Orbit Sum Rules for the Quantum Wave Functions of the Strongly Chaotic Hadamard Billiard in Arbitrary Dimensions

Sum rules are derived for the quantum wave functions of the Hadamard billiard in arbitrary dimensions. This billiard is a strongly chaotic (Anosov) system which consists of a point particle moving freely on a D-dimensional compact manifold (orbifold) of constant negative curvature. The sum rules express a general (two-point)correlation function of the quantum mechanical wave functions in terms of a sum over the orbits of the corresponding classical system. By taking the trace of the orbit sum rule or pre-trace formula, one obtains the Selberg trace formula. The sum rules are applied in two dimensions to a compact Riemann surface of genus two, and in three dimensions to the only non-arithmetic tetrahedron existing in hyperbolic 3-space. It is shown that the quantum wave functions can be computed from classical orbits. Conversely, we demonstrate that the structure of classical orbits can be extracted from the quantum mechanical energy levels and wave functions (inverse quantum chaology).     

Conical Quantum Billiard

The conical quantum billiard is examined. Wavefunctions are obtained in an open domain which excludes the polar axis, involving associated Legendre functions of the first and second kind. The first excited state is three-fold degenerate. One wavefunction is nonnodal. The nodal surface of either of the other states is a bisecting plane which includes the axis of the cone. These nodal properties maintain for 0 < ₀ /2, where ₀ is the half vertex angle of the cone. At > /2, the nonnodal state acquires a nodal at = /2. Thus, as with the image problem in two dimensions, there is critical vertex angle about which the nodal structure of one of the eigenstates suffers a topological change. This nodal transition is accompanied by a geometrical transformation of the cone from convex to concave. Solutions obtained are valid for all conical quantum billiards to the limit of the spherical quantum billiard excluding the polar axis.     

Bound States for the Three-Dimensional Aharonov-Bohm Quantum Wire

The existence of bound states for the three-dimensional Aharonov-Bohm quantum wire, suggested by Dunne and Jaffe, is established provided the wire is thin enough. Recent results on the Aharonov-Bohm Schrödinger operator on a disk are used.     

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov’s fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current density correlation function is found to be integrable in space, in both classical and quantum regimes.     

Quantum Processes beyond the Aharonov-Bohm Effect

We consider QED processes in the presence of an infinitely thin and infinitely long straight string with a magnetic flux inside it. The bremsstrahlung from an electron passing by the magnetic string and the electron-positron pair production by a single photon are reviewed. Based on the exact electron and positron solutions of the Dirac equation in the external Aharonov-Bohm potential we present matrix elements for these processes. The dependence of the resulting cross sections on energies, directions, and polarizations of the involved particles is discussed for low energies.     

Polygonal Approaches to the Circular Billiard: the Lyapunov Exponent

The Lyapunov exponents for three polygonal approaches to the circular billiard quasiperiodic approach, random approach and equilateral approach are calculated, the chaotic behavior in polygonal billiards is discussed. The role of singularity presented by vertex angles is quantitatively discussed. It is found that for the equilateral approach, the Lyapunov exponents vary with the side number N according to a Poisson law, i.e., λ(N) = aN exp(-βN).     

QCD求和规则的张量胶子球(2++)的质量

利用量子色动力学求和规则计算了张量胶子球 (2++ )的质量 ,其结果与北京正负电子对撞机的BES实验组和MARKIII实验组的测量结果一致 ,表明张量胶子球的质量约 2 .2 3GeV左右。The mass of the tensor glueball (2 ++ ) is calculated in quantum chromodynamics(QCD) spectral sum rules. The theoretical prediction is in good agreement with the measurements of BES collaboration at BEPC, Beijing and MARK III, which indicates that the mass of the tensor glueball may be around 2.23 GeV.     

Spectral Statistics of the Rectangular Billiard with a Flux Line

The density of states of a rectangular billiard with an Aharonov–Bohm flux line in its center was calculated in the semiclassical approximation and was used for the calculation of the form factor in the diagonal approximation. The distribution of nearest level spacings and the form factor were calculated also numerically. For some values of the flux these were found to be close to the ones of the semi-Poisson statistics. The difference between the numerical results and the semiclassical ones were found to be much larger than for chaotic and for integrable systems within similar approximations. Possible reasons for these discrepancies are discussed.     

Sum Rules in the Quark Model

With the help of various sum rules we look into the spin-isospin excitations in nuclei within a framework of the quark model. The effect of Pauli correlations is explicitly taken care of. In agreement with the experiments we find negligible amount of M1 strength in heavy nuclei. This is explained in terms of the Fermi gas model.     

Expanded Vandermonde Powers and Sum Rules for the Two-Dimensional One-Component Plasma

The two-dimensional one-component plasma (2dOCP) is a system of N mobile particles of the same charge q on a surface with a neutralizing background. The Boltzmann factor of the 2dOCP at temperature T can be expressed as a Vandermonde determinant to the power Γ=q ²/(k _B T). Recent advances in the theory of symmetric and anti-symmetric Jack polynomials provide an efficient way to expand this power of the Vandermonde in their monomial basis, allowing the computation of several thermodynamic and structural properties of the 2dOCP for N values up to 14 and Γ equal to 4, 6 and 8. In this work we explore two applications of this formalism, to the study of the pair correlation function of the 2dOCP on the sphere, and the distribution of radial statistics of the 2dOCP in the plane. Also provided is a finite N approximation to the pair correlation on the sphere, and a sum rule for the constant term in the large N expansion of the moments of the density in the plane.     

