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	1. Effect of spatial rather than temporal complexity on ecosystems
	Li Dong,M. C. Cross,Zheng Zhigang
	Physics 11 February 2010
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	Abstract:We investigate the role of spatial and temporal complexity on the biomass of diffusive Gause-Lotka-Volterra systems. We find that the average total biomass is insensitive to the temporal complexity. On the other hand increasing diffusion leads to a decrease of the biomass as the spatial complexity plays an important role. At large values of the diffusion the spatial complexity saturates. We understand this region by a scaling analysis of the evolution equations. We propose that investigating the periodic windows that are typically interspersed in chaotic parameter regions is a useful test of the importance of temporal complexities.
	TO cite this article:Li Dong,M. C. Cross,Zheng Zhigang. Effect of spatial rather than temporal complexity on ecosystems[OL].[11 February 2010] http://en.paper.edu.cn/en_releasepaper/content/40173


	2. Bs→K∏ decays and the NLO contributions in the pQCD Approach
	Liu Jing,Zhou Rui,Xiao Zhen-Jun
	Physics 20 January 2010
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	Abstract:In this paper we calculated the partial next-to-leading order (NLO) contributions to $B_s \\to K\\pi$ decays by employing the pQCD approach, we found numerically that (a) for $B_s \\to K^+ \\pi^-$ decay the consistency between the pQCD prediction and the measured value is improved effectively by the inclusion of the NLO contributions; (b) for $B_s \\to K^0\\pi^0$ decay, the NLO enhancement to the branching ratios can be significant, $\\sim 60\\%$, to be tested by the LHC experiment.
	TO cite this article:Liu Jing,Zhou Rui,Xiao Zhen-Jun. Bs→K∏ decays and the NLO contributions in the pQCD Approach[OL].[20 January 2010] http://en.paper.edu.cn/en_releasepaper/content/39230

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	3. Parameter Scaling in the Decoherent Quantum-Classical Transition for
	Mao Ting ,Yu Yang
	Physics 30 December 2009
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	Abstract:We numerically investigated the quantum-classical transition in rf-SQUID systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent Lambda_m, exhibits non-monotonic behavior as a function of the coupling strength D. By measuring the proximity of quantum and classical evolution with the uncertainty of dynamics, we show that the uncertainty is a monotonic function of Lambda_m/D. In addition, the scaling holds in SQUID systems to a relatively smaller hbar_eff, suggesting the universality for this scaling.
	TO cite this article:Mao Ting ,Yu Yang . Parameter Scaling in the Decoherent Quantum-Classical Transition for[OL].[30 December 2009] http://en.paper.edu.cn/en_releasepaper/content/38281


	4. Quantum Key Distribution Control System and Phase Modulator Drive Module Design
	LI linxia
	Physics 23 November 2009
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	Abstract:Recent progress in quantum key distribution (QKD) is briefly reviewed and a control circuit for driving phase modulator is presented using high-speed and high frequency analog switch. Phase modulator is an indispensable optical modulator in quantum key distribution as it can affect the quantum bit error rate. Simulation results show that the output voltage pulse width can be less than 10ns,which can be well applied to quantum key distribution system. The feasibility and reliability of the scheme are verified through theoretical analysis and experiment results.
	TO cite this article:LI linxia. Quantum Key Distribution Control System and Phase Modulator Drive Module Design[OL].[23 November 2009] http://en.paper.edu.cn/en_releasepaper/content/36937


