scholarly journals SUPERSYMMETRY OF PARAFERMIONS

1999 ◽  
Vol 14 (39) ◽  
pp. 2739-2752 ◽  
Author(s):  
SERGEI KLISHEVICH ◽  
MIKHAIL PLYUSHCHAY
Keyword(s):  
Single Mode ◽  
Type Systems ◽  
Characteristic Functions ◽  
Finite Dimensional ◽  
Deformed Oscillator

We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The supersymmetry is realized in both unbroken and spontaneously broken phases. As in the case of parabosonic supersymmetry observed recently by one of the authors, the form of the associated superalgebra depends on the order of the parafermion and can be linear or nonlinear in the Hamiltonian. The list of supersymmetric parafermionic systems includes usual parafermions, finite-dimensional q-deformed oscillator, q-deformed parafermionic oscillator and parafermionic oscillator with internal Z2 structure.

Photon added coherent states of the parity deformed oscillator

2019 ◽  
Vol 34 (14) ◽  
pp. 1950104 ◽  
Author(s):  
A. Dehghani ◽  
B. Mojaveri ◽  
S. Amiri Faseghandis
Keyword(s):  
Coherent States ◽  
Uncertainty Relation ◽  
Annihilation Operator ◽  
Single Mode ◽  
Heisenberg Algebra ◽  
Uncertainty Relations ◽  
Deformed Oscillator ◽  
Cat States ◽  
Poissonian Statistics ◽  
Creation Operators

Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.[Formula: see text] The RDCSs minimize a corresponding uncertainty relation, and resolve an identity condition through a positive definite measure which is explicitly derived. We introduce a class of single-mode excited coherent states (PARDCS) of the PHO through “m” times application of deformed creation operators to RDCS. For the states thus constructed, we analyze their statistical properties such as squeezing and sub-Poissonian statistics as well as their uncertainty relations.

Generalized characteristic functions for a single-mode radiation field

1997 ◽  
Vol 230 (5-6) ◽  
pp. 276-282 ◽  
Author(s):  
Paulina Marian ◽  
Tudor A. Marian
Keyword(s):  
Radiation Field ◽  
Single Mode ◽  
Characteristic Functions

THE PARABOSON REALIZATION OF PARAFERMIONS

1996 ◽  
Vol 11 (24) ◽  
pp. 1971-1975
Author(s):  
HA HUY BANG
Keyword(s):  
Single Mode ◽  
Deformed Oscillator

The paraboson realizations of parafermions have been derived from q-deformed oscillator. Interestingly, they can reproduce the constructing fermions in terms of a single-mode boson1 and its generalization2 in the limiting cases.

scholarly journals Quasi-periodic solutions of the negative-order Jaulent–Miodek hierarchy

2019 ◽  
Vol 32 (03) ◽  
pp. 2050007 ◽  
Author(s):  
Jinbing Chen
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Structure ◽  
Spectral Curve ◽  
Type Systems ◽  
Finite Dimensional ◽  
Zero Curvature ◽  
Negative Order ◽  
Neumann Type ◽  
Jacobi Inversion ◽  
Negative Formula

A uniform construction of quasi-periodic solutions to the negative-order Jaulent–Miodek (nJM) hierarchy is presented by using a family of backward Neumann type systems. From the backward Lenard gradients, the nJM hierarchy is put into the zero-curvature setting and the bi-Hamiltonian structure displaying its integrability. The nonlinearization of Lax pair is generalized to the nJM hierarchy such that it can be reduced to a sequence of backward Neumann type systems, whose involutive solutions yield finite parametric solutions of the nJM hierarchy. The negative [Formula: see text]-order stationary JM equation is given to specify a finite-dimensional invariant subspace for the nJM flows. With a spectral curve determined by the Lax matrix, the nJM flows are linearized on the Jacobi variety of a Riemann surface. Finally, the Riemann–Jacobi inversion is applied to Abel–Jacobi solutions of the nJM flows, by which some quasi-periodic solutions are obtained for the nJM hierarchy.

Two kinds of finite-dimensional integrable reduction to the Harry–Dym hierarchy

2016 ◽  
Vol 30 (32n33) ◽  
pp. 1650396
Author(s):  
Jinbing Chen
Keyword(s):  
Hamiltonian Systems ◽  
Tangent Bundle ◽  
Type Systems ◽  
Lax Pair ◽  
Symplectic Space ◽  
Spatial Variables ◽  
Parametric Solutions ◽  
Finite Dimensional ◽  
Neumann Type ◽  
Temporal And Spatial

In this paper, two kinds of finite-dimensional integrable reduction are studied for the Harry–Dym (HD) hierarchy. From the nonlinearization of Lax pair, the HD hierarchy is reduced to a class of finite-dimensional Hamiltonian systems (FDHSs) in view of a Bargmann map and a set of Neumann type systems by a Neumann map, which separate temporal and spatial variables on the symplectic space [Formula: see text] and the tangent bundle of ellipsoid [Formula: see text], respectively. It turns out that involutive solutions of the resulted finite-dimensional integrable systems (FDISs) directly give rise to finite parametric solutions of HD hierarchy through the Bargmann and Neumann maps. The finite-gap potential to the high-order stationary HD equation is obtained that cuts out a finite-dimensional invariant subspace for the HD flows. Finally, some comparisons of two kinds of integrable reductions are then discussed.

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