Fermi systems

A.B. Migdal, Theory of Finite Fermi Systems and Applications to Atomic Nuclei (Interscience, London, 1967)... 

From BCS theory it is known, that in order to form Cooper pairs at T = 0 in a dense Fermi system, the difference in the chemical potentials of the Fermions to be paired should not exceed the size of the gap. As previous calculations within this type of models have shown [24], there is a critical chemical potential for the occurrence of quark matter pf > 300 MeV and values of the gap in the region A < 150 MeV have been found. Therefore it is natural to consider the problem of the color superconducting (2SC) phase with the assumption, that quark matter is symmetric or very close to being symmetric (pu pd). 

D. J. Thouless, The Quantum Mechanics of Many-Body Systems, Academic Press, New York, 1961 P. Nozieres, Le probleme a N corps, Dunod, Paris, 1963 and The Theory of Interacting Fermi Systems, Benjamin, New York, 1964 1. Lindgren and J. Morrison, Atomic Many-Body Theory, Springer, BerUn, 1982. 

We presented fully self-consistent separable random-phase-approximation (SRPA) method for description of linear dynamics of different finite Fermi-systems. The method is very general, physically transparent, convenient for the analysis and treatment of the results. SRPA drastically simplifies the calculations. It allows to get a high numerical accuracy with a minimal computational effort. The method is especially effective for systems with a number of particles 10 — 10, where quantum-shell effects in the spectra and responses are significant. In such systems, the familiar macroscopic methods are too rough while the full-scale microscopic methods are too expensive. SRPA seems to be here the best compromise between quality of the results and the computational effort. As the most involved methods, SRPA describes the Landau damping, one of the most important characteristics of the collective motion. SRPA results can be obtained in terms of both separate RPA states and the strength function (linear response to external fields). 

Here is the fragment wavefunction and iJ)q is the Q-state wave-function in second quantization representation. Further, as an example, we have limited consideration here to systems of integral total spin Fermi systems can be treated in a similar way. 

P. Noziere, Theory of Interacting Fermi Systems, W. A. Benjamin Inc., New York, 1964. 

Nozieres, P. Theory of interacting fermi systems. New York Benjamin 1964 Abrikosov, A., Gorkov, L., Dzyaloshinski, J. Methods of quantum field theory in statistical physics. Englewood Cliffs Prentice-Hall 1963... 

Migdal, A.B. Theory of Finite Fermi Systems, Wiley-Interscience, New York, 1967. 

While considering ensembles of identical particles, one has to take into account their quantum statistical properties. This imposes additional symmetry restrictions on the ensemble dynamics and requires the inclusion of additional symmetry operations into the group of operations. This situation is discussed in the second paper of the chapter for Fermi systems, where the additional operation is antisymmetrization over the wave functions of individual fermionic qubits. 

In the RPA, the induced potential V" (r, t) is simply obtained as the potential induced in a noninteracting Fermi system by both the probe-particle charge density p (r, t) and the induced electron density p (r, Z), i.e.,... 

In a unified description we show the mathematical equivalence of infrared behaviour for the following model situations 1) 1-d Fermi systems with general interactions, 2) 1-d Bose systems with "Sine-Gordon" interaction, 3) the 2-d magnetic (harmonic) rotator model,... 

This means that we have a chance to find a logarithmic (infrared) divergence and thus an infrared problem if dimension d and dispersion S coincide. As the normal dispersions are S = 1 for quantummechanical systems (massless particle-hole excitations in Fermi systems, massless Bose systems) and 6 = 2 for classical systems with short range forces, we conclude ... 

Energy excitations in 1-d Fermi systems are effectively Bose excitations with zero mass. A suitable representation of Fermion field operators in terms of Bosons has been given by... 

One final result concerns the particle spectrum of the 1-d Fermi system. The existence of a finite correlation length for... 

The thermodynamics of a l-d Fermi system can be perfectly mapped onto the thermodynamics of a two-component classical real gas on the surface of a cylinder. The relationship between these two infrared problems (cf. Zittartz s contribution) is exploited as follows. We treat the classical plasma by a modified Mayer cluster expansion method (the lowest order term corresponding to the Debye Hiickel theory), and obtain an exponentially activated behavior of the specific heat (cf. Luther s contribution) of the original quantum gas by simply reinterpreting the meaning of thermodynamic variables. 

Hamiltonian H of the l-d Fermi system can be represented by Bose-operators [l3 ... 

It turns out that the language of normal and local modes that emerged from the bifurcation analysis of the Darling-Dennison Hamiltonian is not sufficient to describe the general Fermi resonance case, because the bifurcations are qualitatively different from the normal-to-local bifurcation in figure Al.2.10. For example, in 2 1 Fermi systems, one type of bifurcation is that in which resonant collective modes are bom [54]. The resonant collective modes are illustrated in figure A12.11 their difference from the local modes of the Darling-Dennison system is evident. Other types of bifurcations are also possible in Fermi resonance systems a detailed treatment of the 2 1 resonance can be found in [44]. 

In fact, there is still another contribution to the heat capacity, the electronic contribution to the heat capacity [25]. This type of contribution is also referred to as a Fermi system [26, Chap. 15]. The electronic contribution at low temperatures computes as... 

A remarkable consequence of introducing time-dependent one-electron potentials into the calculation is that the well-knovm instability of a degenerate Fermi system to sudden local perturbations (Anderson, 1967) comes into play. This... 

Various mixtures of ultracold atomic species offer a wide playground for ultracold heteronuclear molecules, and the basic interaction properties of many different combinations involving bosonic and fermionic atoms are currently being explored. A new twist to the field is given by ultracold Fermi-Fermi systems, which have recently been realized in mixtures of Li and [99,100]. Molecule formation in such systems will... 

Volume 10 INTERACTING BOSE-FERMI SYSTEMS IN NUCLEI... 

If the forces and fluxes are properly selected, they are canonically conjugated in the sense of irreversible thermodynamics (Lf/ = L ) (Onsager relation). There are two distinctly different kinds of forces which may induce a flux. The first and more familiar is the electrical force. The second kind of forces has its origin in statistics it is not a force in the usual sense, but normally arises from concentration gradients and results in diffusive fluxes. In all our discussions we shall be concerned with an assembly of electrons, i.e. a Fermi system, for which the chemical potential (ji(T)) at r = 0 K is the Fermi energy. Then it is common practice to introduce the electrochemical potential, and to define an effective electric field E = — V(d> + pje), which is the field that is normally observed. 

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