in the microcanonical ensemble) and temperature (in the canonical ensemble) at the transition point and we study their dependence on the degeneracy parameter (for fermions) or on the size of the particles (for a hard-sphere gas). Scaling laws are obtained analytically in the asymptotic limit of a small short distance cutoff. Our analytical model captures the essential physics of the problem and compares remarkably well with the full numerical solutions. We also stress some analogies with the liquid-gas transition and with the Blume-Emery-Griffiths model with infinite range interactions. In particular, our system presents two tricritical points at which the transition passes from first order to second order.

Analysis of the residual entropy of amorphous polyethylene at 0 K*

AbstractThe residual entropy of amorphous polyethylene (PE) at 0 K is discussed within the framework of the heat capacity (Cp). The measured Cp of the liquid was extended from the glass transition to low temperature by separately finding its three parts—the vibrational, conformational, and external contributions—and extrapolating each to low temperature. The vibrational Cp was calculated from the frequency distributions of the group vibrations on the basis of force constants obtained from experimental infrared and Raman spectra as well as the skeletal vibrations in the amorphous solid (glass) obtained from fitting of the appropriate experimental Cp to Debye functions in the form suggested by Tarasov. The conformational part of Cp was evaluated from a fit of the heat capacity of the liquid, decreased by the contributions of the vibrational and external parts, to a one‐dimensional Ising model that can be extrapolated to 0 K and requires two discrete states described by stiffness, cooperativity, and a degeneracy parameter. The external part was computed from the experimental data for expansivity and compressibility, fitted to an empirical equation of state, and modified at low temperatures in accordance with the Nernst–Lindemann approximation. The computed Cp of the liquid PE agreed with the experiment from 600 K to the beginning of the glass transition at about 260 K. Extending the heat capacity to 0 K, bypassing the freezing of the large‐amplitude conformational motion in the glass transition, led to a positive residual entropy and enthalpy and avoided the so‐called Kauzmann paradox. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1245–1253, 2002