Classical and nonclassical symmetries analysis for initial value problems

Classical and nonclassical symmetries are considered to reduce evolution equations with initial conditions in two independent variables. First of all, we rearrange the classical infinitesimal operators such that they leave the initial value problems invariant. Secondly, we give a sufficient condition for the nonclassical symmetry reductions of initial value problems. The generalized Kuramoto-Sivashinsky equation with dispersive effects is considered to examine the algorithms.     

Analysis of all dimensionful parameters relevant in gravitational dressing of conformal theories

Starting from a covariant and background independent definition of normal ordered vertex operators we give an alternative derivation of the KPZ relation between conformal dimensions and their gravitational dressed partners. With our method we are able to study for arbitrary genus the dependence of N-point functions on all dimensional parameters. Implications for the interpretation of gravitational dressed dimensions are discussed.     

On the Casimir operators associated with any Lie algebra

We give a characterization of the Casimir operators of a Lie algebra by polynomial solutions of a system of first-order partial differential equations. Further an upper bound is stated for the number of independent Casimir operators of a nilpotent Lie algebra.     

The q-Deformation of the Superoscillators and Their q-Supercoherent States

We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q-deformed operators, we also give the q-deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q-supercoherent states associated with the q-deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q-supercoherent states are discussed as well.     

A Note of Coherence for Duality Quantum Computers Acting on Pure States

In this paper, we discuss the coherence for duality quantum computers under taking different unitary operators acting on pure states. Firstly, for arbitrary unitary operators, we give some general quantitative results of the coherence of output states. Secondly, for incoherence unitary operators, we obtain that the coherence of output states satisfies an inequality. In addition, we also give a conclusion of the coherence of output states under unitary permutation operators.     

CPT Violating Neutrino Oscillation Under Planck Scale Effects

We give a phenomenological model of CPT violating neutrino oscillation above the GUT scale. In this paper, we consider the effect of Planck scale operators on neutrino mixing. We assume that the main part of neutrino masses and mixing arise through GUT scale operators The dispersion relation for the CPT violating neutrino and anti-neutrino oscillation are discussed.     

Structure of the Hilbert-space of the infinite-dimensional Hubbard model

An iterative procedure for the explicit construction of the nontrivial subspace of all symmetry-adapted configurations with non-zero weight in the ground-state of the -dimensional Hubbard model is developed on the basis of a symmetrized representation of the transition operators on a sequence of Bethe-Lattices of finite depth. The relationship between these operators and the well-known mapping of the -dimensional Hubbard model onto an effective impurity problem coupled to a (self-consistent) bath on non-interacting electrons is given. As an application we calculate the properties of various Hubbard stars and give estimates for the half-filled Hubbard model with up to accuracy. Received 22 June 1998     

An ?-Deformed Virasoro Algebra as Hidden Symmetry of the Restricted sine-Gordon Model

As the Yangian double with center, which is deformed from affine algebra by the additive loop parameter ?, we get the commutation relation and the bosonization of quantum ?-deformed Virasoro algebra. The corresponding Miura transformation, the associated screening operators and the BRST charge have been studied. Moreover, we also construct the bosonization for type Ⅰ and type Ⅱ intertwiner vertex operators. Finally, we show that the commutation relations of these vertex operators in the case of p^′ = γ, p = γ - 1 and ? = π actually give the exact scattering matrix of the restricted sine-Gordon model.     

Energy-scale dependence of the lepton flavor-mixing matrix

We study an energy-scale dependence of the lepton flavor-mixing matrix in the minimal supersymmetric standard model with the effective dimension-five operators, which give Majorana masses of neutrinos. We analyze the renormalization group equations of the coefficients () of these effective operators under an approximation that neglects terms of order . We find that only (where is the generation number) real independent parameters in the lepton flavor-mixing matrix depend on the energy scale. In particular, all the phases in are scale-independent. Received: 10 April 1999 / Revised version: 23 May 1999 / Published online: 28 September 1999     

基于相位匹配的量子行走搜索算法及电路实现

量子行走是经典随机行走在量子力学框架下的对应, 理论上可以用来解决一类无序数据库的搜索问题. 因为携带信息的量子态的扩散速度与经典相比有二次方式的增长, 所以量子行走优于经典随机行走, 量子行走的特性值得加以利用. 量子行走作为一种新发现的物理现象的数学描述, 引发了一种新的思维方式, 孕育了一种新的理论计算模型. 最新研究表明, 量子行走本身也是一种通用计算模型, 可被视为设计量子算法的高级工具, 因此受到部分计算机理论科学领域学者的关注和研究. 对于多数问题求解方案的量子算法的设计, 理论上可以只在量子行走模型下进行考虑. 基于Grover算法的相位匹配条件, 本文提出了一个新的基于量子行走的搜索算法. 理论演算表明: 一般情况下本算法的时间复杂度与Grover算法相同, 但是当搜索的目标数目多于总数的1/3时, 本算法搜索成功的概率要大于Grover算法. 本文不但利用Grover算法中相位匹配条件构造了一个新的量子行走搜索算法, 而且在本研究室原有的量子电路设计研究成果的基础上给出了该算法的量子电路表述.     

