355 research outputs found
The Free Quon Gas Suffers Gibbs' Paradox
We consider the Statistical Mechanics of systems of particles satisfying the
-commutation relations recently proposed by Greenberg and others. We show
that although the commutation relations approach Bose (resp.\ Fermi) relations
for (resp.\ ), the partition functions of free gases are
independent of in the range . The partition functions exhibit
Gibbs' Paradox in the same way as a classical gas without a correction factor
for the statistical weight of the -particle phase space, i.e.\ the
Statistical Mechanics does not describe a material for which entropy, free
energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE
Unbounded representations of -deformation of Cuntz algebra
We study a deformation of the Cuntz-Toeplitz -algebra determined by the
relations . We define well-behaved unbounded
*-representations of the *-algebra defined by relations above and classify all
such irreducible representations up to unitary equivalence.Comment: 13 pages, Submitted to Lett. Math. Phy
Coherent States of the q--Canonical Commutation Relations
For the -deformed canonical commutation relations for in some Hilbert
space we consider representations generated from a vector
satisfying , where .
We show that such a representation exists if and only if .
Moreover, for these representations are unitarily equivalent
to the Fock representation (obtained for ). On the other hand
representations obtained for different unit vectors are disjoint. We
show that the universal C*-algebra for the relations has a largest proper,
closed, two-sided ideal. The quotient by this ideal is a natural -analogue
of the Cuntz algebra (obtained for ). We discuss the Conjecture that, for
, this analogue should, in fact, be equal to the Cuntz algebra
itself. In the limiting cases we determine all irreducible
representations of the relations, and characterize those which can be obtained
via coherent states.Comment: 19 pages, Plain Te
Synchronization and Coarsening (without SOC) in a Forest-Fire Model
We study the long-time dynamics of a forest-fire model with deterministic
tree growth and instantaneous burning of entire forests by stochastic lightning
strikes. Asymptotically the system organizes into a coarsening self-similar
mosaic of synchronized patches within which trees regrow and burn
simultaneously. We show that the average patch length grows linearly with
time as t-->oo. The number density of patches of length L, N(L,t), scales as
^{-2}M(L/), and within a mean-field rate equation description we find
that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for
x-->oo. In one dimension, we develop an event-driven cluster algorithm to study
the asymptotic behavior of large systems. Our numerical results are consistent
with mean-field predictions for patch coarsening.Comment: 5 pages, 4 figures, 2-column revtex format. To be submitted to PR
Constituent Quark Model Calculation for a possible J^P=0^-,T=0 Dibaryon
There exists experimental evidence that a dibaryon resonance d' with quantum
numbers J^P=0^-,T=0 and mass 2065 MeV could be the origin of the narrow peak in
the (\pi^+ ,\pi^- ) double charge exchange cross--sections on nuclei. We
investigate the six--quark system with these quantum--numbers within the
constituent quark model, with linear confinement, effective one--gluon exchange
at short range and chiral interactions between quarks (\pi and \sigma
exchange). We classify all possible six quark states with J^P=0^-,T=0, and with
N=1 and N=3 harmonic oscillator excitations, using different reduction chains.
The six--quark Hamiltonian is diagonalized in the basis including the unique
N=1 state and the 10 most important states from the N=3 shell. We find, that
with most of the possible sets of parameters, the mass of such a "dibaryon"
lies above the N(939)+N^\ast(1535) threshold. The only possibility to describe
the supposed d'(2065) in the present context is to reduce the confinement
strength to very small values, however at the expense of describing the
negative parity resonances N^\ast. We also analyze the J^P=0^-,T=2,N=1
six--quark state.Comment: 42 pages, Latex, submitted to Nucl.Phys.
Applications of patching to quadratic forms and central simple algebras
This paper provides applications of patching to quadratic forms and central
simple algebras over function fields of curves over henselian valued fields. In
particular, we use a patching approach to reprove and generalize a recent
result of Parimala and Suresh on the u-invariant of p-adic function fields, for
p odd. The strategy relies on a local-global principle for homogeneous spaces
for rational algebraic groups, combined with local computations.Comment: 48 pages; connectivity now required in the definition of rational
group; beginning of Section 4 reorganized; other minor change
Negative Parity 70-plet Baryon Masses in the 1/Nc Expansion
The masses of the negative parity SU(6) 70-plet baryons are analyzed in the
1/Nc expansion to order 1/Nc and to first order in SU(3) breaking. At this
level of precision there are twenty predictions. Among them there are the well
known Gell-Mann Okubo and equal spacing relations, and four new relations
involving SU(3) breaking splittings in different SU(3) multiplets. Although the
breaking of SU(6) symmetry occurs at zeroth order in 1/Nc, it turns out to be
small. The dominant source of the breaking is the hyperfine interaction which
is of order 1/Nc. The spin-orbit interaction, of zeroth order in 1/Nc, is
entirely fixed by the splitting between the singlet states Lambda(1405) and
Lambda(1520), and the spin-orbit puzzle is solved by the presence of other
zeroth order operators involving flavor exchange.Comment: 31 pages, 3 figure
Panspermia, Past and Present: Astrophysical and Biophysical Conditions for the Dissemination of Life in Space
Astronomically, there are viable mechanisms for distributing organic material
throughout the Milky Way. Biologically, the destructive effects of ultraviolet
light and cosmic rays means that the majority of organisms arrive broken and
dead on a new world. The likelihood of conventional forms of panspermia must
therefore be considered low. However, the information content of dam-aged
biological molecules might serve to seed new life (necropanspermia).Comment: Accepted for publication in Space Science Review
Implications of Space-Time foam for Entanglement Correlations of Neutral Kaons
The role of invariance and consequences for bipartite entanglement of
neutral (K) mesons are discussed. A relaxation of leads to a modification
of the entanglement which is known as the effect. The relaxation of
assumptions required to prove the theorem are examined within the context
of models of space-time foam. It is shown that the evasion of the EPR type
entanglement implied by (which is connected with spin statistics) is
rather elusive. Relaxation of locality (through non-commutative geometry) or
the introduction of decoherence by themselves do not lead to a destruction of
the entanglement. So far we find only one model which is based on non-critical
strings and D-particle capture and recoil that leads to a stochastic
contribution to the space-time metric and consequent change in the neutral
meson bipartite entanglement. The lack of an omega effect is demonstrated for a
class of models based on thermal like baths which are generally considered as
generic models of decoherence
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