广义测不准关系与三维BTZ黑洞熵

通过应用在量子引力中,由广义测不准关系得出的新的态密度方程,研究三维BTZ背景下黑洞的熵.当取广义测不准关系中引入的,具有Planck量级与空间维数有关的常数λ为特定值时,得到BTZ黑洞Bekenstein-Hawking 熵和修正项.由于利用新的态密度方程,在计算中不存在用brick-wall模型计算黑洞熵时出现的发散项和小质量近似.所得结论,从量子统计力学角度给出了黑洞Bekenstein-Hawking 熵的修正值,使人们对黑洞熵的修正值有更深入的认识. 关键词： 广义测不准关系 量子统计 BTZ黑洞熵     

Singular Dimensions of the¶N= 2 Superconformal Algebras. I

Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N= 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu–Schwarz N= 2 algebra (0, 1 or 2) and for the Ramond N= 2 algebra (0, 1, 2 or 3). Received: 19 August 1998 / Accepted: 15 March 1999     

<Emphasis Type="Italic">Bulk Scale Factor</Emphasis> at Very Early Universe

In this paper we propose a higher dimensional Cosmology based on FRW model and brane-world scenario. We consider the warp factor in the brane-world scenario as a scale factor in 5-dimensional generalized FRW metric, which is called as bulk scale factor, and obtain the evolution of it with space-like and time-like extra dimensions. It is then showed that, additional space-like dimensions can produce exponentially bulk scale factor under repulsive strong gravitational force in the empty universe at a very early stage.     

The geometry of chaotic dynamics — a complex network perspective

Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques, recurrence-based concepts and prominently ε-recurrence networks, most faithfully represent the geometrical fine structure of the attractors underlying chaotic (and less interestingly non-chaotic) time series. In this paper we demonstrate that the well known graph theoretical properties local clustering coefficient and global (network) transitivity can meaningfully be exploited to define two new local and two new global measures of dimension in phase space: local upper and lower clustering dimension as well as global upper and lower transitivity dimension. Rigorous analytical as well as numerical results for self-similar sets and simple chaotic model systems suggest that these measures are well-behaved in most non-pathological situations and that they can be estimated reasonably well using ε-recurrence networks constructed from relatively short time series. Moreover, we study the relationship between clustering and transitivity dimensions on the one hand, and traditional measures like pointwise dimension or local Lyapunov dimension on the other hand. We also provide further evidence that the local clustering coefficients, or equivalently the local clustering dimensions, are useful for identifying unstable periodic orbits and other dynamically invariant objects from time series. Our results demonstrate that ε-recurrence networks exhibit an important link between dynamical systems and graph theory.     

Three-Body Phase Shift in One-Dimensional 2 + 1 Scattering

For a model of three particles on a line, subject to attractive delta-function interactions, we consider the phase shift. We do this from the point of view of the calculation of the S-matrix in a hyperspherical adiabatic basis (an adiabatic S-matrix), and for energies ranging from the (negative) energy of the two-body bound state to a total energy of zero. We derive analytical expansions and present numerical work, for different approximations, and compare with the exact results that we obtain from the work of McGuire, whose model we have borrowed. We show that the simplest adiabatic approximation gives results that are qualitatively wrong, but that better approximations yield, for most of our range, excellent agreement with the exact result. Understanding the threshold behaviour, however, requires a zero-energy three-body bound state, or resonance, previously unsuspected for this model. The methods developed for the case of the simplest adiabatic approximation also yield threshold and low-energy results applicable to the two-body problem in two dimensions. Received December 23, 1996; revised May 13, 1997; accepted for publication June 19, 1997     

Mutual Chern-Simons theory and its applications in condensed matter physics

In this paper, the mutual Chern-Simons (MCS) theory is introduced as a new kind of topological gauge theory in 2+1 dimensions. We use the MCS theory in gapped phase as an effective low energy theory to describe the Z ₂ topological order of the Kitaev-Wen model. Our results show that the MCS theory can catch the key properties for the Z ₂ topological order. On the other hand, we use the MCS theory as an effective model to deal with the doped Mott insulator. Based on the phase string theory, the t-J model reduces to a MCS theory for spinons and holons. The related physics in high T _c cuprates is discussed.      

