Asymptotic Level State Density for Parabosonic Strings

Making use of some results concerning the theory of partitions, relevant in number theory, the complete asymptotic behavior, for large $n$, of the level density of states for a parabosonic string is derived. It is also pointed out the similarity between parabosonic strings and membranes.Comment: 9 pages , LaTe

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 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 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 ${\mathbb R}^9\otimes{mathbb T}^2$. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.Comment: 16 pages, published in Mod. Phys. Lett. A16(2001)224

A Meinardus theorem with multiple singularities

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journa

Thermodynamic Properties of the 2N-Piece Relativistic String

The thermodynamic free energy F(\beta) is calculated for a gas consisting of the transverse oscillations of a piecewise uniform bosonic string. The string consists of 2N parts of equal length, of alternating type I and type II material, and is relativistic in the sense that the velocity of sound everywhere equals the velocity of light. The present paper is a continuation of two earlier papers, one dealing with the Casimir energy of a 2N--piece string [I. Brevik and R. Sollie (1997)], and another dealing with the thermodynamic properties of a string divided into two (unequal) parts [I. Brevik, A. A. Bytsenko and H. B. Nielsen (1998)]. Making use of the Meinardus theorem we calculate the asymptotics of the level state density, and show that the critical temperatures in the individual parts are equal, for arbitrary spacetime dimension D. If D=26, we find \beta= (2/N)\sqrt{2\pi /T_{II}}, T_{II} being the tension in part II. Thermodynamic interactions of parts related to high genus g is also considered.Comment: 15 pages, LaTeX, 2 figures. Discussion in section 8 expande

Applications of the Mellin-Barnes integral representation

We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions. These results are then employed in different topics of quantum field theory, which include the high-temperature expansion of the free energy of a scalar field in ultrastatic curved spacetime, the asymptotics of the $p$-brane density of states, and an explicit approach to the asymptotics of the determinants that appear in string theory.Comment: 20 pages, LaTe

Correlations, spectral gap, and entanglement in harmonic quantum systems on generic lattices

We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of correlations follows for both the ground state and thermal states. Considering the converse direction, we show that an energy gap can follow from algebraic decay and always does for exponential decay. The underlying lattices are described as general graphs of not necessarily integer dimension, including translationally invariant instances of cubic lattices as special cases. Any local quadratic couplings in position and momentum coordinates are allowed for, leading to quasi-free (Gaussian) ground states. We make use of methods of deriving bounds to matrix functions of banded matrices corresponding to local interactions on general graphs. Finally, we give an explicit entanglement-area relationship in terms of the energy gap for arbitrary, not necessarily contiguous regions on lattices characterized by general graphs.Comment: 26 pages, LaTeX, published version (figure added

Many-body physics and the capacity of quantum channels with memory

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