177 research outputs found
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 , 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 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 . The
critical temperature at large coupling constant is computed by considering
M-theory on manifold with topology .
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 , 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 -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
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