	5. Bound States for Spin-0 and Spin-1/2 Particles with Vector and Scalar Hyperbolic Tangent and Cotangent Potentials
	Tian Wenjie
	Physics 20 November 2009
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	Abstract:This paper analyzes the relativistic bound states with the direct coupling of a vector and a scalar hyperbolic tangent or cotangent potential, viz V_0 tanh(lambda r) and V_0 (lambda r), for particular under the coupling of V(r)=S(r) for s-wave states. The two kinds of potentials are calculated separately as two cases, the comparison of which reflects elegant correspondence throughout the process. To solve the Klein-Gordon equation(KGE) under such circumstances is the crucial work, which lays the foundation to solve Dirac equation(DE), and manifold variable-transformations lead to an object equation which has the familiar structure of hypergeometric equation. The replacements should be carefully selected, among which the technique of flexible parameter is employed for the crucial simplification. The normalization requirement excludes the other induced function of hypergeometric type as a component of the eigenfunction, and breaks off the regular Gauss function to a polynomial, which gives rise to the energy spectrum. Yet, since its the solution of a sextic algebraic equation, an implicit formalism is employed for simplicity. The case of hyperbolic tangent potential and the hyperbolic cotangent potential share the same structure of the object dynamical equation and energy spectrum, yet their eigenfunctions slightly differ on the induced independent variable via -xi and xi. Whereafter, bound states of Dirac equation(DE) based on the complete set [hatH,hatkappa,hatmathbf J 2,hat J_z] is calculated. The specific coupling manner and $s$-wave condition lead to the identical radial DE with that of KGE, which yields the solution for the up component straightforwardly, and subsequently induces the down component. ( Comments: 11 pages, no figure)
	TO cite this article:Tian Wenjie . Bound States for Spin-0 and Spin-1/2 Particles with Vector and Scalar Hyperbolic Tangent and Cotangent Potentials[OL].[20 November 2009] http://en.paper.edu.cn/en_releasepaper/content/36868


	6. Solutions of Klein-Gordon Equation with the Direct Coupling of Vector and Scalar Linear Potentials
	Tian Wenjie
	Physics 18 November 2009
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	Abstract:This paper solves Klein-Gordon equation (KGE) with the direct coupling of linear vector and scalar potentials, viz $V(r)=V_0r$ and $S(r)=S_0r$ with the order $V_0<S_0$ on $mathbb{R}+$. The work begins with the general formulation of KGE under the coupling of a vector and a scalar potential. Firstly, the $s$-wave KGE in coupling linear potentials is solved. Transformations lead the dynamical equation into parabolic cylinder equation, Webers equation and confluent hypergeometric equation, respectively, and these three approaches give rise to the identical energy spectrum and eigenfunction. Subsequently, the coupling KGE with nonvanishing centrifugal effect is calculated via Frobenius method of series expansion, which firstly yields the recurrence relation of the series coefficients. Since the indicial indexes are $s_1=-l$, $s_2=l+1$, when $l=0$, the solution belongs to the special case with indeterminate coefficient; when $l geq1$ with centrifugal effect, one encounters the special case with integer index difference. These two cases share the same $z(r,s)$ kernel of solution, and in the $l=0$ case, emphasis is shifted to the resolved $s$-wave states, while in the $l geq 1$ case, the kernel $z(r,s)$ and the asymptotic eigenfunction are established. Its argued that the theory of exactly-solvable high-order difference equation should be further developed. [(Comment: 12 pages, no figure)]
	TO cite this article:Tian Wenjie. Solutions of Klein-Gordon Equation with the Direct Coupling of Vector and Scalar Linear Potentials[OL].[18 November 2009] http://en.paper.edu.cn/en_releasepaper/content/36806


	7. Klein-Gordon Bound States in Coulombic Vector and Scalar Singular Potentials with Nonvanishing Centrifugal Effect
	Tian Wenjie
	Physics 17 November 2009
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	Abstract:This paper analyzes Klein-Gordon bound states with the direct coupling of Coumlombic vector and scalar singular potentials, viz V(r)=-(hcα)/r and S(r)=-(hcα’)/r with the order α’<α on R,where nonvanishing centrifugal effect is taken into account. To obtain the eigenfunction and energy spectrum, two approaches are put forward, the difference between which origins from the manipulations of the coefficient of the centrifugal term. In the first approach, the induced energy spectrum depends on the complete set of quantum numbers {n,l,m} explicitly; in the second approach this dependence is implicit, but it provides a simpler description of the asymptotic behaviors of the wave function at the infinity for compensation. Except for these differences, those two approaches share the same formulation and are in pleasant correspondence. Variable transformations lead the dynamical equation to a confluent hypergeometric equation, subsequently boundary conditions and normalization requirement abandon Kummer’s function of the second kind as a component of the eigenfunction, and break Kumemer’s function of the first kind off to a polynomial to act as the eigenfunction, which also yields the energy spectrum, analytically and explicitly. Eventually, calculation shows that the degree of degeneracy of the energy levels is n^2, and a brief numerical analysis is performed to explore whether extra constraints on {α,α’} would arise or not to guarantee the existence of bound states.
	TO cite this article:Tian Wenjie. Klein-Gordon Bound States in Coulombic Vector and Scalar Singular Potentials with Nonvanishing Centrifugal Effect[OL].[17 November 2009] http://en.paper.edu.cn/en_releasepaper/content/36769


