Jing Si-Cong

The q-deformed binomial distribution and its asymptotic behaviour

The q-analogue of the binomial distribution is defined by virtue of the q-binomial theorem, which takes the Euler distribution as its limiting form and is new to the literature.

Wigner Functions for the Bateman System on Noncommutative Phase Space

We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra.

Wigner Functions for Non-Hamiltonian Systems on Noncommutative Space

We propose a modified form of Wigner functions for generic non-Hamiltonian systems on noncommutative space and prove that it satisfies the corresponding *-genvalue equation. In addition, as an example, we derive exact energy spectra and Wigner functions for a non-Hamiltonian toy model on the noncommutative space.

State-Vector Space and Canonical Coherent States in Noncommutative Plane

The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose-Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which lead to noncommutative Fock space. By this we mean that creation and annihilation operators corresponding to different degrees of freedom of the bosons do not commute each other. The main character of the noncommutative Fock space is there are no ordinary number representations because of the non-commutativity between different number operators. However, eigenvectors of several pairs of commuting Hermitian operators are obtained which can also be served as bases in this Fock space. As a simple example, an explicit form of two-dimensional canonical coherent state in this noncommutative Fock space is constructed and its properties are discussed.The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose–Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which leads to a kind of deformed Heisenberg-Weyl algebra. Although there is no ordinary number representation in this state-vector space, several set of orthogonal and complete state-vectors can be derived which are common eigenvectors of corresponding pairs of commuting Hermitian operators. As a simple application of this state-vector space, an explicit form of two-dimensional canonical coherent state is constructed and its properties are discussed.

Modified Form of Wigner Functions for Non-Hamiltonian Systems

Quantization of non-Hamiltonian systems (such as damped systems) often gives rise to complex spectra and corresponding resonant states, therefore a standard form calculating Wigner functions cannot lead to static quasi-probability distribution functions. We show that a modified form of the Wigner functions satisfies a -genvalue equation and can be derived from deformation quantization for such systems.

Solving Solar Neutrino Puzzle via LMA MSW Conversion

We analyze the existed solar neutrino experiment data and show the allowed regions. The result from SNO’s salt phase itself restricts quite a lot the allowed region’s area. Reactor neutrinos play an important role in determining oscillation parameters. KamLAND gives decisive conclusion on the solution to the solar neutrino puzzle, in particular, the spectral distortion in the 766.3 Ty KamLAND data gives another new improvement in the constraint of solar MSW-LMA solutions. We confirm that at 99.73% C.L. the high-LMA solution is excluded. ∗email: qiuyu@ustc.edu.cn 1We analyze the existing solar neutrino experiment data and show the allowed regions. The result from SNOs salt phase itself restricts quite a lot the allowed regions area. Reactor neutrinos play an important role in determining oscillation parameters. KamLAND gives decisive conclusion on the solution to the solar neutrino puzzle, in particular, the spectral distortion in the 766.3 Ty KamLAND data gives another new improvement in the constraint of solar MSW-LMA solutions. We confirm that at 99.73% C.L. the high-LMA solution is excluded.

A Note on Wigner Functions and *-Genvalue Equation

In deformation quantization, static Wigner functions obey functional *-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form Ĥ = (1/2)2 + V() [D. Fairlie, Proc. Camb. Phil. Soc. 60 (1964) 581]. In this note we generalize this proof to a very general Hamiltonian Ĥ(, ) and give examples to support it.

A New Type of Seiberg-Witten Map and Its Application

Deformation quantization is a powerful tool to deal with systems in noncommutative space to get their energy spectra and corresponding Wigner functions, especially for the case of both coordinates and momenta being noncommutative. In order to simplify solutions of the relevant *-genvalue equation, we introduce a new kind of Seiberg–Witten-like map to change the variables of the noncommutative phase space into ones of a commutative phase space, and demonstrate its role via an example of two-dimensional oscillator with both kinetic and elastic couplings in the noncommutative phase space.

Generalized Wigner Functions for Damped Systems in Deformation Quantization

Quantization of damped systems usually gives rise to complex spectra and corresponding resonant states, which do not belong to the Hilbert space. Therefore, the standard form of calculating Wigner function (WF) does not work for these systems. In this paper we show that in order to let WF satisfy a -genvalue equation for the damped systems, one must modify its standard form slightly, and this modification exactly coincides with the results derived from a -Exponential expansion in deformation quantization.

Parabose Squeezed Operator and Its Applications

By virtue of the parabose squeezed operator, propagator of a parabose parametric amplifier, explicit forms of parabose squeezed number states and normalization factors of excitation states on a parabose squeezed vacuum state are calculated, which generalize the relevant results from ordinary Bose statistics to the parabose case.By virtue of the parabose squeezed operator, propagator of a parabose parametric amplifier, explicit form of parabose squeezed number states and normalization factors of excitation states on a parabose squeezed vacuum atate are calculated in this letter, which generalize the relevant results from ordinary Bose statistics to parabose case.