Spin Accumulation in a Double Quantum Dot Aharonov-Bohm Interferometer

We investigate the spin accumulation in a double quantum dot Aharonov-Bohm （AB） interferometer in which both the Rashba spin-orbit （RSO） interaction and intradot Coulomb interaction are taken into account. Due to the existence of the RSO interaction, the electron, flowing through different arms of the AB ring, will acquire a spin-dependent phase factor in the tunnel-coupling strengths. This phase factor will induce various interesting interference phenomena. It is found that the electrons of the different spin directions can accumulate in the two dots by properly adjusting the bias and the intradot level with a fixed RSO interaction strength. Moreover, both the magnitude and direction of the spin accumulation in each dot can be conveniently controlled and tuned by the gate voltage acting on the dot or the bias on the lead.     

Quantum transport through double-dot Aharonov-Bohm interferometry in Coulomb blockade regime

Transport through two quantum dots laterally embedded in Aharonov-Bohm interferometry with infinite intradot and arbitrary interdot Coulomb repulsion is analyzed in the weak coupling and Coulomb blockade regime. By employing the modified quantum rate equations and the slave-boson approach, we establish a general dc current formula at temperatures higher than the Kondo temperature for the case that the spin degenerate levels of two dots are close to each other. For further discussion, we examine two simple examples for identical dots - no doubly occupied states and no empty state. In the former, completely destructive coherent transport and phase locking appear at magnetic flux and respectively; in the latter, partially coherent transport exhibits an oscillation with magnetic flux having a period of .Received: 23 July 2003, Published online: 30 January 2004PACS: 73.21.La Quantum dots - 73.23.-b Electronic transport in mesoscopic systems - 73.23.Hk Coulomb blockade and single-electron tunneling.     

Scalar Hidden-Charm Tetraquark States with QCD Sum Rules

In this article, we study the masses and pole residues of the pseudoscalar-diquark-pseudoscalar-antidiquark type and vector-diquark-vector-antidiquark type scalar hidden-charm cud(cus) tetraquark states with QCD sum rules by taking into account the contributions of the vacuum condensates up to dimension-10 in the operator product expansion.The predicted masses can be confronted with the experimental data in the future. Possible decays of those tetraquark states are also discussed.     

全同粒子维数与角动量耦合求和规则

结合工作,讨论了3个和4个全同粒子的状态数解析表达式与角动量耦合中的6j和9j系数的求和规则、单轨道中J级对力、核子系统的自旋和同位旋都确定的空间维数等核结构基本理论方面的新进展。 In this paper I would like to discuss the strategy in obtaining analytical formulas of number of spin I states of identical particles, and the relationship between dimension and sum rules for angular momentum couplings such as six-j and nine-j symbols. I shall also discuss the J-pairing interaction, number of states with spin I and isospin T, i. e. , number of states for nucleons in a single-j shell.     

Bc（B）→DIv^- Form Factors in Light-Cone Sum Rules and the D-Meson Distribution Amplitude

We calculate the weak form factors of the decays Be（B） → Dlv^- by using the chiral current correlator within the framework of the QCD light-cone sum rules （LCSRs）. The expressions of the form factors only depend on the leading twist distribution amplitude （DA） of the D meson. Three models of the D-meson distribution amplitude are employed. Our prediction, by using the D-meson distribution amplitude with the exponential suppression at the end points, favours the three-points sum rule （3PSR） approach with the Coulomb corrections included, and is compatible with other approaches.     

Trading by Quantum Rules: Quantum Anthropic Principle

This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is discussed and Quantum Anthropic Principle is put forward. The review is addressed to nonspecialists.     

Relativistic Quantum Statistical Aharonov-Bohm Effect of Many-Boson System in Mesoscopic Ring

The relativistic quantum ktatistical properties of charged many-boson system with rest mass mo for each boson confined in a mesoscopic ring are investigated. The small ring is threaded by Aharonov-Bohm magnetic flux ф. At low temperature, m₀ > K_BT, we have performed analytical calculations starting from evaluating the logarithm of grand partition function by using Mellin transform. The pair-production problem is excluded from our consideration for the temperature is low. The number density, total energy, specific heat and persistent current are obtained in general. These thermodynamic functions oscillate periodically in ф with period ф₀ = h/q, and they are related to the modified Bessel functions of the second kind K_v(γ) The chemical potential μ is restricted by μ< m₀ to ensure the positive number density of particles and the convergence of fugacity expansions. We find that these functions decay exponentially with temperat hre, and they also decrease as the circumference L increases. The non-relativistic and ultra-relativistic behaviors of these functions are discussed by considering the asymptotic behaviors of K_v(γ). There is no Bose-Einstein condensation in this system.     

Non-Classical Rules in Quantum Games

Over the last twenty years, quantum game theory has given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing bimatrix games introduced by J. Eisert, M. Wilkens and M. Lewenstein. The scheme assumes that players’ strategies are unitary operations and the players act on the maximally entangled two-qubit state. The quantum nature of the scheme has been under discussion since the article by Eisert et al. came out. The aim of our paper was to identify some of non-classical features of the quantum scheme.