Corrected Entropy of BTZ Black Holes

In this paper, corrected entropy of a class of BTZ black holes, include charge and rotation, studied. We obtain corrected Bekenstein-Hawking entropy and find that effect of charge viewed at order A ^?2, and effect of rotation viewed at order A ^?6, therefore Q and J don’t have contribution in corrected entropy lower than the second order. We also write the first law of black hole thermodynamics for the case of charged rotating BTZ black hole.     

Entropy function approach to charged BTZ black hole

We find solution to the metric function f(r) = 0 of charged BTZ black hole making use of the Lambert function. The condition of extremal charged BTZ black hole is determined by a non-linear relation of M _e (Q) = Q ²(1 − ln Q ²). Then, we study the entropy of extremal charged BTZ black hole using the entropy function approach. It is shown that this formalism works with a proper normalization of charge Q for charged BTZ black hole because AdS₂ × S¹ represents near-horizon geometry of the extremal charged BTZ black hole. Finally, we introduce the Wald’s Noether formalism to reproduce the entropy of the extremal charged BTZ black hole without normalization when using the dilaton gravity approach.     

Construction of Fredholm representations and a modification of the Higson-Roe corona

The Fredholm representation theory is well adapted to the construction of homotopy invariants of non-simply-connected manifolds by means of the generalized Hirzebruch formula [σ(M)] = 〈L(M)ch _A f*ξ, [M]〉 ∈ K _A ⁰(pt) ⊗ Q, where A = C*[π] is the C*-algebra of the group π, π = π ₁(M). The bundle ξ ∈ K _A ⁰(Bπ) is the canonical A-bundle generated by the natural representation π → A. Recently, the first author constructed a natural family of Fredholm representations that lead to a symmetric vector bundle on the completion of the fundamental group with a modification of the Higson-Roe corona, provided that the completion is a closed manifold.     

Dimer state in the two-dimensional anisotropic alternated-exchange Heisenberg model

An analysis is made of the two-dimensional Heisenberg model with S=1/2, anisotropic exchange interaction between nearest neighbors, and alternating exchange in two directions, [100] and [010] (corresponding to condensation of the (π, π) mode) and in one direction [100] (corresponding to condensation of the (π, 0) mode). The quantum Monte Carlo method is used to calculate the thermodynamic characteristics and the spin correlation functions which are used as the basis to determine the boundary of stability of an anisotropic antiferromagnetic with respect to alternation of exchange δ=(1−J ^x,y /J ^z )^0.4 in the (π,π) model and δ=(1−J ^x,y /J ^z )^0.31 in the (π,0) model. In the (π,0) model a disordered quantum state exists in the range (1−J ^x,y /J ^z )^0.31<δ<(0.3–0.35). The energy (E−0.68)=0.36δ ^1.80(6) and 0.21 δ ^2.0(5), the energy gap between the ground and excited states H _c (δ)=1.96δ ^2.(1), 1.8(1) (δ−0.35(3))^0.67(2) were determined as a function of the alternation of exchange in the (π,π)-and (π,0) models, respectively. Fiz. Tverd. Tela (St. Petersburg) 40, 1080–1085 (June 1998)     

