# Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator

@article{DazBautista2016NonlinearSS, title={Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator}, author={Erik D{\'i}az-Bautista and David J Fern{\'a}ndez C}, journal={The European Physical Journal Plus}, year={2016}, volume={131}, pages={1-18} }

Abstract.Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the…

## 4 Citations

Multiphoton supercoherent states

- PhysicsThe European Physical Journal Plus
- 2019

Abstract.In this paper we are going to build the multiphoton supercoherent states for the supersymmetric harmonic oscillator as eigenstates of the m -th power of a special form (but still with a free…

Graphene coherent states

- Physics
- 2017

Abstract.In this paper we will construct the coherent states for a Dirac electron in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene surface. First of…

## References

SHOWING 1-10 OF 75 REFERENCES

Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states

- Mathematics
- 1999

Using an iterative construction of the first-order intertwining technique, we find k-parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the…

On the coherent states, displacement operators and quasidistributions associated with deformed quantum oscillators

- Mathematics
- 2000

The Wigner (W), Husimi-Kano (Q) and Glauber-Sudarshan (P) quasidistributions are generalized to f-deformed quasidistributions which extend the parametric family of s-ordered quasidistributions of…

Cyclic quantum evolution and Aharonov-Anandan geometric phases in SU(2) spin-coherent states.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1990

It is shown that cyclic quantum evolution can be realized and the Aharonov-Anandan (AA) geometric phase can be determined for any spin-j system driven by periodic fields and a SU(2) Lie-group formulation of the AA geometric phase in the spin-coherent state is presented.

Uncertainties of coherent states for a generalized supersymmetric annihilation operator

- Physics
- 2013

This study presents supersymmetric coherent states that are eigenstates of a general four-parameter family of annihilation operators. The elements of this family are defined as operators in Fock…

f-oscillators and nonlinear coherent states

- Physics
- 1997

The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of…

Cyclic states, Berry phases and the Schrodinger operator

- Physics
- 1993

The evolution of a quantum mechanical system under a nonadiabatic external perturbation at a time interval (0,T) is considered. It is shown that all the cyclic states of the system, mod Psi (T))=ei…

Polynomial Heisenberg algebras

- Mathematics
- 2004

Polynomial deformations of the Heisenberg algebra are studied in detail. Some of their natural realizations are given by the higher order susy partners (and not only by those of first order, as is…

Aharonov-Anandan geometric phase for spin-1/2 periodic Hamiltonians

- Physics
- 1992

The authors calculate exactly the Aharonov-Anandan phase for the evolution of a spin-1/2 in some periodic time-dependent magnetic fields, and give a discussion of the results versus the adiabatic…