Dense Fermi Research Articles

Fluid Turbulence in Quantum Plasmas

Nonlinear fluid simulations are developed by us to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a very dense Fermi (quantum) plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations (EPO) is determined critically by a ratio of the energy density of the EPOs and the electron kinetic energy density of quantum plasmas. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory.

Long and short time quantum dynamics: II. Kinetic regime

Non-equilibrium Green's functions reduce to quantum kinetic equations in the kinetic regime, that is, if the quasi-classical, quasi-particle picture is valid. The classical tool yielding the kinetic equations, the Kadanoff–Baym Ansatz, has been improved and generalized to a whole Ansatz family including the so-called extended quasi-particle approximation. Each Ansatz produces a quantum kinetic theory: a quasi-particle kinetic equation and a functional of the quasi-particle distribution returning the average values of observables. In the extended quasi-particle model, the theory is physically consistent: causal, gauge invariant and conserving. This model leads to kinetic equations for dense Fermi liquids which combine the Landau quasi-particle drift with non-local scattering integrals in the spirit of the Enskog equation.

Threshold of molecular bound state and BCS transition in dense ultracold Fermi gases with Feshbach resonance

We consider the normal state of a dense ultracold atomic Fermi gas in the presence of a Feshbach resonance. We study the BCS and the molecular instabilities and their interplay, within the framework of a recent many-body approach. We find surprisingly that, in the temperature domain where the BCS phase is present, there is a non zero lower bound for the binding energy of molecules at rest. This could give an experimental mean to show the existence of the BCS phase without observing it directly.

Possible Origin of Magnetic Fields in Very Dense Stars

We discuss the bosonization of a relativistic very dense Fermi gasin a magnetic field and the consequent Bose–Einstein condensationof the resulting relativistic vector gas of charged particles. Themodel may be applied to paired spin-up electrons. We show that suchsystems may maintainself-consistently magnetic fields of order 1010−1013 G. That pairing could be the origin of large magnetic fieldsin some white dwarfs and neutron stars. For fields largeenough (~1013 for white dwarfs), the system becomesunstable and collapses.

Feshbach resonance in dense ultracold Fermi gases.

We propose a coherent framework allowing one to treat many-body effects in dense ultracold Fermi gases in the presence of a Feshbach resonance. We show that the simple effect of Pauli exclusion induces a strong modification of the basic scattering properties. In particular, this washes out the Feshbach resonance and provides a natural explanation for recent experimental findings.

Shift of the molecular bound state threshold in dense ultracold Fermi gases withFeshbach resonance

We consider a dense ultracold Fermi gas in the presence of a Feshbach resonance.We investigate how the threshold for bound state formation, which is just at theFeshbach resonance for a dilute gas, is modified due to the presence of the Fermisea. We make use of a preceding framework of handling this many-body problem.We restrict ourselves to the simple case where the chemical potential μ isnegative, which allows us to cover in particular the classical limit where the effectis seen to disappear. We show that, within a simple approach where basically onlythe effect of Pauli exclusion is included, the Fermi sea produces a largeshift of the threshold, which is of the order of the width of the Feshbachresonance. This is in agreement with very recent experimental findings.

Kinetic equation for strongly interacting dense Fermi systems

We review the non-relativistic Green's-function approach to the kinetic equations for Fermi liquids far from equilibrium. The emphasis is on the consistent treatment of the off-shell motion between collisions and on the non-instant and non-local picture of binary collisions. The resulting kinetic equation is of the Boltzmann type, and it represents an interpolation between the theory of transport in metals and the theory of moderately dense gases. The free motion of particles is renormalised by various mean field and mass corrections in the spirit of Landau's quasiparticles in metals. The collisions are non-local in the spirit of Enskog's theory of non-ideal gases. The collisions are moreover non-instant, a feature which is absent in the theory of gases, but which is shown to be important for dense Fermi systems. In spite of its formal complexity, the presented theory has a simple implementation within the Monte-Carlo simulation schemes. Applications in nuclear physics are given for heavy-ion reactions and the results are compared with the former theory and recent experimental data. The effect of the off-shell motion and the non-local and non-instant collisions on the dynamics of the system can be characterised in terms of thermodynamic functions such as the energy density or the pressure tensor. Non-equilibrium counterparts of these functions and the corresponding balance equations are derived and discussed from two points of view. Firstly, they are used to prove the conservation laws. Secondly, the role of individual microscopic mechanisms in fluxes of particles and momenta and in transformations of the energy is clarified.

Nonlocal corrections to the Boltzmann equation for dense Fermi systems

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second-order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e. an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed.

CIRCUMSTANCES OF FERMION FRACTIONIZATION IN HIGH DENSITY FERMI GAS

We consider a (3 + 1)-dimensional SU(2)-gauge theory which is known to possess the fractional fermions. These are the monopoles. We compute the fermion number of a monopole in the dense Fermi gas and find the conditions under which fermions decay into the monopoles.

Many-body theory of atomic deuterium.

Deuterium atoms form a fascinating spin-one Fermi fluid of moderate density. Several properties of this fluid are evaluated using the self-consistent Green-function method of many-body theory. The aim is both to determine the properties and to see how well Green-function methods can be implemented in a moderately dense Fermi liquid. Approximations begin with the self-energy. This is separated into Brueckner-Hartree-Fock terms and correlation or two-hole\char21{}one-particle (HHP) terms. We find ground-state energies E in reasonable agreement with Monte Carlo values. While the HHP terms are not so important for E, they lead to a significant enhancement of the effective mass ${\mathit{m}}^{\mathrm{*}}$ at the Fermi surface ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{F}}$. The particle-hole interaction is calculated from the self-energy using the conserving Baym-Kadanoff method. This leads to Landau parameters ${\mathit{F}}_{0}^{\mathit{s}}$ that are positive and an ${\mathit{F}}_{1}^{\mathit{s}}$ that is consistent with ${\mathit{m}}^{\mathrm{*}}$.