“Regge-like” relations for stable (non-evaporating) black holes

Within a purely classical formulation of “strong gravity,” we associated hadron constituents (and even hadrons themselves) with suitable stationary, axisymmetric solutions of certain new Einsteintype equations supposed to describe the strong field inside hadrons. Such equations are nothing but Einstein equations—with cosmological term—suitably scaled down. As a consequence, the cosmological constant Λ and the massesM result in our theory to be scaled up, and transformed into a “hadronic constant” and into “strong masses,” respectively. Due to the unusual range of Λ andM values considered, we met a series of solutions of the Kerr-Newman-de Sitter (KNdS) type with rather interesting properties: aim of the present work is putting forth such results, while “translating” them into the more popular language of ordinary gravity. The requirement that those solutions be stable, i.e., that their temperature (or surface gravity) bevanishingly small, implies the coincidence of at least two of their (in general, three) horizons. Imposing the stability condition of a certain horizon does yield (once chosen the values ofJ, q and Λ) mass and radius of the associated black hole. In the case of ordinary Einstein equations and for stable blackholes of the KNdS type, we get in particular Regge-like relations among massM, angular momentumJ, chargeq and cosmological constant Λ; which did not receive enough attention in the previous literature. For instance, with the standard definitionsQ ² = Gq²/(4πε ₀ c ⁴), a ≡ J/(Mc), m ≡GM/c ², in the case Λ=0 in whichm ²=a²+Q² and ifq is negligible, we findm ²=J. When considering, for simplicity, Λ>0 andJ=0 (andq still negligible), then we obtainm ² = 1/(9Λ). In the most general case, the condition, for instance, of “triple coincidence” among the three horizons yields for |Λa ²|<< 1 the couple of independent relationsm ² = 2/(9Λ) andm ² = 8(a ² + Q². Another interesting point is that—with few exceptions—all such relations (amongM, J, q, Λ) lead to solutions that can be regarded as (stable) cosmological models. Work partially supported by INFN, MURST, and CNR and by CNPq, FAPESP, and CAPES.     

Study of N*(1440) from J/Ψ decays

For J/Ψ↦ pπ⁰ and pπ⁺π^-, the π⁰ p and pπ⁺π^- systems are limited to be pure isospin-(1/2) due to isospin conservation. This is a big advantage in studying N^* resonances from J/Ψ decays, compared with πN and γN experiments. The process J/Ψ↦ N ^* or p provides a new way to probe the internal structure of the N^* resonances. Here we report a quark model calculation for J/Ψ↦ p, N ^*(1440) and N ^*. The implication for the internal structure of N ^*(1440) is discussed. Received: 1 June 2001 / Accepted: 20 June 2001     

Correction to Entropy of Schwarzschild Black Hole by Modified Dispersion Relation

Taking WKB approximation to solve the scalar field equation in the Schwarzschild black hole spacetime, we can get the classical momenta. Substituting the classical momenta into state density equation corrected by the modified dispersion relation, we will obtain the number of quantum states with energy less than ω. Then, it is used to calculate the statistical-mechanical entropy of the scalar field in the Schwarzschild black hole spacetime. By taking exact method, we obtained the leader term of entropy which is proportional to the event horizon area and correction terms take the forms of ln A, A ⁻¹ln A, A ⁻¹ and so on.     

Schwarzschild black hole with global monopole charge

We derive the metric for a Schwarzschild black hole with global monopole charge by relaxing asymptotic flatness of the Schwarzschild field. We then study the effect of global monopole charge on particle orbits and the Hawking radiation. It turns out that existence, boundedness and stability of circular orbits scale up by (1−8πη ²)⁻¹, and the perihelion shift and the light bending by (1−8πη ²)^−3/2, while the Hawking temperature scales down by (1−8πη ²)² the Schwarzschild values. Hereη is the global charge.     

Two-dimensional t-J model at moderate doping

Using the method which retains the rotation symmetry of spin components in the paramagnetic state and has no preset magnetic ordering, spectral and magnetic properties of the two-dimensional t-J model in the normal state are investigated for the ranges of hole concentrations 0 ⩽ x ⩽ 0.16 and temperatures 0.01t ⩽ T ⩽ 0.2t. The used hopping t and exchange J parameters of the model correspond to hole-doped cuprates. The obtained solutions are homogeneous which indicates that stripes and other types of phase separation are not connected with the strong electron correlations described by the model. A series of nearly equidistant maxima in the hole spectral function calculated for low T and x is connected with hole vibrations in the region of the perturbed short-range antiferromagnetic order. The hole spectrum has a pseudogap in the vicinity of (0,π) and (π, 0). For x ≈ 0.05 the shape of the hole Fermi surface is transformed from four small ellipses around (±π/2,±π/2) to two large rhombuses centered at (0, 0) and (π,π). The calculated temperature and concentration dependencies of the spin correlation length and the magnetic susceptibility are close to those observed in cuprate perovskites. These results offer explanations for the observed scaling of the static uniform susceptibility and for the changes in the spin-lattice relaxation and spin-echo decay rates in terms of the temperature and doping variations in the spin excitation spectrum of the model. Received 14 November 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: alexei@fi.tartu.ee     

Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10⁻³, Q ₀= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q ₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q ² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G _A(x,Q ₀ ²) /AG _N(x,Q ₀ ²)_{|x ≤ 10−3}∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q ₀ scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10⁻³ unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s ⁻²≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F _2A(x,Q ²) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed. Received: 12 March 1999     

The volume inside a black hole

The horizon (the surface) of a black hole is a null surface, defined by those hypothetical “outgoing” light rays that just hover under the influence of the strong gravity at the surface. Because the light rays are orthogonal to the spatial two-dimensional surface at one instant of time, the surface area of the black hole is the same for all observers (i.e. the same for all coordinate definitions of “instant of time”). This value is 4π(2Gm/c ²)² for nonspinning black holes, with G = Newton’s constant, c = speed of light, and m = mass of the black hole. The three-dimensional spatial volume inside a black hole, in contrast, depends explicitly on the definition of time, and can even be time dependent, or zero. We give examples of the volume found inside a standard, nonspinning spherical black hole, for several different standard time-coordinate definitions. Elucidating these results for the volume provides a new pedagogical resource of facts already known in principle to the relativity community, but rarely worked out.     

New hadronic states observed at BES II

The report includes the new observation of X(1835) in J/ψ→γη ^′ π ⁺ π ^-, the ωφ threshold enhancement in J/ψ→γωφ, the ωω structure in J/ψ→γωω and the broad 1^- structure at the low K ⁺ K ^- invariant-mass spectrum in J/ψ→K ⁺ K ^- π ⁰.     

On Meson Masses

It is shown that in the framework of an analytical confinement, when quark and gluon propagators are induced by a vacuum self-dual gluon field with constant strength, the masses of mesons with quantum numbers Q = (J ^P ,n), where n is the radial quantum number, and quark constituents m ₁, m ₂ are described with reasonable accuracy by the formula The positive parameter A _Q is unique for all mesons with a fixed quantum number Q. Sets of mesons J ^P = 1⁻, 0⁺, 1⁺, 2⁺, 3⁻ for n = 0 and 1⁻ , 2⁺ for n > 0 and different flavor constituent quarks (u = d, s, c, b) are considered.     

Effective Lagrangians and IG(JPC)=1?(1?+) exotic resonance state in the VP and the PP channel

For I ^G (J ^PC)=1⁻(1⁻⁺) exotic waves in the reactions ρπ → ρπ, ρπ → ηπ, ρπ → η′π, and ρπ → and in allied reactions, a model is constructed that satisfies the conditions of unitarity and analyticity and which employs, as an input, an “anomalous” nondiagonal VPPP interaction relating the ρπ, ηπ, η′π, and channels. The possibility of obtaining, within this simple field-theoretical model, a resonance behavior of the I ^G(J ^PC)=1⁻(1⁻⁺) amplitudes corresponding to the {10} − and {8} representations of the SU(3) group and their mixing is demonstrated explicitly in the mass range 1.3–1.6 GeV, where data of present-day experiments suggest a rich exoticism. __________ Translated from Yadernaya Fizika, Vol. 65, No. 3, 2002, pp. 579–588. Original Russian Text Copyright ? 2002 by Achasov, Shestakov.     

Photon-pion transition form factor at high photon virtualities within the nonlocal chiral quark model

Recently, the BABAR collaboration reported the measurements of the photon-pion transition form factor F _πγγ*(Q ²), which are in strong contradiction to the predictions of the standard factorization approach to perturbative QCD. In the present work, based on a nonperturbative approach to the QCD vacuum and on rather universal assumptions, we show that there exist two asymptotic regimes for the pion transition form factor. One regime with the asymptotic behavior F _πγ*γ(Q ²) ∼ 1/Q ² corresponds to the result of the standard QCD factorization approach, while other violates the standard factorization and leads to asymptotic behavior as F _πγ*γ(Q ²) ∼ ln(Q ²)/Q ². Furthermore, considering specific nonlocal chiral quark models, we find the region of parameters, where the existing CELLO, CLEO and BABAR data for the pion transition form factor are successfully described.     