Observational Constraints with Recent Data on the DGP Modified Gravity

We study one of the simplest covariant modified-gravity models based on the Dvali-Gabadadze-Porrati (DGP) brane cosmology, a self-accelerating universe. In this model gravitational leakage into extra dimensions is responsible of late-time acceleration. We mainly focus on the effects of the model parameters on the geometry and the age of universe. Also we investigate the evolution of matter density perturbations in the modified gravity model, and obtain an analytical expression for the growth index, f. We show that increasing leads to less growth of the density contrast δ, and also decreases the growth index. We give a fitting formula for the growth index at the present time and indicate that dominant term in this expression verifies the well-known approximation relation f≃Ω _m ^γ . As the observational test, the new Supernova Type Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS) data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and the Cluster Baryon Gas Mass Fraction (gas) are used to constrain the parameters of the DGP model. We also combine previous results with large scale structure formation (LSS) from the 2dFGRS survey. Finally to check the consistency of the DGP model, we compare the age of old cosmological objects with age of universe in this model.     

Hidden Measurements,Hidden Variables and the Volume Representation of Transition Probabilities

We construct, for any finite dimension n, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For n=2 our model is equivalent to the Aerts sphere model and serves as a generalization of it for dimensions n . 3 We also show how to construct a hidden variables scheme based on hidden measurements and we discuss how joint distributions arise in our hidden variables scheme and their relationship with the results of Fine [J. Math. Phys. 23 1306 (1982)].     

Dimensional Reduction Formulas for Branched Polymer Correlation Functions

In [BI01] we have proven that the generating function for self-avoiding branched polymers in D+2 continuum dimensions is proportional to the pressure of the hard-core continuum gas at negative activity in D dimensions. This result explains why the critical behavior of branched polymers should be the same as that of the i ³ (or Yang–Lee edge) field theory in two fewer dimensions (as proposed by Parisi and Sourlas in 1981). In this article we review and generalize the results of [BI01]. We show that the generating functions for several branched polymers are proportional to correlation functions of the hard-core gas. We derive Ward identities for certain branched polymer correlations. We give reduction formulae for multi-species branched polymers and the corresponding repulsive gases. Finally, we derive the massive scaling limit for the 2-point function of the one-dimensional hard-core gas, and thereby obtain the scaling form of the 2-point function for branched polymers in three dimensions.     

Monte Carlo simulations for two-dimensional quantum systems

The Trotter-Suzuki transformation has been used to obtain the classical representation ford-dimensional lattice systems with boson and fermion degrees of freedom. A Monte Carlo algorithm for the equivalent (d+1)-dimensional classical system is presented. Numerical results are shown for the Heisenberg-spin-glass, the XY model and the spinless fermion lattice gas in two dimensions.     

A Stochastic Model for Wound Healing

We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In one dimension we can give analytic results for the front speed as a power series expansion in a parameter, p, that gives the relative size of proliferation and diffusion processes for the invading cells. In two dimensions the model becomes the Eden model for p ≈ 1. In both one and two dimensions for small p, front propagation for this model should approach that of the Fisher-Kolmogorov equation. However, as in other cases, this discrete model approaches Fisher-Kolmogorov behavior slowly.     

Duality in noncommutative topologically massive gauge field theory revisited

We introduce a master action in non-commutative space, out of which we obtain the action of the non-commutative Maxwell-Chern-Simons theory. Then, we look for the corresponding dual theory at both first and second order in the non-commutative parameter. At the first order, the dual theory happens to be, precisely, the action obtained from the usual commutative self-dual model by generalizing the Chern-Simons term to its non-commutative version, including a cubic term. Since this resulting theory is also equivalent to the non-commutative massive Thirring model in the large fermion mass limit, we remove, as a byproduct, the obstacles arising in the generalization to non-commutative space, and to the first non-trivial order in the non-commutative parameter, of the bosonization in three dimensions. Then, performing calculations at the second order in the non-commutative parameter, we explicitly compute a new dual theory which differs from the non-commutative self-dual model and, further, differs also from other previous results and involves a very simple expression in terms of ordinary fields. In addition, a remarkable feature of our results is that the dual theory is local, unlike what happens in the non-Abelian, but commutative case. We also conclude that the generalization to non-commutative space of bosonization in three dimensions is possible only when considering the first non-trivial corrections over ordinary space.Received: 12 November 2003, Published online: 23 March 2004M. Botta Cantcheff: mbotta_c@ictp.trieste.itP. Minces: Permanent address Centro Brasileiro de Pesquisas Físicas (CBPF), Departamento de Teoria de Campos e Partículas (DCP), Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil     

