Non-Hermitian Oscillator-Like Hamiltonians and lambda-Coherent States Revisited (original) (raw)
Related papers
Non-Hermitian Oscillator-Like Hamiltonians and Λ-Coherent States Revisited
Modern Physics Letters A, 2001
Previous λ-deformed non-Hermitian Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to take into account their property of selfadjointness. The corresponding deformed λ-states lead to new families of coherent states according to the DOCS, AOCS and MUCS points of view.
Annals of Physics, 2018
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a mathematical procedure to satisfy the superposition principle. In this form the non-Hermitian oscillators can be studied in much the same way as in the Hermitian approaches. Two different nonlinear algebras generated by properly constructed ladder operators are found and the corresponding generalized coherent states are obtained. The non-Hermitian oscillators can be steered to the conventional one by the appropriate selection of parameters. In such limit, the generators of the nonlinear algebras converge to generalized ladder operators that would represent either intensity-dependent interactions or multi-photon processes if the oscillator is associated with single mode photon fields in nonlinear media.
Nonclassical States for Non-Hermitian Hamiltonians with the Oscillator Spectrum
Quantum Reports
In this paper, we show that the standard techniques that are utilized to study the classical-like properties of the pure states for Hermitian systems can be adjusted to investigate the classicality of pure states for non-Hermitian systems. The method is applied to the states of complex-valued potentials that are generated by Darboux transformations and can model both non- P T -symmetric and P T -symmetric oscillators exhibiting real spectra.
Springer Proceedings in Physics 205 (2018) 209-242, Proceedings of "Coherent States and their Applications: A Contemporary Panorama", CIRM Marseille, France, 2018
It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Ken-nard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as " coherent states " today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Non-classical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superse-lection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the sem-inal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here originate from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics community. CONTENTS
Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties
The European Physical Journal D, 2013
In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of dynamical symmetries associated with the system under consideration. These states admit a resolution of the identity through positive definite measures on the complex plane. We have shown that the realization of these states for different values of the deformation parameters leads to the well-known Klauder-Perelomov and Barut-Girardello CSs associated with the su(1, 1) Lie algebra. This is why we call them the generalized su(1, 1) CSs for the PHO. Finally, study of some statistical characters such as squeezing, anti-bunching effect and sub-Poissonian statistics reveals that the constructed GCSs have indeed nonclassical features.
New construction of coherent states for generalized harmonic oscillators
Reports on Mathematical Physics, 2002
A dynamical algebra A q , englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the type A q is discussed. The construction following this method is carried out for the special case.
Two dimensional non-Hermitian harmonic oscillator: coherent states
Physica Scripta
In this study, we introduce a two dimensional complex harmonic oscillator potential with space and time reflection symmetries. The corresponding time independent Schrödinger equation yields real eigenvalues with complex eigenfunctions. We also construct the coherent state of the system by using a superposition of 12 eigenfunctions. Using the complex correspondence principle for the probability density we investigate the possible modifications in the probability densities due to the non-Hermitian aspect of the Hamiltonian.
Non-Hermitian oscillator and R-deformed Heisenberg algebra
Journal of Mathematical Physics, 2013
A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation. A set of deformed creation annihilation operators is introduced whose algebra shows that the transformed Hamiltonian has conformal symmetry. The spectrum is obtained using algebraic technique. The superconformal structure of the system is also worked out in detail. An anomaly related to the spectrum of the Hermitian counterpart of the non-Hermitian Hamiltonian with generalized ladder operators is shown to occur and is discussed in position dependent mass scenario.
Deformed Harmonic Oscillator for Non-Hermitian Operator and the Behavior of pt and CPT Symmetries
International Journal of Modern Physics B - IJMPB, 2006
In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator H=(alpha )/(2m) (hat{p}1+ (lambda)/(hbar )hat q2;)2+ (beta momega 2)/(2)(hat q1-(theta )/(2 hbar ) hat p2; )2 where lambda,theta are real positive parameters, since the parameters alpha,beta,m are for the general case complex. For the case alpha=1,beta=1 and mass m real, we find the eigenfunctions and eigenvalues of energy, the coherent states, the time evolution of the operators \hat{q}_i, \hat{p}_j$ in the Heisenberg picture and the uncertainty relations. In this case the operator ℋ is Hermitian and PT-symmetric. Also for the case m complex alpha=1,beta=1, the operator ℋ is non-Hermitian and no more PT symmetric, but CPT symmetric with real discrete positive spectrum and the CPT symmetry is preserved. In the general case alpha,beta,m complex, for the non-Hermitian operator ℋ, we obtain complex spectrum and for the special values of the complex parameters alpha,beta the spectrum is real di...