High-spin states in <Superscript>36</Superscript>Ar and their underlying shell model configurations

Eight high-spin states in ³⁶Ar below 10MeV excitation energy, among them a prospective J ^π = 8^- state at 9408keV and the J? 8 levels of the recently discovered superdeformed rotational band, have been observed by n-γ coincidence measurements with the ³³S(α, nγ) reaction at E _α = 14.4 and 13.4MeV. High-spin assignments of, respectively, J ^π = 6⁺ and 5^- were obtained for the E _p = 1209 and 1462keV (E _x = 9682 and 9927keV) resonances of the ³⁵Cl (p,γ) reaction by a measurement of γ-ray angular distributions. The spectrum of the high-spin and of the E _x? 7.4MeV levels is decomposed according to the underlying shell model configurations with n = 0, 1, 2, 4 particles excited from the N = 2 into the N = 3 major shell. The role of four-particle excitations, all connected with large prolate distortions, is elucidated for the entire A = 36-40 mass region. Received: 21 December 2001 / Accepted: 25 March 2002     

Precise Quadrupole Moment of the Doubly Closed Shell Plus One Proton Nucleus 41Sc

In order to precisely determine the |eqQ(⁴¹Sc)/h| of ⁴¹Sc(I ^π=7/2⁻, T _1/2=0.596 s) implanted in a TiO₂ single crystal the electric field gradient tensor and anisotropic chemical shift were determined by detecting the Fourier Transformed Pulse-NMR of ⁴⁵Sc(I ^π=7/2⁻, stable) in the crystal at a high field of 7.0 T and 9.4 T. Combining the new |eqQ(⁴¹Sc)/h| value with the Q(⁴⁵Sc)=−(23.6±0.2) fm², also renewed by using the known atomic hyperfine interaction constants and Sternheimer polarization effect, the |Q(⁴¹Sc;I ^π=7/2⁻,T _1/2=0.596 s)|=(15.6±0.3) fm² has been precisely determined. The value is compared with the theoretical Q(⁴¹Sc) given by a shell model code. This revised version was published online in September 2006 with corrections to the Cover Date.     

Spin susceptibilities for the Hubbard model in a band approach

The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω(Q)=c|Q−(π, π)| near Q∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X″(Q,ω→0) gives the same mode with a peak at Q∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X″(Q,ω→0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector. Zh. éksp. Teor. Fiz. 116, 1058–1080 (September 1999)     

Monte Carlo calculations of angular momentum projected many-body matrix elements in the Pairing Plus Quadrupole Model

We extend the recently presented formalism for Monte Carlo calculations of the partition function, for both even and odd particle number systems (Phys. Rev. C 59, 2500 (1999)), to the calculation of many-body matrix elements of the type <ψ| e ^{- βℋ}|ψ> where |ψ> is a many-body state with a definite angular momentum, parity, neutron and proton numbers. For large β such matrix elements are dominated by the lowest eigenstate of the many-body Hamiltonian ℋ, corresponding with a given angular momentum parity and particle number. Emphasis is placed on odd-mass nuclei. Negligible sign fluctuations in the Monte Carlo calculation are found provided the neutron and proton chemical potentials are properly adjusted. The formalism is applied to the J ^π = 0⁺ state in ¹⁶⁶ Er and to the J ^π = 9/2^-, 13/2⁺, 5/2^- states in ¹⁶⁵ Er using the pairing-plus-quadrupole model. Received: 28 April 2000 / Accepted: 20 September 2000     

On lower scalar quark-antiquark nonets

Two-and three-channel analyses of experimental data on the coupled processes ππ → ππ, k, ηη in the channel with I ^G J ^PC = 0⁺0⁺⁺ are carried out and discussed. In a model-independent approach, confirmation of the σ-meson below 1GeV and definite indications of the QCD nature of other f₀ resonances are obtained. An assignment of the scalar mesons below 1.9 GeV to lower nonets is proposed.