Scaling exponents for kinetic roughening in higher dimensions

We discuss the results of extensive numerical simulations in order to estimate the scaling exponents associated with kinetic roughening in higher dimensions, up tod=7 + l. To this end, we study the restricted solid-on-solid growth model, for which we employ a novel fitting ansatz for the spatially averaged height correlation function¯G(t)t ² to estimate the scaling exponent. Using this method, we present a quantitative determination of ind=3 + 1 and 4+1 dimensions. To check the consistency of these results, we also compute the interface width and determine andx from it independently. Our results are in disagreement with all existing theories and conjectures, but in four dimensions they are in good agreement with recent simulations of Forrest and Tang for a different growth model. Above five dimensions, we use the time dependence of the width to obtain lower bound estimates for. Within the accuracy of our data, we find no indication of an upper critical dimension up tod = 7 + 1.     

高维微分-差分模型的Virasoro对称子代数，多线性变量分离解和局域激发模式

寻找高维可积模型是非线性科学中的重要课题.利用无穷维Virasoro对称子代数［σ(f₁),σ(f₂)］=σ(f′₁f₂-f′₂f₁)和向量场的延拓结构理论，能够得到各种高维模型.选取一些特殊的实现，可以给出具有无穷维Virasoro对称子代数意义下的高维微分可积模型.把该方法推广到微分-差分模型上，构造出具有弱多线性变量分离可解性的(3+1)维类Toda晶格.另外，该模型的一个约化方程为具有多线性变量分离可解性的(2+1)维特殊Toda晶格.连续运用对称约化方法可以得到此特殊Toda晶格的一个(1+1)维约化方程具有多线性变量分离可解性.因为得到的精确解里含有低维任意函数，从而可以构造出丰富地局域激发模式，如dromion解，lump解，环孤子解，呼吸子解，瞬子解，混沌斑图和分形斑图等等. 关键词： Virasoro代数 微分-差分模型 变量分离 局域激发模式     

The Percolation Signature of the Spin Glass Transition

Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin–Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering—both in short-range (EA) and infinite-range (SK) models—within a two-replica FK representation and also within the different Chayes–Machta–Redner two-replica graphical representation. Based on numerical studies of the ±J EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of two percolating clusters of unequal densities.     

O(n) tricriticality in two dimensions

We present exact results for several universal parameters of the tricritical O(n) model in two dimensions. The results apply to the range −2⩽n⩽3/2, and include the central charge and three scaling dimensions, associated with temperature, magnetic field and the introduction of an interface. Since these results are based on an extrapolation of known relations between the O(n) and the Potts model, they cannot be considered as rigorous. For this reason, we perform an accurate numerical analysis of the central charge and the critical exponents. This analysis, which is based on transfer-matrix calculations on the honeycomb lattice, is in a full and precise agreement with the theoretical predictions.      

Differential real-space renormalization of thed-Dimensional Gaussian model

With the aid of the differential real-space method we derive exact renormalization group (RG) equations for the Gaussian model ind dimensions. The equations involved + 1 spatially dependent nearest-neighbor interactions. We locate a critical fixed point and obtain the exact thermal critical indexy _T = 2. A special trajectory of the full nonlinear RG transformation is found and the free energy of the corresponding initial state calculated.Supported by Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 130 Ferroelektrika.     

Search for large extra dimensions in final states containing one photon or jet and large missing transverse energy produced in pp collisions at square root[s]=1.96 TeV

We present the results of searches for large extra dimensions in samples of events with large missing transverse energy E_{T} and either a photon or a jet produced in pp[over ] collisions at sqrt[s]=1.96 TeV collected with the Collider Detector at Fermilab II. For gamma+E_{T} and jet+E_{T} candidate samples corresponding to 2.0 and 1.1 fb;{-1} of integrated luminosity, respectively, we observe good agreement with standard model expectations and obtain a combined lower limit on the fundamental parameter of the large extra dimensions model M_{D} as a function of the number of extra dimensions in the model.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q ⁻⁴⁷ (resp. q ⁻⁴⁶). Finally, we compute chromatic roots for strips of widths 9≤m≤12 with free boundary conditions and locate roughly the limiting curves.