Thermodynamics of a one-dimensional interacting Fermi system with magnetic impurities

The thermodynamics of a model of a one-dimensional metal with an attractive electron-electron and an antiferromagnetic electron-impurity interaction is fotmulated. The impurity contribution to the specific heat and magnetic susceptibility is calculated numerically.     

Thermodynamics of a trapped unitary Fermi gas

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value T(c) = 0.23(2)epsilon(F) in the bulk, as predicted by the present authors in their Monte Carlo calculations.     

Thermodynamics of nonstoichiometric multicomponent uranium oxides

A simple graphic method is described for calculating the thermodynamic properties of U and other metals in a nonstoichiometric r-component (r ⩾ 3) uranium oxide U_1-yM′_y3M_y4… O_2+x from the known oxygen potential. Only one set of graphic integration and (r − 2) sets of graphic differentiation are needed. Experimental data in an iso-x (r − 1)-component subsystem for which the oxygen potential is a linear function of y_i(i = 3,4,…, r) may easily be used to give a more accurate integration constant for the calculation. Sample calculations have been done for the U_t-yGd_yO_2+x solid solutions. This method can also be applied to other nonstoichiometric multicomponent solid compounds of importance in nuclear technology such as thorium-based and plutonium-based fuels.     

From fractional exclusion statistics back to Bose and Fermi distributions

Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this Letter I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.     

Thermodynamics of a Fermi liquid beyond the low-energy limit

We consider the nonanalytic temperature dependences of the specific heat coefficient, C(T)/T, and spin susceptibility, chi(s)(T), of 2D interacting fermions beyond the weak-coupling limit. We demonstrate within the Luttinger-Ward formalism that the leading temperature dependences of C(T)/T and chi(s)(T) are linear in T, and are described by the Fermi liquid theory. We show that these temperature dependences are universally determined by the states near the Fermi level and, for a generic interaction, are expressed via the spin and charge components of the exact backscattering amplitude of quasiparticles. We compare our theory to recent experiments on monolayers of He3.     

Thermodynamics of two-parameter quantum group Bose and Fermi gases

The high and low temperature thermodynamical properties of the two-parameter deformed quantum group Bose and Fermi gases with SU _p/q (2) symmetry are studied. Starting with a SU _p/q (2)-invariant bosonic as well as fermionic Hamiltonian, several thermodynamical functions of the system such as the average number of particles, internal energy and equation of state are derived. The effects of two real independent deformation parameters p and q on the properties of the systems are discussed. Particular emphasis is given to a discussion of the Bose-Einstein condensation phenomenon for the two-parameter deformed quantum group Bose gas. The results are also compared with earlier undeformed and one-parameter deformed versions of Bose and Fermi gas models. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Thermodynamics of Small Fermi Systems: Quantum Statistical Fluctuations

We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the thermodynamic function considered, and on temperature, we find that the probability distributions are dominated either (i) by the local fluctuations of the single-particle spectrum on the scale of the mean level spacing, or (ii) by the long-range modulations of that spectrum produced by the short periodic orbits. In case (i) the probability distributions are computed using the appropriate local universality class, uncorrelated levels for integrable systems, and random matrix theory for chaotic ones. In case (ii) all the moments of the distributions can be explicitly computed in terms of periodic orbit theory and are system-dependent, nonuniversal, functions. The dependence on temperature and on number of particles of the fluctuations is explicitly computed in all cases, and the different relevant energy scales are displayed.     

Thermodynamics of an interacting Fermi system in the static fluctuation approximation

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable approximation allows obtaining the so-called far-distance equations. These equations connecting the quantum states of a Fermi particle with variables of the local field operator contain all necessary information related to the calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system. The basic expressions for the mean energy and heat capacity for the electron gas at low temperatures in the high-density limit were obtained. All expressions are given in the units of r _s , where r _s determines the ratio of a mean distance between electrons to the Bohr radius a ₀. In these expressions, we calculate terms of the respective order r _s and r _s ². It is also shown that the static fluctuation approximation allows finding the terms related to higher orders of the decomposition with respect to the parameter r _s .     

Asymmetry of velocity distributions in peripheral reactions with heavy ions at Fermi energies

The asymmetry of velocity distributions of projectile-like fragments produced in heavy ion collisions is considered. The calculations performed in the transport model approach (Vlasov kinetic equation with the collision term) are compared with the experimental data for the ²²Ne (40MeV/nucleon) + ⁹Be and ¹⁸O (35 MeV/nucleon) + ⁹Be(¹⁸¹Ta) reactions. It is found that the velocity distributions contain two components: a direct component centered at the beam velocity and a dissipative component at lower energies, leading to asymmetry of velocity distributions. The direct component is interpreted empirically within the Goldhaber model, and the centroids and widths σ₀ of the distributions for each fragment are extracted. It is found that value of σ₀ derived from experimental data is smaller by a factor of 2 than the theoretical one. The dissipative (also called deep inelastic) component is described well by the transport calculations. It is shown that the ratio of yields of direct and dissipative components, which determines the asymmetry of velocity distributions, depends on shape of the deflection function. Original Russian Text ? T.I. Mikhailova, B. Erdemchimeg, G. Kaminski, A.G. Artyukh, M. Colonna, M. Di Toro, I.N. Mikhailov, Yu.M. Sereda, H.H. Wolter, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 6, pp. 898–903.     

Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases

A strongly correlated Fermi system plays a fundamental role in very different areas of physics, from neutron stars, quark–gluon plasmas, to high temperature superconductors. Despite the broad applicability, it is notoriously difficult to be understood theoretically because of the absence of a small interaction parameter. Recent achievements of ultracold trapped Fermi atoms near a Feshbach resonance have ushered in enormous changes. The unprecedented control of interaction, geometry and purity in these novel systems has led to many exciting experimental results, which are to be urgently understood at both low and finite temperatures. Here we review the latest developments of virial expansion for a strongly correlated Fermi gas and their applications on ultracold trapped Fermi atoms. We show remarkable, quantitative agreements between virial predictions and various recent experimental measurements at about the Fermi degenerate temperature. For equations of state, we discuss a practical way of determining high-order virial coefficients and use it to calculate accurately the long-sought third-order virial coefficient, which is now verified firmly in experiments at ENS and MIT. We discuss also virial expansion of a new many-body parameter—Tan’s contact. We then turn to less widely discussed issues of dynamical properties. For dynamic structure factors, the virial prediction agrees well with the measurement at the Swinburne University of Technology. For single-particle spectral functions, we show that the expansion up to the second order accounts for the main feature of momentum-resolved rf-spectroscopy for a resonantly interacting Fermi gas, as recently reported by JILA. In the near future, more practical applications with virial expansion are possible, owing to the ever-growing power in computation.     

Kronecker products of matrices and an application to Fermi systems

An identity for the trace of an exponential function of Kronecker products of matrices is proved. This identity plays an important role for the calculation of the grand potential of interacting Fermi systems. For the HamiltonianH= _i n _i n _i wheren _i =c _i ⁺ n _i (c _i ⁺ : Fermi creation operator at the ith site with spin) we calculate the specific heat for different numbers of electrons per lattice site. Finally, we extend our calculations to find approximative solutions of the Hubbard model.     

Effect of the Minimal Length on the Thermodynamics of Ultra-Relativistic Ideal Fermi Gas

Based on the generalized uncertainty principle, the thermodynamics ot Petrol gas m mgl~ u~ll~l~y, H,8,, ~ and high temperature are calculated. As the temperature and density increases, the energy and entropy becomes saturated and the pressure blows up without any bound. Using the conservation equation of the Robertson- Walker cosmology, we find that, when the energy exceeds the EH = β0-1/2c2Mp, the expansion cannot be driven by the photon gas and the fermion gas. This requires some new physical mechanism related to quantum gravitym such as tachyons and dilatons.     

Spin- and isospin-dependent momentum distributions in Fermi liquids at nonzero temperatures

We explore the structure of momentum distributions of Fermi liquids such as completely polarized ³He, unpolarized liquid ³He, and nuclear matter at nonzero temperatures. The study employs correlated density matrix theory and adapts the algorithm to deal with spin- and isospin-dependent correlations. The analysis is based on the factor decomposition of the one-body reduced density matrix. The decomposition permits to distinguish between statistical correlations and dynamic (direct) correlations. Together with the concept of renormalized fermions the formal results open the pathway to investigate the thermal boundaries of normal Fermi phases within the correlated density matrix theory. We also discuss possible transitions from normal phases to anomalous fermion phases triggered by statistical correlations or by periodic phase-phase structures.     

On the Fermi and Gamow-Teller strength distributions in medium-heavy mass nuclei

An isospin-self-consistent approach based on the continuum-random-phase approximation (CRPA) is applied to describe the Fermi and Gamow-Teller strength distributions within a wide excitation-energy interval. To take into account nucleon pairing in open-shell nuclei, we formulate an isospin-self-consistent version of the proton-neutron-quasiparticle-CRPA (pn-QCRPA) approach by incorporating the BCS model into the CRPA method. The isospin and configurational splittings of the Gamow-Teller giant resonance are analyzed in single-open-shell nuclei. The calculation results obtained for the ²⁰⁸Bi, ⁹⁰Nb, and Sb isotopes are compared with the available experimental data.     

Pseudopotential charge distributions for characteristic k-states on the Fermi surface of aluminium

Stimulated by the existence of very anisotropic scattering effects in aluminium we have calculated wave functions and charge distributions for some selected k-state on the Fermi surface. For this purpose the pseudopotential method together with Ashcroft's potential has been used. The results show marked and characteristic differences in the various charge distributions and allow a qualitative interpretation of the scattering anisotropies observed in Hall effect experiments.     

Instabilities of a Fermi Gas with Nested Fermi Surfaces

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a vector Q commensurate with the lattice in conjunction with the interaction between the quasiparticles can give rise to a rich phase diagram. Of particular importance is itinerant antiferromagnetic order in the context of pnictides and heavy fermion compounds. By mismatching the nesting the order can gradually be suppressed and as the Néel temperature tends to zero a quantum critical point is obtained. A superconducting dome above the quantum critical point can be induced by the transfer of pairs of electrons between the pockets. The conditions under which such a dome arises are studied. In addition numerous other phases may arise, e.g. charge density waves, non‐Fermi liquid behavior, non‐s‐wave superconductivity, Pomeranchuk instabilities of the Fermi surface, nematic order, and phases with persistent orbital currents.     

A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive SU(w) Fermi Gases

We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional(1 D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z=2 and correlation length exponent v=1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU(w) and non-SU(w) symmetries in one dimension.