Li Hong-Qi

Quantum Fluctuations of Current and Voltage for Mesoscopic Quartz Piezoelectric Crystal at Finite Temperature

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.

Quantum fluctuations of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling in thermal excitation state ∗

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.

New representation of the multimode phase shifting operator and its application

Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the multimode coordinate{momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the multimode phase shifting operator.

New approach for analysing master equations of generalized phase diffusion models in the entangled state representation

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.

Wigner function for the generalized excited pair coherent state

This paper introduces the generalized excited pair coherent state (GEPCS). Using the entangled state |η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state |η1, η2, τ1, τ2〉. The entangled states |η〉 and η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.

New Representation of Rotation Operator and Its Application

By employing the technique of integration within an ordered product of operators, we derive natural representations of the rotation operator, the two-mode Fourier transform operator and the two-mode parity operator in entangled state representations. As an application, it is proved that the rotation operator constructed by the entangled state representation is a useful tool to solve the exact energy spectra of the two-mode harmonic oscillators with coordinate-momentum interaction.

New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application ⁄

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.

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

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.

Mutual transformations between the P—Q, Q—P, and generalized Weyl ordering of operators

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.

New Route to Deducing Integration Formulas by Virtue of the IWOP Technique

We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product (IWOP) of operators we derive some new integration formulas, which seems concise. As a by-product, some new operator identities also appear.