Another finite field analogue for Appell series F_{1}

In this paper we introduce another finite field analogue for Appell series F_{1} and obtain certain reduction formulae and a generating function for this analogue.Comment: arXiv admin note: text overlap with arXiv:1704.0350

Quantum Optomechanics beyond Linearization

The quantum dynamics of optomechanical systems was mostly studied for their fluctuations around classical steady states. We present a theoretical approach to determining the system observables of optomechanical systems as genuine quantum objects, for example, a coupled quantum mechanical oscillator to a cavity single photon. In this approach we study the dynamics of such systems in strong coupling regime. We find that, under strong optomechanical coupling, steady quantum states of optomechanical systems driven by continuous-wave single photons exhibit periodic oscillation and cavity noise considerably affects system observables.Comment: 11 pages, 7 figures; the version to be publishe

A finite field analogue for Appell series F_3

In this paper we introduce a finite field analogue for the Appell series F_3 and give some reduction formulae and certain generating functions for this function over finite fields.Comment: 16 pages. Any critical suggestions and comments are always welcomed. arXiv admin note: text overlap with arXiv:1709.0901

On zeros of some entire functions

Let \begin{equation*} A_{q}^{(\alpha)}(a;z) = \sum_{k=0}^{\infty} \frac{(a;q)_{k} q^{\alpha k^2} z^k} {(q;q)_{k}}, \end{equation*} where $\alpha >0,~0<q<1.$ In a paper of Ruiming Zhang, he asked under what conditions the zeros of the entire function $A_{q}^{(\alpha)}(a;z)$ are all real and established some results on the zeros of $A_{q}^{(\alpha)}(a;z)$ which present a partial answer to that question. In the present paper, we will set up some results on certain entire functions which includes that $A_{q}^{(\alpha)}(q^l;z),~l\geq 2$ has only infinitely many negative zeros that gives a partial answer to Zhang's question. In addition, we establish some results on zeros of certain entire functions involving the Rogers-Szeg\H{o} polynomials and the Stieltjes-Wigert polynomials.Comment: 16page

Magnetic response of baryon properties in a skyrmion model

An axially symmetric ansatz is proposed to investigate the properties of baryon in a uniform magnetic field. The baryon number is shown to be conserved, while the baryon shape is stretched along the magnetic field. It is found that with increasing magnetic field strength, the static mass of the baryon first decreases and then increases, while the size of the baryon first increases and then decreases. Finally, in the core part of the magnetar, the equation of state strongly depends on the magnetic field, which modifies the mass limit of the magnetar.Comment: 5 pages, 7 figure

Magnetic field dependence of Delta isobars properties in a Skyrme model

The properties of $\Delta$ isobars in a uniform magnetic field are investigated. In the weak magnetic field region, the general relations between magnetic moment of nucleons and $\Delta$ isobars are given. In the strong magnetic field region, the mass and size of $\Delta$ isobars depend on the increasing of magnetic field strength in different ways: the effective mass of $\Delta^{++}$, $\Delta^{+}$ and $\Delta^{0}$ first decreases and then increases, consequently, the size of $\Delta^{++}$, $\Delta^{+}$ and $\Delta^{0}$ first increases and then decreases; whereas, the effective mass of $\Delta^{-}$ always increases, and consequently, the size of $\Delta^{-}$ always decreases. The estimation shows in the core part of the magnetar, the equation of state for $\Delta$ isobars depends on the magnetic field, which affects the mass limit of the magnetar.Comment: 5 pages, 4 figure

Weaving independently generated photons into an arbitrary graph state

The controlled Z (CZ) operations acting separately on pairs of qubits are commonly adopted in the schemes of generating graph states, the multi-partite entangled states for the one-way quantum computing. For this purpose, we propose a setup of cascade CZ operation on a whole group of qubits in sequence. The operation of the setup starts with entangling an ancilla photon to the first photon as qubit, and this ancilla automatically moves from one entanglement link to another in assisting the formation of a string in graph states. The generation of some special types of graph states, such as the three-dimensional ones, can be greatly simplified in this approach. The setup presented uses weak nonlinearities, but an implementation using probabilistic linear optics is also possible.Comment: 6 pages, 7 figures. Accepted by Phys. Rev.

Two q-summation formulas and q-analogues of series expansions for certain constants

From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certain constants.Comment: This is a joint work with Dr. Zhai and a replacement of arXiv:1804.08210v1. All critical comments are always welcom

Highly Efficient Processing Multi-photon States

How to implement multi-qubit gates is an important problem in quantum information processing. Based on cross phase modulation, we present an approach to realizing a family of multi-qubit gates that deterministically operate on single photons as the qubits. A general $n$-qubit unitary operation is a typical example of these gates. The approach greatly relax the requirement on the resources, such as the ancilla photons and coherent beams, as well as the number of operations on the qubits. The improvement in this framework may facilitate large scale quantum information processing.Comment: to be published in Scientific Reports. 14 pages, 5 figures (plus 5 pages and 2 figures in supplementary materials

Proof for a q-trigonometric identity of Gosper

W. Gosper in 2001 introduced the q-trigonometric functions and conjectured many interesting q-trigonometric identities. In this paper we apply Riemann's addition formula to deduce two Jacobi theta function identities. From these theta function identities we confirm a q-trigonometric identity conjectured by W. Gosper and establish two other similar results. As an application, two theta function analogues for Ptolemy's theorem are given.Comment: 7 pages. Critical comments are always welcom