Time evolution law of the Laguerre-polynomial-weighted chaotic photon field in an amplitude-damping channel

We examine how a Laguerre-polynomial-weighted chaotic photon field (LPWCPF), whose density operator is [Formula: see text], evolves in an amplitude-damping channel. By using a newly derived generating function of two-variable Hermite polynomials we obtain the evolution law of LPWCPF, which turns out to be a new LPWCPF with a new parameter, depending on 1 − e−2κt, where κ represents decay rate. The technique of integration (summation) within an ordered product of operators is used in our discussions.

Download Full-text

Photon-added chaotic field and its damping in a thermo enviroment

Canadian Journal of Physics ◽

10.1139/cjp-2014-0405 ◽

2015 ◽

Vol 93 (4) ◽

pp. 456-459 ◽

Cited By ~ 1

Author(s):

Hong-Yi Fan ◽

Rui He

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Density Operator ◽

Laguerre Polynomial ◽

Quantum Field ◽

Initial Field ◽

Normal Ordering ◽

Chaotic Field ◽

Amplitude Damping Channel ◽

Time Evolution Equation

We propose a new photon field in quantum field theory, named Laguerre-polynomial-weighted chaotic field. This field will emerge when an initial photon-added chaotic field, which is represented by its density operator [Formula: see text], dissipates in an amplitude damping channel described by time evolution equation [Formula: see text], where κ is a damping coefficient, that is, the initial field will evolve into [Formula: see text] with [Formula: see text], where Ls is the s-order Laguerre-polynomial, and : : denotes normal ordering. We employ the method of summation within an ordered product of operators to obtain our result.

Download Full-text

Evolution law of photocounting probability in a diffusion channel

Modern Physics Letters B ◽

10.1142/s0217984914501450 ◽

2014 ◽

Vol 28 (18) ◽

pp. 1450145 ◽

Cited By ~ 1

Author(s):

Hong-Yi Fan ◽

Fang Jia ◽

Peng-Fei Zhang ◽

Rui He

Keyword(s):

Diffusion Process ◽

Density Operator ◽

Laguerre Polynomial ◽

Initial Density ◽

Optical Fields ◽

Diffusion Channel ◽

Normal Ordering ◽

Evolution Law ◽

Field L ◽

New Formula

We find that in optical fields' diffusion process, the l-photocounting probability formula [Formula: see text] at time t = 0 should be generalized to a new formula [Formula: see text] at time t, where ρ(0) is the initial density operator of the field, Ll is the Laguerre polynomial, : : denotes normal ordering, and ξ is the quantum efficiency of the photocounting detector. This new formula brings much convenience for different ρ0, because for deriving [Formula: see text] there is no need to derive the corresponding ρ(t) in the diffusion channel.

Download Full-text

Time evolution of a squeezed chaotic field in an amplitude damping channel when used as a generating field for a squeezed number state

Chinese Physics B ◽

10.1088/1674-1056/24/7/070306 ◽

2015 ◽

Vol 24 (7) ◽

pp. 070306 ◽

Cited By ~ 1

Author(s):

Xing-Lei Xu ◽

Hong-Qi Li ◽

Hong-Yi Fan

Keyword(s):

Time Evolution ◽

Amplitude Damping ◽

Number State ◽

Chaotic Field ◽

Amplitude Damping Channel

Download Full-text

A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials

Symmetry ◽

10.3390/sym13040648 ◽

2021 ◽

Vol 13 (4) ◽

pp. 648

Author(s):

Ghulam Muhiuddin ◽

Waseem Ahmad Khan ◽

Ugur Duran ◽

Deena Al-Kadi

Keyword(s):

Generating Function ◽

Functional Equations ◽

Laguerre Polynomials ◽

Hermite Polynomials ◽

Bernoulli Polynomials ◽

Higher Order ◽

New Class

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

Download Full-text

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

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887820500218 ◽

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.

Download Full-text