Nuclear interface energy at finite temperatures

The thermodynamic properties at finite temperatures of the plane interface between two phases of nuclear matter in equilibrium are examined theoretically, and explored numerically. The microscopic hamiltonian, the Skyrme I′ interaction, is used in the Thomas-Fermi approximation to obtain the finite-temperature extensions of earlier zero-temperature results which used the Hartree-Fock and Thomas-Fermi methods. Approximate analytic fits are given to the χ_i (proton fraction on the dense-matter side) dependence of the critical temperature, and to the T and χ_i dependences of the surface thermodynamic potentials, the density of surface neutrons, the surface entropy and the neutron and proton chemical potentials at phase equilibrium. These fits are an ingredient in a compressible liquid-drop nuclear model, the basis of an equation of state for hot, dense matter needed in certain astrophysical applications.The liquid-drop model is used here to construct an isolated, low-T nucleus, whose properties are compared with the original zero-T Hartree-Fock calculations which lead to the Skyrme I interaction, and with other mass formulae. The low-temperature expansion of the surface energy is compared with that obtained in other calculations. The nuclear level density at the Fermi surface, related to the low-T expansion of the entropy of the whole nucleus, is also discussed.     

Interaction effects on atomic laboratory trapped Bose-Einstein condensates

We discuss the effect of inter-atoms interactions on the condensation temperature T _c of an atomic laboratory trapped Bose-Einstein condensate. We show that, in the mean-field Hartree-Fock and semiclassical approximations, interactions produce a shift Δ T _c /T _c ⁰ ≈ b ₁(a/λ _{T c} ) + b ₂(a/λ _{T c} )² + ψ[a / λ _{T c} ] with a the s-wave scattering length, λ _T the thermal wavelength and ψ[a / λ _{T c} ] a non-analytic function such that ψ[0] = ψ′[0] = ψ′′[0] = 0 and |ψ′′′[0]| = ∞. Therefore, with no more assumptions than Hartree-Fock and semiclassical approximations, interaction effecs are perturbative to second order in a / λ _{T c} and the expected non-perturbativity of physical quantities at critical temperature appears only to third order. We compare this finding with different results by other authors, which are based on more than the Hartree-Fock and semiclassical approximations. Moreover, we obtain an analytical estimation for b ₂ ? 18.8 which improves a previous numerical result. We also discuss how the discrepancy between b ₂ and the empirical value of b ₂ = 46 ± 5 may be explained with no need to resort to beyond-mean field effects.     

Surface instability of a nuclear fermi liquid drop

A mechanical instability of an incompressible Fermi liquid drop with respect to surface distortions is considered. It is shown that the Fermi surface distortion (FSD) reduces the instability-growth rate for surface fluctuations due to its effects on both the viscosity and the increase in the stiffness coefficient. The dependence of the limiting temperature T_lim on the mass number and the multipolarity of the nuclear-surface distortion is calculated. It is shown that T_lim is not influenced by the FSD effect.     

Electronic thermal conduction in suspended graphene

The electronic thermal conductivity (ETC), κ_e, of suspended graphene (SG) is studied for 15<T<400 K, following the Boltzmann transport formalism. The electrons are considered to be scattered from defects along with the intrinsic in-plane acoustic phonons, out-of-plane flexural phonons (FPs) and optical phonons. The ETC is evaluated by computing the first-order perturbation distribution function by directly solving the linearized Boltzmann equation by an iterative method. Numerical calculations of the temperature and concentration dependences of κ_e show the dominance of charged impurity scattering at lower temperatures (T<75 K) and of FPs at higher temperatures. The results are compared with the commonly used low-temperature and high-energy relaxation time approximations. Our calculations are in good agreement with recent κ_e data extracted for high-mobility SG samples. The validity of Wiedemann–Franz law is also discussed.     

Effect of quantum fluctuations and isotopic substitution on the curie temperature of BaTiO3, PbTiO3, and KNbO3

The Hartree-Fock formalism and density functional theory are used in first-principles calculations of the Landau-Ginzburg free-energy expansion coefficients in the Devonshire-Barrett one-ion model for BaTiO₃, PbTiO₃, and KNbO₃. The Curie temperature T ₀ and the Curie-Weiss constant are calculated. The effect of quantum fluctuations on T ₀ is considered in the approximation of the first quantum correction to the free energy. The quantum shift of the Curie temperature ΔT ₀ ^quant for BaTiO₃, PbTiO₃, and KNbO₃ and the isotopic shift ΔT ₀ ^iso for barium titanate due to the substitution ⁴⁸Ti → ⁴⁶Ti or ⁴⁸Ti → ⁵⁰Ti are calculated.     

