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Europhysics Letters (EPL)

Pair Mode in Two-Level Parafermion Systems

Michio Hama, M Sawamura, H Suzuki

Published Feb 1, 1993• 2 citations
Publisher

Abstract

For the system of two parafermionic degrees of freedom, we obtain the partition function which is very compact. It exhibits pair mode behaviour, the total excitation number of three modes corresponding to the energies E 1 , E 2 and E 1 + E 2 being not more than the order p . We compare it with those of para-Bose systems which also show similar pair mode behaviour.

DOI
10.1209/0295-5075/21/4/001

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For the system of two parafermionic degrees of freedom, we obtain the partition function which is very compact. It exhibits pair mode behaviour, the total excitation number of three modes corresponding to the energies E 1 , E 2 and E 1 + E 2 being not more than the order p . We compare it with those of para-Bose systems which also show similar pair mode behaviour.
We address the problem of two pairs of fermions living on an arbitrary number of single particle levels of a potential well (mean field) and interacting through a pairing force. The associated solutions of the Richardson’s equations are classified in terms of a number vl, which reduces to the seniority v in the limit of large values of the pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G → ∞ limit. We express analytically, through the moments of the single particle levels distribution, the collective mode energy and the two critical values G + cr and G − cr of the coupling which can exist on a single particle level with no pair degeneracy. Notably G + cr and G − cr merge when the number of single particle levels goes to infinity, where they coincide with the Gcr (when it exists) of a one pair system, not envisioned by the Richardson theory. In correspondence of Gcr the system undergoes a transition from a mean field to a pairing dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes finding out that the former, for G> G − cr, come close to the BCS predictions, whereas the latter display a divergence at Gcr, signaling the onset of a long range off-diagonal order in the system. PACS numbers: 21.60.-n, 21.30 Fe, 24.10.Cn 1 1
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This study aims to determine the thermodynamic properties of the parastatistics system of order two. The thermodynamic properties to be searched include the Grand Canonical Partition Function (GCPF) Z, and the average number of particles N. These parastatistics systems is in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD) and Bose-Einstein (BE). Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple thermodynamic functions for parastatistics system of order two are derived. The recursion linkages are then used to calculate the thermodynamic functions of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. From these results we concluded that from the Grand Canonical Partition Function (GCPF), Z, the thermodynamics properties of parastatistics system of order two (paraboson and parafermion) can be derived and have similar shape with parastatistics system of order one (Boson and Fermion). The similarity of the graph shows similar thermodynamic properties. Keywords: parastatistics, thermodynamic properties