scholarly journals Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states

2013 ◽  
Vol 54 (1) ◽  
pp. 013506 ◽  
Author(s):  
K. Thirulogasanthar ◽  
S. Twareque Ali
Keyword(s):  
Hilbert Space ◽  
Coherent States ◽  
Hermite Polynomials ◽  
Quaternionic Hilbert Space

Nonclassicality of photon-modulated spin coherent states in the Holstein-Primakoff realization

2021 ◽  
Author(s):  
Xiaoyan Zhang ◽  
Jisuo Wang ◽  
Lei Wang ◽  
Xiangguo Meng ◽  
Baolong Liang
Keyword(s):  
Coherent States ◽  
Wigner Distribution ◽  
Hermite Polynomials ◽  
Photon Number ◽  
Spin Ladder ◽  
Bernoulli Distribution ◽  
Ladder Operators ◽  
Spin Number ◽  
Photon Number Distribution ◽  
Spin Coherent States

Abstract Two new photon-modulated spin coherent states (SCSs) are introduced by operating the spin ladder operators J ± on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution, second-order correlation function, photocount distribution and negativity of Wigner distribution. Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials. Compared with the ordinary SCS, the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j, which means that the nonclassicality can be enhanced by selecting suitable parameters.

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Coherent States ◽  
Finite Interval ◽  
Hermite Polynomials ◽  
Oscillator Algebra ◽  
Text Representation ◽  
Ladder Operators ◽  
Recursion Relations ◽  
Wilson Operator

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

DETECTION OF THE SPATIAL CURVATURE EFFECTS THROUGH PHYSICAL PHENOMENA: THE NONLINEAR COHERENT STATES APPROACH

2012 ◽  
Vol 09 (01) ◽  
pp. 1250009 ◽  
Author(s):  
A. MAHDIFAR ◽  
R. ROKNIZADEH ◽  
M. H. NADERI
Keyword(s):  
Hilbert Space ◽  
Geometric Phase ◽  
Coherent States ◽  
Transition Probability ◽  
Physical Space ◽  
Spatial Curvature ◽  
Curved Space ◽  
Curvature Effects ◽  
Projective Hilbert Space ◽  
Physical Phenomena

In this paper, by using the nonlinear coherent states approach, we find a relation between the geometric structure of the physical space and the geometry of the corresponding projective Hilbert space. To illustrate the approach, we explore the quantum transition probability and the geometric phase in the curved space.

MAGNETIC GROUP ON THE PSEUDOSPHERE

1992 ◽  
Vol 06 (21) ◽  
pp. 3525-3537 ◽  
Author(s):  
V. BARONE ◽  
V. PENNA ◽  
P. SODANO
Keyword(s):  
Magnetic Field ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Constant Magnetic Field ◽  
Coherent States ◽  
Compact Operators ◽  
Point Of View ◽  
Algebraic Point ◽  
Planar Limit ◽  
Discrete Part

The quantum mechanics of a particle moving on a pseudosphere under the action of a constant magnetic field is studied from an algebraic point of view. The magnetic group on the pseudosphere is SU(1, 1). The Hilbert space for the discrete part of the spectrum is investigated. The eigenstates of the non-compact operators (the hyperbolic magnetic translators) are constructed and shown to be expressible as continuous superpositions of coherent states. The planar limit of both the algebra and the eigenstates is analyzed. Some possible applications are briefly outlined.

scholarly journals Groupoids and Coherent States

2019 ◽  
Vol 26 (04) ◽  
pp. 1950017 ◽  
Author(s):  
F. di Cosmo ◽  
A. Ibort ◽  
G. Marmo
Keyword(s):  
Hilbert Space ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum Mechanical ◽  
Natural Setting ◽  
Invariant Subset ◽  
Quantum Mechanical System ◽  
Generalized Coherent States ◽  
Invertible Elements ◽  
Groupoid Algebra

Schwinger’s algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids. Thus given a quantum mechanical system with associated Hilbert space determined by a representation of a groupoid, it is shown that any invariant subset of the group of invertible elements in the groupoid algebra determines a family of generalized coherent states provided that a completeness condition is satisfied. The standard coherent states for the harmonic oscillator as well as generalized coherent states for f-oscillators are exemplified in this picture.

scholarly journals Examples of enhanced quantization: Bosons, fermions and anyons

2014 ◽  
Vol 29 (22) ◽  
pp. 1450119
Author(s):  
T. C. Adorno ◽  
J. R. Klauder
Keyword(s):  
Hilbert Space ◽  
Coherent States ◽  
Canonical Quantization ◽  
Action Functional ◽  
Classical Action ◽  
Unitary Transformations ◽  
Classical Quantum ◽  
Quantum Action ◽  
Space Vectors ◽  
Gaussian Vectors

Enhanced quantization offers a different classical/quantum connection than that of canonical quantization in which ℏ > 0 throughout. This result arises when the only allowed Hilbert space vectors allowed in the quantum action functional are coherent states, which leads to the classical action functional augmented by additional terms of order ℏ. Canonical coherent states are defined by unitary transformations of a fixed, fiducial vector. While Gaussian vectors are commonly used as fiducial vectors, they cannot be used for all systems. We focus on choosing fiducial vectors for several systems including bosons, fermions and anyons.

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