Mean field at finite temperature and symmetry breaking

For an infinite system of nucleons interacting through a central spin-isospin schematic force we discuss how the Hartree-Fock theory at finite temperature T yields back, in the T=0 limit, the standard zero-temperature Feynman theory when there is no symmetry breaking. The attention is focused on the mechanism of cancellation of the higher order Hartree-Fock diagrams and on the dependence of this cancellation upon the range of the interaction. When a symmetry breaking takes place it turns out that more iterations are required to reach the self-consistent Hartree-Fock solution, because the cancellation of the Hartree-Fock diagrams of order higher than one no longer occurs. We explore in particular the case of an explicit symmetry breaking induced by a constant, uniform magnetic field B acting on a system of neutrons. Here we compare calculations performed using either the single-particle Matsubara propagator or the zero-temperature polarization propagator, discussing under which perturbative scheme they lead to identical results (if B is not too large). We finally address the issue of the spontaneous symmetry breaking for a system of neutrons using the technique of the anomalous propagator: in this framework we recover the Stoner equation and the critical values of the interaction corresponding to a transition to a ferromagnetic phase.     

Wilson renormalization group formulation of real time thermal field theories

We apply Renormalization Group techniques to the Real Time formulation of thermal field theory. Due to the separation between the T = 0 and the T ≠ 0 parts of the propagator in this formalism, one can derive exact evolution equations for the Green functions describing the effect of integrating out thermal fluctuations of increasing wavelengths, the initial conditions being the renormalized Green functions of the T = 0 theory. As a first application, we study the phase transition for the real scalar theory, computing the order of the transition, the critical temperature, and critical exponents, in different approximations to the evolution equations for the scalar potential.     

From chemical freeze-out to critical conditions in heavy ion collisions

We compare the statistical thermodynamics of hadron resonance gas with recent LGT results at finite chemical potential. We argue that for T≤T _cthe equation of state derived from Monte-Carlo simulations of 2-quark-flavor QCD at finite chemical potential is consistent with that of a hadron resonance gas when applying the same set of approximations as used in LGT calculations. We indicate the relation of chemical freeze-out conditions obtained from a detailed analysis of particle production in heavy ion collisions with the critical conditions required for deconfinement. We argue that the position of a hadron quark-gluon boundary line in temperature chemical potential plane can be determined in terms of the resonance gas model by the condition of fixed energy density.     

Fluctuations in high field superconductors

We present calculations for the influence of fluctuations in high field superconductors where the critical field is limited by Pauli paramagnetism. Due to the fact that the critical field at the second order phase transition point as function of temperature may have a maximum atT≠0 the additional conductivity due to fluctuations may have a nonmonotonic temperature dependence. This way we can account for recent experimental findings by Tedrow, Meservey and Schwartz. We also calculate the additional tunneling density of states due to fluctuations. Under proper conditions it exhibits a maximum at zero frequency like in the gapless regime. Finally we show that our findings of a nonmonotonic resistivity should also apply to superconductors containing magnetic impurities such as La_3-x Gd _x In in an external field.     

Central peak for a scalar ϕ 4-model: mode coupling approach revisited

We reinvestigate the mode coupling approach to the central peak which occurs in the vicinity of a structural phase transition at T _c. For a scalar ? ⁴-model it is shown that the use of renormalized vertices leads to quite different results compared to recent calculations with bare vertices. Particularly, we prove that the latter are obtained in leading order of the anharmonicity constant of the on-site potential from a perturbational treatment of the renormalized vertices. Again, this mode coupling approach may yield a dynamical transition at a temperature T _c'(≥ T _c) at which the dynamics becomes nonergodic, i.e. a central peak occurs. For a ? ⁴- model with infinite range interactions our theoretical predictions are consistent with numerical results. Furthermore, if the fluctuations in the vicinity of Tc are Gaussian, no dynamical transition occurs above Tc. Therefore the temperature T ₀'obtained from the Ginzburg criterion sets an upper bound for T _c'. If a dynamical transition occurs, it is shown that the nonergodicity parameter as function of wave vector q and temperature T follows from an universal master function.     

First-principles band-structure calculations as a tool for the quantitative interpretation of Raman spectra of high temperature superconductors

We have performed first-principles band structure calculations in order to investigate vibronic and optical properties of YBa₂Cu₃O₇. A formalism describing temperature dependent Raman spectra from such ab-initio results has been applied to the 500 cm^?1 apex oxygen mode and its overtone in good agreement with experimental results. The dynamical matrix of the five A_1g modes established by atomic-force calculations is studied in detail showing rather good agreement with experimental eigen-frequencies and normal coordinates. The effect of isotope substitutions on the phonon frequencies is investigated. We demonstrate that the calculated vibronic properties of high T_c materials are improved by applying a generalized gradient correction scheme for the treatment of exchange and correlation effects instead of the local-density approximation.     

