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Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector |qλ,ν of linear combination of the coordinate and momentum operator, (λQ + νP), where λ, ν are real numbers, and |qλν is complete, then the projector |qλνq| must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.

The coherent-intermediate-entangled state |α, xλ,ν is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The |α,xλ,ν makes up a new quantum mechanical representation, and the completeness relation of |α,xλ,ν is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state |α,xλ,ν and the Schmidt decomposition of |α,xλ,ν is investigated.

We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix |ξ1, ξ2〉C,D C,D〈ξ1, ξ2| is a Radon transform of Wigner operator.

By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective. This method can also be applied to solve other master equations.

We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new intermediate coordinate-momentum representation for a two-particle system is proposed and applied to some two-body dynamic problems.

This paper constructs the new common eigenvectors of n intermediate coordinate-momentum operators which are complete and orthonormal. The intermediate coordinate-momentum representation of a multi-particles system is proposed and applied to a generaln-mode quantum harmonic oscillators system with coordinate-momentum coupling.

By using the technique of integration within an ordered product (IWOP) of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.

By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product (IWOP) of operators is employed in our discussions.

Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics (TFD), the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance–inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.

We employ the coherent thermal states (a kind of entangled states) in thermal field dynamics to establish a complete entangled state formalism expressing pseudo-classical representations of density operator for light field. Especially, the relationship between the coherent thermal state and the characteristic function and the positive P representation in quantum optics theory are obtained.

The mesoscopic quartz piezoelectric crystal equivalent circuit is quantized by the method of damped harmonic oscillator quantization. It is shown that the quantum fluctuations of voltage and current of each loop are related to not only the equivalent circuit inherent parameter and squeezing parameter, but also the temperature, and decay according to exponent along with time in the thermal vacuum state, the thermal coherent state and the thermal squeezed state.

In the preceding paper (Commun. Theor. Phys. 51 (2009) 321) we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators composed of angular momentum operators. We mainly disentangle the form of exp[2hJz + gJ+ + kJ−] as the ordering exp(...J+)exp(...Jz)exp(...J−), we employ the Schwinger Bose realization J− = b†a, J+ = a†b, Jz = (a†a − b†b)/2 to fulfil this task, without appealing to Lie algebra method. Note that this operator's disentangling is different from its decomposition in normal ordering.

We investigate how an optical squeezed chaotic field (SCF) evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also show that the density operator of SCF can be viewed as a generating field of the squeezed number state.

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ωk (p, q) with a real k parameter and can unify the P—Q, Q—P, and Weyl ordering of operators in k = 1, − 1, 0, respectively, we find the mutual transformations between δ(p — P)δ(q — Q), δ(q — Q)δ(p — P), and Ωk(p, q), which are, respectively, the integration kernels of the P—Q, Q—P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The — and — ordered forms of Ωk (p, q) are also derived, which helps us to put the operators into their — and — ordering, respectively.

Differential quotient rule of composite function operator and its applications in quantum physics, quantum statistics, operator ordering theory, matrix theory and control theory are given. The integration problem of Wigner operator and Weyl corresponding rules are studied. Two kinds of typical operator identity formulas are proved. The differential form of Wigner operator in ordered product of operators and new differential form of important functions are obtained. Finally, a Wigner operator with parameter for unifying regular order, Weyl sequencing and abnormal order is introduced.