Superfluidity of heated Fermi systems in the static fluctuation approximation
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CLEI Theory
Superfluidity of Heated Fermi Systems in the Static Fluctuation Approximation A. A. Khamzin1)* , A. S. Nikitin2), and A. S. Sitdikov2) Received January 19, 2015
Abstract—Superfluidity properties of heated finite Fermi systems are studied in the static fluctuation approximation, which is an original method. This method relies on a single and controlled approximation, which permits taking correctly into account quasiparticle correlations and thereby going beyond the independent-quasiparticle model. A closed self-consistent set of equations for calculating correlation functions at finite temperature is obtained for a finite Fermi system described by the Bardeen–Cooper– Schrieffer Hamiltonian. An equation for the energy gap is found with allowance for fluctuation effects. It is shown that the phase transition to the supefluid state is smeared upon the inclusion of fluctuations. DOI: 10.1134/S1063778815060137
1. INTRODUCTION In recent years, the growth of variety of systems formed by a finite number of fermions and created and studied under laboratory conditions was among the factors that quickened interest in such systems. In addition to nuclei known for a long time, objects of this type that are being vigorously studied at present include quantum dots and clusters containing a finite number of atoms or molecules. At least some of the aforementioned Fermi systems are long-lived even in highly excited states, with the result that the evolution of their properties versus temperature can be studied experimentally. Available information about the behavior of so-called heated nuclei (those whose excitation energy is about several MeV units or even higher) is quite extensive. It includes information about changes in their shape and in collective vibrations. The main problem in theoretically studying highly excited systems stems from an extremely high level density, in which case realistic calculations on the basis of a microcanonical ensemble are impossible, so that one has to resort to a statistical description. Therefore, it is of importance to construct an efficient statistical theory that would describe a broad range of phenomena in heated finite Fermi systems. In studying the properties of highly excited finite Fermi systems, one usually generalizes methods and 1)
Kazan (Volga Region) Federal University, Institute of Physics, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008 Russia. 2) Kazan State Power Engineering University (KSPEU), Krasnoselskaya ul. 51, Kazan, Tatarstan, 420066 Russia. * E-mail: [email protected]
approximations developed for weakly excited systems (at T = 0). However, many of the approximations used give no way to take correctly into account various correlation effects, which could play an important role in explaining observed statistical properties. By employing the concept of temperature, one can generalize a number of methods developed for studying weakly excited Fermi systems to the case of highly excited systems treated as heated ones. The method of temperature (Matsubara) Green’s functions [1]
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