Avoided critical behavior in a uniformly frustrated system

We study the effects of weak long-ranged antiferromagnetic interactions of strength Q on a spin model with predominant short-ranged ferromagnetic interactions. In three dimensions, this model exhibits an avoided critical point in the sense that the critical temperature T_c(Q = 0) is strictly greater than lim_Q→0T_c(Q). The behavior of this system at temperatures less than T_c(Q = 0) is controlled by the proximity to the avoided critical point. We also quantize the model in a novel way to study the interplay between charge-density wave and superconducting order.     

Re-entry in ferromagnetic superconductors

The re-entry phenomenon in magnetic superconductors is studied using the generalized Ginzburg-Landau free energy introduced by Blount and Varma. The re-entry temperature T_c2 is simply that temperature at which the magnetization acts as a source of induction strong enough to destroy superconductivity. Above T_c2 ferromagnetism and superconductivity coexist. The structure is an Abrikosov vortex lattice, with ferromagnetic magnetization spreading widely around the vortex cores. Within our approximations, the phase transition at T_c2 is of second order.     

Methods for calculating the desorption rate of molecules from a surface at non-zero coverage: Water on MgO(0 0 1)

We present calculations of the desorption rate of water molecules from MgO(0 0 1) at a range of coverages θ and temperatures T. Our aim is to demonstrate that this can be done without making uncontrollable statistical mechanical approximations, and we achieve this by using the potential of mean force method reported previously. As in our earlier work on desorption of isolated molecules, we use a classical interaction model. We find that correlations between adsorbed molecules greatly increase the simulation time needed to obtain good statistical accuracy, compared with the isolated molecule. The activation energy for desorption varies significantly with coverage. The calculations also yield the chemical potential of adsorbed molecules as a function of θ and T, from which we can deduce the critical temperature and coverage for phase separation of adsorbed molecules.     

Liquid drop parameters for hot nuclei

Using the semi-classical extended Thomas-Fermi (ETF) density variational method, we derived self-consistently the liquid drop model (LDM) coefficients for the free energy of hot nuclear systems from a realistic effective interaction (Skyrme SkM¹). We expand the temperature (T) dependence of these coefficients up to the second order in T and test their application to the calculation of the fission barriers of the nuclei ²⁰⁸Pb and ²⁴⁰Pu.     

Die Hartree-Fock-Theorie mit Zwischenzuständen: Klärung ihrer Struktur bei Zeitumkehrinvarianz und Anwendung auf das Kleinsche Rotations-Vibrationsmodell

In an earlier paper we have extended the new Tamm-Dancoff method to the “New Tamm-Dancoff method with intermediate states”. This extension makes it possible to treat the effect of nearby levels in many body systems with Green's functions. In addition to well-known approximations, such as the Hartree-Fock theory and the Hartree-Bogoliubov theory, we obtain a series of new approximations. The “Hartree-Fock theory with intermediate states”, which is the subject of the present investigation, is one of these. By using time reversal invariance we have succeeded in clarifying its structure, and we give the solution procedure. The exchange terms in theN-particle intermediate states can be represented by an additional potentialY, which (as is the case for the generalized density matrixρ) has to be determined selfconsistently. In this way we have overcome the difficulties, that Kerman and Klein met in their “generalized Hartree-Fock approximation”, which has some close similarities with our Hartree-Fock theory with intermediate states. We demonstrate our method for the exactly soluble rotational-vibrational model of Klein et al. Hereby we show how to treat conservation laws and the degeneracy of levels. The Hartree-Fock equations with three intermediate states turn out to give analytical expressions for the energies and the matrix elements. These agree excellently with the exact values in the rotational part of the spectrum.     

Thermostatic properties of symmetric nuclear matter

The thermostatic properties of symmetric nuclear matter are calculated by extension of a recent Thomas-Fermi approach to ground-state nuclei by Myers and Swiatecki [1]. We have computed the free energy per nucleon f(T, n) in Landau's quasiparticle approximation and have derived from it the relevant thermostatic properties. In view of its application to finite excited nuclei, the degenerate limit of nuclear matter is discussed in particular. As an interesting result we find at higher temperatures van-der-Waals-like isotherms in the p-n plane. Below the critical temperature T_c = 17.3 MeV two phases of nuclear matter, liquid and vapour, are defined by these. Comparing these results with the reduced phase transition data of ³He, ⁴He, and “inert gases,” we find that nuclear matter is similar to the He-isotopes, but differs considerably from the inert gases.     

Oscillator strengths for selected 3dn4s−3dn4p transitions of the iron-group elements

Absolute transition probabilities are calculated for selected 3dⁿ4s?3dⁿ4p transitions of the iron-group elements; configuration interaction effevts are taken into account. Comparisons with Hartree-Fock and multi-configuration Hartree-Fock results and with experimental data show that the scaled Thomas-Fermi method for calculation radial wave functions is useful procedure.