Renormalized Bose condensation in the presence of fermions.

Bose condensation of a dilute charged Bose gas in contact with a dense Fermi liquid is examined. The particles have hard cores and hop on a lattice. It is argued that a ``Bose metal phase,'' i.e., a phase with vanishing condensate fraction, is unlikely to exist in this problem at zero temperature. However very strong renormalizations of the properties of the Bose system occur when the boson band is narrower than the fermion band. We find that the condensate fraction at zero temperature is suppressed by a factor 4(W/${\mathit{w}}_{\mathit{b}}$${)}^{2}$ exp(-W/${\mathit{w}}_{\mathit{b}}$) in two dimensions over Gutzwiller-type variational estimates. Here, ${\mathit{w}}_{\mathit{b}}$ and W are the boson and fermion half-band-widths, respectively. There is a similar reduction in the transition temperature. Thus the possibility that high-${\mathit{T}}_{\mathit{c}}$ superconductors are Bose metals in their normal states cannot be excluded on the basis of present experimental or theoretical evidence.

Femtosecond carrier dynamics in modulation-doped quantum wells

We discuss experiments which elucidate the carrier-carrier scattering dynamics of electrons and holes in the presence of a Fermi sea of excess electrons or holes. We find that the presence of a dense Fermi sea changes carrier-carrier scattering dynamics as well as the renormalization kinetics at the band edge.

Topological solitons in a hot and dense fermi gas

States with a fractional fermion number have been discovered in various relativistic field theory models, and in this paper the effects of a finite temperature and chemical potential are investigated. A general approach for the evaluation of the fermion number is developed and its various aspects are discussed; in particular the topological nature of the fermion number at finite temperature and chemical potential is revealed. The connection between the fermion number and the partition function of a hot and dense Fermi gas in the presence of a topologically nontrivial background is emphasized and the use of the fermion number as an order parameter is suggested. As an application, the solitons in the SU(2) × SU(2) Skyrme model are investigated, and it is suggested that the breakdown of the Skyrme model at high temperature and density can be related to the formation of a quark-gluon plasma in QCD. The critical values of the temperature and chemical potential are estimated in the adiabatic limit to be T c ≈ 100–300 MeV and μ c ≈ 300 MeV per quark.

Finite size effects for the non-interacting Fermi system at finite temperature and finite density

From the euclidean form of the partition function for a non-interaction dense Fermi system placed on a finite lattice we evaluate its energy density and particle density, using different forms of lattice action. Comparing them with the corresponding well-known results in the continuum, we obtain a measure of finite lattice size effects.

Generalized Jastrow variational method for dense Fermi systems

In this paper, we outline a simple method whereby the antisymmetry of the wave function can be incorporated exactly in the Jastrow many-body theory. Applications of this method to the “homework problem” for neutron matter using the hypernetted-chain approximation give results in very good agreement with the Fermi-hypernetted chain approximation calculations of Fantoni and Rosati. The calculations for liquid3He at a Fermi wave numberkF=0.75 A−1 give results close to the Monte Carlo calculations of Ceperley, Chester, and Kalos.

A generalized perturbation theory for dense Fermi systems

We review the rudiments of a powerful temperature-dependent Green function formalism for examining the ground state and low-lying excited states of dense Fermi systems. This formalism is based on the pioneering work of Galitskii and Migdal and heavily employs the refined language which Feynman developed in his formulation of quantum electrodynamics. We summarize the results hitherto obtained and outline the merits and deficiencies of the formalism.

A numerical study of the Fermi hypernetted chain method

We compare several elaborations of the Fermi hypernetted chain (FHNC) method for the calculation of ground-state properties of dense Fermi systems. A variety of simple nuclear potentials is employed. Consistency tests give estimates for the convergence of the resulting FHNC expansions with respect to elementary diagrams, and to antisymmetry corrections.

Variational method for liquid3He. I. The Fermi hypernetted-chain approach

We develop a systematic procedure for the computation of ground-state properties of dense Fermi liquids, which is based on a Jastrow trial wave function and forms a systematic extension of the hypernetted-chain technique to Fermi statistics. The derivation of the Fermi hypernetted-chain equations is described in detail, and preliminary numerical results are reported.

A semiclassical description of Fermions with spin-dependent forces

It is shown how to generalize the semiclassical treatment of dense Fermi gases in the presence of spin-dependent forces. One constructs the Wigner transform of the singlet density matrix in that representation in which the position operator and thez component of the spin operator are diagonal. This way one obtains a matrix in the spin indices which is a function of the semiclassicalp andq variables. Rules are then given how to calculate with this matrix, theμ-matrix. Next, this matrix is explicitly evaluated for independent Fermions in a spherically symmetrical potential, subject to spin-orbit forces. Finally a brief discussion is given about the nature of this matrix and possible uses are proposed.

Renormalized and Unrenormalized Jastrow Expansions of the Liquid Structure Function for Dense Fermi Liquids

We present approximate representations of the liquid structure function S(k) for Fermi systems in the framework of the renormalized and unrenormalized Jastrow theory. Using short range correlations we study the behavior of S(k) in the range of low momenta and compare our numerical results with the experimental data of the liquid structure function of liquid 3He. We conclude that the usual Jastrow ansatz Ψ = Πi<i f(rij)Φ for the trial wave function of a dense Fermi system, together with an application of the cluster expansion method developed by Clark and Westhaus, does not sufficiently describe these systems. Improvements are discussed