Correlation Spectrum of Quenched and Annealed Equilibrium States for Random Expanding Maps

We show that the integrated transfer operators for positively weighted independent identically distributed smooth expanding systems give rise to annealed equilibrium states for a new variational principle. The unique annealed equilibrium state coincides with the unique annealed Gibbs state. Using work of Ruelle [1990] and Fried [1995] on generalised Fredholm determinants for transfer operators, we prove that the discrete spectrum of the transfer operators coincides with the correlation spectrum of these invariant measures (yielding exponential decay of correlations), and with the poles of an annealed zeta function, defined also for complex weights. A modified integrated transfer operator is introduced, which describes the (relativised) quenched states studied e.g. by Kifer [1992], and conditions (including SRB) ensuring coincidence of quenched and annealed states are given. For small random perturbations we obtain stability results on the quenched and annealed measures and spectra by applying perturbative results of Young and the author [1993]. Received: 16 April 1996 / Accepted: 25 October 1996     

Intertwining operator realization of non-relativistic holography

We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory (without specifying any action). Further we show that these operators and the bulk-to-boundary operators are intertwining operators. In analogy to the relativistic case, we show that each bulk field has two boundary fields with conjugated conformal weights. These fields are related by another intertwining operator given by a two-point function on the boundary. Analogously to the relativistic result of Klebanov–Witten we give the conditions when both boundary fields are physical. Finally, we recover in our formalism earlier non-relativistic results for scalar fields by Son and others.     

Implications of the LHCb evidence for charm CP violation

The LHCb collaboration recently announced preliminary evidence for CP violation in D meson decays. We discuss this result in the context of the standard model (SM), as well as its extensions. In the absence of reliable methods to evaluate the hadronic matrix elements involved, we can only estimate qualitatively the magnitude of the non-SM tree level operators required to generate the observed central value. In the context of an effective theory, we list the operators that can give rise to the measured CP violation and investigate constraints on them from other processes.     

Induced Operators in QCD

Light-cone quantization always involves the solution of differential constraint equations. The solutions to these equations include integration constants (fields independent ofx₋). These fields are unphysical but when they are consistently removed from the dynamics, additional operators (induced operators), which would not be present if the integration constants were simply set to zero, are included in the dynamics. These induced operators can be taken to act in the usual light-cone subspace, for instance, the space used for DLCQ. Here, I shall give a derivation of two such operators. The operators are derived starting from the QCD Lagrangian but the derivation involves some guesses. The operators will provide for the linear growth of the pion mass squared with the quark bare mass and for the splitting of the pi and the rho at zero quark mass.     

Avron–Herbst Type Formula in Crossed Constant Magnetic and Time-Dependent Electric Fields

In this paper, we give an Avron?CHerbst type formula for the propagator generated by the free Hamiltonian with crossed constant magnetic and time-dependent electric fields. As an application of the formula, we give a result of the existence of the wave operators under some appropriate conditions on the time-dependent electric field and the potential. Finally, in the case where the electric field is time-independent, we consider the problem of the asymptotic completeness of the wave operators.     

A quantum model for the stock market

Beginning with several basic hypotheses of quantum mechanics, we give a new quantum model in econophysics. In this model, we define wave functions and operators of the stock market to establish the Schrödinger equation for stock price. Based on this theoretical framework, an example of a driven infinite quantum well is considered, in which we use a cosine distribution to simulate the state of stock price in equilibrium. After adding an external field into the Hamiltonian to analytically calculate the wave function, the distribution and the average value of the rate of return are shown.     

The analysis of elliptic families

In this paper we specialize the results obtained in [BF1] to the case of a family of Dirac operators. We first calculate the curvature of the unitary connection on the determinant bundle which we introduced in [BF1].We also calculate the odd Chern forms of Quillen for a family of self-adjoint Dirac operators and give a simple proof of certain results of Atiyah-Patodi-Singer on êta invariants.We finally give a heat equation proof of the holonomy theorem, in the form suggested by Witten [W 1, 2].     

Anomalous dimensions of gauge-invariant three fermion local operators of twist three

The matrices of anomalous dimensions of gauge-invariant three-fermion local operators of twist three are calculated in QCD with massless quarks. Furthermore we explicitly give the eigenvalues for operators containing up to eight derivatives, and the eigenvectors for operators containing up to three derivatives. The correspondence between eigenvectors of the anomalous dimension matrices and decuplet local baryon operators is derived by means of Fierz transformations.     

Various Re-ordering Expressions of General Exponential Quadratic Operators in Mutli-Mode Boson System

In this paper, we give various explicit expressions and transform equalities among usual, normal and anti-normal orderings for the exponential inhomogeneous quadratic (EIQ) operators and their inverse operators in multi-mode boson systems.