Journal of Optics B Quantum and Semiclassical Optics

-representation, positive -representation, and antinormally ordering expansion of density matrices in nonlinear coherent states

Hong-Yi Fan, Yue Fan, Junhua Chen

Published Sep 2, 2002• 2 citations

Abstract

Based on the newly constructed overcompleteness relation of the nonlinear coherent states (NLCSs) and corresponding 𝒫-representation we derive: (1) a new antinormally ordered expansion of density matrices; and (2) the corresponding positive 𝒫-representation. Our derivation employs the technique of integration within an ordered product of nonlinear Bose operator functions. A relationship between the positive 𝒫-representation and the generalized characteristic function in the context of NLCSs is also obtained.

DOI: 10.1088/1464-4266/4/5/316

Related papers

The P -representation on Nonlinear Coherent State Basis

Fan Hong‐Yi, Cheng Hai-Ling

Using the technique of integration within an ordered product of nonlinear Bose operators and by composing the nonlinear coherent state's over-completeness relation, we construct the corresponding P -representation theory. The generalized P -representation for some nonlinear Bose operators can be established.

Communications in Theoretical PhysicsJun 15, 20027 citations

The P—representation on Nonlinear Coherent State Basis

FANHong-Yi, CHENGHai-Ling

Using the technique of integration within an ordered product of nonlinear Bose operators and by composing the nonlinear coherent state's over-completeness relation, we construct the corresponding P-representation theory. The generalized P-representation for some nonlinear Bose operators can be established.

理论物理通讯：英文版Jan 1, 20020 citations

Generalized Weyl Ordering and Nonlinear Coherent States

Fan Hong-Yi

In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl ordering operator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operator functions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship between normal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistent theory for NLCS.

Communications in Theoretical PhysicsDec 15, 20023 citations

Nonlinear coherent state representation and related generalized Wigner function

Hong-Yi Fan, Hailing Cheng

The generalized Wigner operator and Wigner distribution function in phase space corresponding to the field-intensity-dependent operators is constructed in the nonlinear coherent state representation. The generalized Wigner theorem is also derived. The whole discussion is based on the technique of integration within an ordered product of the field-intensity-dependent operators.

Journal of Optics B Quantum and Semiclassical OpticsNov 23, 200112 citations

Generalized Weyl Ordering and Nonlinear Coherent States

FANHong-Yi, Hong-Yi

In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl orderingoperator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operatorfunctions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship betweennormal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistenttheory for NLCS.

理论物理通讯：英文版Jan 1, 20020 citations

Normally Ordered and Antinormally Ordered Expansions of Some Exponential Operators in Hilbert Space

Fan Hong-Yi

In this paper, the completeness relations of the fundamental representations in quantum mechanics, together with the "integration within orderd product" technique are exploited to derive normally ordered and antinormally ordered expansions of some exponential operators in Hilbert space. Applications of the normally ordered exponential operators to evaluating Feynman matrix element in coherent state representation are given, which seems to be a new approach.

Communications in Theoretical PhysicsSep 1, 19897 citations