	8. Klein-Gordon and Dirac Bound States with Vector and Scalar Type-II Exponential Potentials
	Tian WenJie
	Physics 12 November 2009
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	Abstract:This paper analyzes the relativistic bound states with the direct coupling of vector and scalar type-II exponential potentials, for particular under the manner of equal coupling, viz $(potential)$ for s-wave states. To solve the Klein-Gordon equation(KGE) under such circumstances is the crucial work, and manifold variable-transformations leads to an object equation whose solutions distinguish with different V_1. For V_1>0, one proceeds to obtain a parabolic cylinder equation(PCE) of the first type, which has an even and an odd parabolic cylinder series as two linearly independent solutions. Normalization requirements exclude the odd function and break the even function off to a polynomial, which gives rise to an elegant structure of the energy spectrum that explicitly increase along the radii. The case V_1<0, which leads to PCE of the second type, is in serious correspondence with that of V_1>0. As to the wave function in both cases, besides the canonical polynomial arising from parabolic cylinder series which can be complex, another terminated Taylor expansions are introduced on R. Subsequently, bound states of Dirac equation(DE) based on the complete set [H,kappa,J2,J_z] is calculated. The specific coupling manner and s-wave condition lead to the identical radial DE with that of KGE, which yields the solution for the up component straightforwardly, and subsequently induces the down component.
	TO cite this article:Tian WenJie . Klein-Gordon and Dirac Bound States with Vector and Scalar Type-II Exponential Potentials[OL].[12 November 2009] http://en.paper.edu.cn/en_releasepaper/content/36614


	9. Bound States and Band Gaps for Spin-0 and Spin-1/2 Particles with Vector and Scalar Woods-Saxon Potentials
	Tian Wenjie
	Physics 26 October 2009
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	Abstract:We analyze the relativistic bound states with mixed vector and scalar Woods-Saxon potentials, for particular under the specific coupling of V(r)=S(r) for s-wave states. As to spin-0 particles, the investigation via Klein-Gordon equation(KGE) indicates that besides the bound states and scattering states, an extra band gap with vanishing wave function arises. For the bound states, KGE is transformed into a hypergeometric equation with standard composition of the parameters, and on the analytic intervals of the extended argument R we obtain the solution via Gaussian series. The practical argument (0,1) and the Kummer solution at the regular singular point x=0, together with the boundary constraints, give rise to the s-wave discrete spectrum, analytically and explicitly. For the band gap, we prove its existence and investigate the properties. For this very energy interval, KGE differs slightly with that of the bound states after the same transformation, and could only be solved via series expansion, which shows that the wave function vanishes completely. This way, we obtain the structure of the bound state and band gap, the analytic wave function and the explicit energy spectrum for spin-0 particles. As to spin-1/2 particles, we apply Dirac equation(DE) based on the complete set [H,k,J2,J_z]. Under the specific coupling manner, the s-wave bound states lead to the identical radial DE with that of KGE, which yields the solution for the up component immediately, and subsequently induces the down component. These draw a clear picture of the behaviors of the spin-1/2 particles under such conditions.
	TO cite this article:Tian Wenjie. Bound States and Band Gaps for Spin-0 and Spin-1/2 Particles with Vector and Scalar Woods-Saxon Potentials[OL].[26 October 2009] http://en.paper.edu.cn/en_releasepaper/content/36135


	10. Bound States of Klein-Gordon and Dirac Equation with Type-I Vector and Scalar Poschl-Teller Potential
	Tian WenJie
	Physics 14 October 2009
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	Abstract:We analyze the stationary radial Klein-Gordon equation with mixed vector and scalar potentials, and specifically for the case with V(r)=S(r) type-I Poschl-Teller potentials for s-wave bound states, we obtain the exact wave function and the energy spectrum via hypergeometric functions. As for Dirac equation, we introduce the radial functions in two ways, based on the complete sets [H, kappa, J, P] and (H, kappa,J^2,J_z), respectively. Its s-wave bound states with V(r)=S(r) lead to the identical radial equation with that of the Klein-Gordon equation, which give rise to an immediate solution.
	TO cite this article:Tian WenJie . Bound States of Klein-Gordon and Dirac Equation with Type-I Vector and Scalar Poschl-Teller Potential[OL].[14 October 2009] http://en.paper.edu.cn/en_releasepaper/content/35810

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