Quantum state density and critical temperature in M-theory

We discuss the asymptotic properties of quantum states density for fundamental p-branes which can yield a microscopic interpretation of the thermodynamic quantities in M-theory. The matching of the BPS part of spectrum for superstring and supermembrane gives the possibility of getting membrane's results via string calculations. In the weak coupling limit of M-theory, the critical behavior coincides with the first-order phase transition in the standard string theory at temperature less than the Hagedorn's temperature T-H. The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology R-9 circle times T-2. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.

Finite-momentum condensate of magnetic excitons in a bilayer quantum Hall system

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

Discrete generator coordinate: Symmetry restoration in finite-dimensional spaces

Group theoretical-based techniques and fundamental results from number theory are used in order to allow for the construction of exact projectors in finite-dimensional spaces. These operators are shown to make use only of discrete variables, which play the role of discrete generator coordinates, and their application in the number symmetry restoration is carried out in a nuclear BCS wave function which explicitly violates that symmetry. © 1999 Published by Elsevier Science B.V. All rights reserved.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Final state and thermodynamics of a dark energy universe

As it follows from the classical analysis, the typical final state of a dark energy universe where a dominant energy condition is violated is a finite-time, sudden future singularity (a big rip). For a number of dark energy universes (including scalar phantom and effective phantom theories as well as specific quintessence models) we demonstrate that quantum effects play the dominant role near a big rip, driving the universe out of a future singularity (or, at least, moderating it). As a consequence, the entropy bounds with quantum corrections become well defined near a big rip. Similarly, black hole mass loss due to phantom accretion is not so dramatic as was expected: masses do not vanish to zero due to the transient character of the phantom evolution stage. Some examples of cosmological evolution for a negative, time-dependent equation of state are also considered with the same conclusions. The application of negative entropy (or negative temperature) occurrence in the phantom thermodynamics is briefly discussed.

Alternate treatments of jacobian singularities in polar coordinates within finite-difference schemes

Jacobian singularities of differential operators in curvilinear coordinates occur when the Jacobian determinant of the curvilinear-to-Cartesian mapping vanishes, thus leading to unbounded coefficients in partial differential equations. Within a finite-difference scheme, we treat the singularity at the pole of polar coordinates by setting up complementary equations. Such equations are obtained by either integral or smoothness conditions. They are assessed by application to analytically solvable steady-state heat-conduction problems.

Scales, Universality and Finite-Range Correction in Three-body Systems

The scale invariance manifested by the weakly-bound Efimov states implies that all the Efimov spectrum can be merged in a single scaling function. By considering this scaling function, the ratio between two consecutive energy levels, E3 (N+1) and E3 (N), can be obtained from a two-body low-energy observable (usually the scattering length a), given in units of the three-body energy level N. The zero-ranged scaling function is improved by incorporating finite range corrections in first order of r0/a (r0 is the potential effective range). The critical condition for three-identical bosons in s-wave, when the excited E3 (N+1) state disappears in the 2 + 1 threshold, is given by √E2/E3 (N) ≈ 0.38+0.12(r0/a). © 2012 Springer-Verlag.

Finite approximate controllability for semilinear heat equations in noncylindrical domains

Este artigo é dedicado ao estudo da controlabilidade finito-aproximada para a equação não linear de transferência de calor em domínios com fronteira móvel. A demonstração do resultado principal baseia-se no princípio de continuação única de Carolina Fabre 1996 e em argumentos de ponto fixo do tipo Leray-Schauder.

Characterization of the Al-3wt.%Si alloy in unsteady-state horizontal directional solidification

The main purpose of this paper is to investigate both the columnar to equiaxed transition and primary dendritic arm spacings of Al-3wt.%Si alloy during the horizontal directional solidification. The transient heat transfer coefficient at the metal-mold interface is calculated based on comparisons between the experimental thermal profiles in castings and the simulations provided by a finite difference heat flow program. Simulated curve of the interfacial heat transfer coefficient was used in another numerical solidification model to determine theoretical values of tip growth rates, cooling rates and thermal gradients that are associated with both columnar to equiaxed transition and primary dendritic arm spacings. A good agreement was observed between the experimental values of these thermal variables and those numerically simulated for the alloy examined. A comparative analysis is carried out between the experimental data of this work and theoretical models from the literature that have been proposed to predict the primary dendritic spacings. In this context, this study may contribute to the understanding of how to manage solidification operational parameters aiming at designing the microstructure of Al-Si alloys.

Multi-vortex State Induced by Proximity Effects in a Small Superconducting Square

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams

We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half-filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U -> infinity and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U -> 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and eta-spin SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U = 0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a van Hove singularity that persists as a consequence of integrability.

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.