New Version of q-Deformed Supersymmetric Quantum Mechanics

Abstract

A new version of the q-deformed supersymmetric quantum mechanics (q-SQM), which is inspired by the Tamm-Dankoff-type (TD-type) deformation of quantum harmonic oscillator, is constructed. The obtained algebra of q-SQM is similar to that in Spiridonov's approach. However, within our version of q-SQM, the ground state found explicitly in the special case of superpotential yielding q-superoscillator turns out to be non-Gaussian and takes the form of special (TD-type) q-deformed Gaussian.

The symmetric Tamm–Dancoffq-oscillator: the representation, quasi-Fibonacci nature, accidental degeneracy and coherent states

“…Next, this same angle θ c may be of relevance when a q-Bose gas model with phase-like q is used to effectively describe [25] existing data on the correlation intercepts of pions generated in relativistic heavy-ion collisions. In the third application, concerning 2+1 quantum gravity, the approach of J.Nelson and T.Regge leads [26] to the nonstandard q-algebras U ′ q (so n ), see [27], with the deformation parameter linked to cosmological constant Λ as q = , Λ < 0, and h being Planck constant. At last, within the p, q-deformed Bose gas model involving mutually conjugate complex p, q, the deformed critical temperature T p,q c was found to rise [16] with growing extent of deformation.…”

“…Thus, it should be viewed as quasi-Fibonacci one. The proof proceeds similarly to that based on (20), but now the analogous system of 4 equations stems from equating the coefficient expressions (involving q, p, Q, P, λ, ρ) at p n , q n , P n and Q n viewed as independent basis elements. Remark.…”

“…(adding (28) to (29) recovers (27)). Here K(q, n) is an arbitrary function incorporating the arbitrariness of splitting eq.…”

“…Consider the fiveparameter oscillator whose structure function is build by "gluing" (using the weight-like t-parameter, see formula (22) in [20]) the two different structure functions (here -two different copies of p, q-oscillator):…”

The Statistical Properties of theq-Deformed Dirac Oscillator in One and Two Dimensions

“…They have found the spectrum and eigenvalues of such a harmonic oscillator under the assumption that there is a state with a lowest energy eigenvalue. Recently, the theory of the q-deformed has become a topic of great interest in the last few years, and it has been finding applications in several branches of physics because of its possible applications in a wide range of areas, such as a q-deformation of the harmonic oscillator [7], a q-deformed Morse oscillator [8], a classical and quantum q-deformed physical systems [9], Jaynes-Cummings model and the deformed-oscillator algebra [10], q-deformed super-symmetric quantum mechanics [11], for some modified q-deformed potentials [12], on the Thermo-statistic properties of a q-deformed ideal Fermi gas [13], Q-Deformed Tamm-Dancoff oscillators [14], q-qeformed fermionic oscillator algebra and thermodynamics [15], and finally on the fermionic q deformation and its connection to thermal effective mass of a quasi-particle [16].…”