Physics of a Kind of Normally Ordered Gaussian Operators in Quantum Optics

Based on the technique of integration within an ordered product of operators we investigate a completeness relation of pure states （such as the coordinate eigenstate, the momentum eigenstate and the coherent state） into normally ordered Gaussian forms. The Weyl ordering invariance under similarity transformations is employed to reveal physical meaning of a kind of normally ordered Gaussian operators, which have the similar forms to the bivariate normal distributions in statistics, i.e., the thermo mixed state density matrix.

Quantum fluctuations of mesoscopic biological cell at finite temperature

On the basis of the quantization of mesoscopic biological cell equivalent circuit,we studied the quantum fluctuations of voltage and current of mesoscopic biological cell equivalent circuit as finite temperature by Bogoliuov transformation.The result shows that the quantum fluctuations of voltage and current not only relate with the parameters of equivalent circuit,temperature,but also decay with time.This result may have significant value on the design and application of the bio-electronic apparatus.

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

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.

Quantum fluctuations of mesoscopic damped mutual capacitance coupled double resonance RLC circuit in thermal excitation state

Mesoscopic damped mutual capacitance coupled double resonance circuit is quantized by the method of damped harmonic oscillator quantization. Hamiltonian is diagonalized by the method of unitary transformation. The energy spectra of this circuit are given. The quantum fluctuations of the charge and current of each loop are investigated by the method of thermo- field dynamics (TFD) in thermal excitation state,thermal squeezed vacuum state, thermal vacuum state and vacuum state. It is shown that the quantum fluctuations of the charge and current are related to not only circuit inherent parameter and coupled magnitude, but also quantum number of excitation, squeezed coefficients, squeezed angle and environmental temperature. And the quantum fluctuations increase with the increase of temperature and decay with time.

Thermal radiation and nonthermal radiation of the slowly changing dynamic Kerr-Newman black hole

Using the related formula of dynamic black hole, we have calculated the instantaneous radiation energy density of the slowly changing dynamic Kerr-Newman black hole. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature of the event horizon in the same direction. By using the Hamilton-Jacobin equation of scalar particles in the curved spacetime, the spontaneous radiation of the slowly changing dynamic Kerr-Newman black hole is studied. The energy condition for the occurrence of the spontaneous radiation is obtained.

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 mnltimode coordinate-momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the rnultimode phase shifting operator.

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 coordinat-momentum interaction.

New Route to Deducing Integration Formulas by Virtue of the IWOP Techniqu~

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.

Wigner Function of Density Operator for Negative Binomial Distribution

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.

Radiation energy flux of Dirac field of static spherically symmetric black holes

By the statistical entropy of the Dirac field of the static spherically symmetric black hole, the result is obtained that the radiation energy flux of the black hole is proportional to the quartic of the temperature of its event horizon. That is, the thermal radiation of the black hole always satisfies the generalised Stenfan-Boltzmann law. The derived generalised Stenfan-Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient related to the space-time metric near the event horizon and the average radial effusion velocity of the radiation particles from the thin film. Finally, the radiation energy fluxes and the radiation powers of the Schwarzschild black hole and the Reissner-NordstrSm black hole are derived, separately.

The generalized Stefan-Boltzmann law of a rectilinear non-uniformly accelerating Kinnersley black hole

Using entropy density of Dirac field near the event horizon of a rectilinear non-uniformly accelerating Kinnersley black hole, the law for the thermal radiation of black hole is studied and the instantaneous radiation energy density is obtained. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature on event horizon in the same direction. That is to say, the thermal radiation of a black hole always satisfies the generalized Stefan-Boltzmann law. In addition, the derived generalized Stefan Boltzmann coefficient is no longer a constant, but a dynamic coefficient related to the space-time metric near the event horizon and the changing rate of the event horizon in black holes.

The q-analogues of two-mode squeezed states constructed by virtue of the IWOP technique

The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product （IWOP） of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state S＇s（τ） │00） are investigated. It is found that, in different ranges of the squeezed parameter τ, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.

Recapitulating Quantum Phase Space Representation by Virtue of Normally Ordered Gaussian Form of Wigner Operator

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 ｜q〉λ,v of linear combination of the coordinate and momentum operator, （λQ ＋ vP）, where λ,v are real numbers, and ｜q〉λv is complete, then the projector ｜q〉λ,vλ,v〈q｜ must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.

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.

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 Ok （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 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （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 （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.

Oscillation behaviour in the photon-number distribution of squeezed coherent states

From the normally ordered form of the density operator of a squeezed coherent state（SCS）,we directly derive the compact expression of the SCS＇s photon-number distribution（PND）.Besides the known oscillation characteristics,we find that the PND is a periodic function with a period of π and extremely sensitive to phase.If the squeezing is strong enough,and the compound phase which is relevant to the complex squeezing and displacement parameters are assigned appropriate values,different oscillation behaviours in PND for even and odd photon numbers appear,respectively.

A New Kind of Bipartite Entangled State Representation 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 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.

New Convenient Way for Disentangling Exponential Operator Composed of Angular Momentum Operators

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 desentangle the form of exp[2hJz ＋ g J＋ ＋ kJ_] as the ordering exp（... J＋）exp（... Jz）exp（... J_）, we employ the Schwinger Bose realization J_ = bta, J＋ = atb, Jz=（ata - btb）/2 to fulfil this task, without appealing to Lie algebra method. Note that this operator＇s desentanglng is different from its decomposition in normal ordering.

Production of intense attosecond vector beam pulse trains based on harmonics

We provide the first report on the harmonics generated by an intense femtosecond vector beam that ~s normally mcment on a solid target. By using 2D particle-in-cell （PIC） codes, we observe the third and the fifth harmonic signals with the same vector structure as the driving beam, and obtain an attosecond vector beam pulse train. We also show that the conversion efficiencies of the third and the fifth harmonics reach their maxima for a plasma density of four times the critical density due to the plasma resonating with the driving force. This method provides a new means of generating intense extreme ultraviolet （XUV） vector beams via ultra-intense laser-driven harmonics.