49,058 research outputs found
Squared Bessel processes of positive and negative dimension embedded in Brownian local times
The Ray--Knight theorems show that the local time processes of various path
fragments derived from a one-dimensional Brownian motion are squared Bessel
processes of dimensions , , and . It is also known that for various
singular perturbations of a reflecting Brownian motion
by a multiple of its local time process at ,
corresponding local time processes of are squared Bessel with other real
dimension parameters, both positive and negative. Here, we embed squared Bessel
processes of all real dimensions directly in the local time process of .
This is done by decomposing the path of into its excursions above and below
a family of continuous random levels determined by the Harrison--Shepp
construction of skew Brownian motion as the strong solution of an SDE driven by
. This embedding connects to Brownian local times a framework of point
processes of squared Bessel excursions of negative dimension and associated
stable processes, recently introduced by Forman, Pal, Rizzolo and Winkel to set
up interval partition evolutions that arise in their approach to the Aldous
diffusion on a space of continuum trees.Comment: 12 pages, 2 figure
A Gauge-Independent Mechanism for Confinement and Mass Gap: Part I -- The General Framework
We propose a gauge-independent mechanism for the area-law behavior of Wilson
loop expectation values in terms of worldsheets spanning Wilson loops
interacting with the spin foams that contribute to the vacuum partition
function. The method uses an exact transformation of lattice-regularized
Yang-Mills theory that is valid for all couplings. Within this framework, some
natural conjectures can be made as to what physical mechanism enforces the
confinement property in the continuum (weak coupling) limit. Details for the
SU(2) case in three dimensions are provided in a companion paper.Comment: 16 pages, 4 figure
Some Comments on QCD String
We try to draw lessons for higher dimensions from the string representations
recently derived for large Yang-Mills theory by Gross and Taylor, Kostov,
and others, and call attention to three characteristics that should be expected
of a string theory precisely equivalent to a higher dimensional gauge theory:
continuous world-sheets; strong coupling at short distances; and negative
weights. To appear in the proceedings of the Strings '93 Berkeley conference.Comment: RU-94-9. (harvmac, 9 pp.
Topology on the lattice; 2d Yang-Mills theories with a theta term
We study two-dimensional U() and SU() gauge theories with a topological
term on arbitrary surfaces. Starting from a lattice formulation we derive the
continuum limit of the action which turns out to be a generalisation of the
heat kernel in the presence of a topological term. In the continuum limit we
can reconstruct the topological information encoded in the theta term. In the
topologically trivial cases the theta term gives only a trivial shift to the
ground state energy but in the topologically nontrivial ones it remains to be
coupled to the dynamics in the continuum. In particular for the U() gauge
group on orientable surfaces it gives rise to a phase transition at , similar to the ones observed in other models. Using the equivalence of 2d
QCD and a 1d fermion gas on a circle we rewrite our result in the fermionic
language and show that the theta term can be also interpreted as an external
magnetic field imposed on the fermions.Comment: 19 pages LaTe
Radiative accelerations on Ne in the atmospheres of late B stars
Radiative accelerations on Ne are calculated for the atmospheres of main
sequence stars with 11000 < Teff < 15000 K, corresponding to the range of the
HgMn stars. The calculations take into account neon fine structure as well as
shadowing of neon lines using the entire Kurucz line list, bound-bound,
bound-free, and free-free opacity of H, He, and C as well as some NLTE effects.
NLTE effects modify the radiative acceleration by a factor of order 100 in the
outer atmosphere. The dependence of the radiative acelerations on the Ne
abundance, Teff, and gravity is studied. Radiative accelerations are well below
gravity in the entire range of Teff and it is predicted that in stable
atmospheres Ne should sink and be observed as underabundant. This agrees with
recent observations of low Ne abundances in HgMn stars.Comment: Accepted by Monthly Notices of the Royal Astronomical Society, 2002
August 21. 10 pages, 9 Postscript figures (needed new version due to error in
the listed originally-received date; corrected typo in author line)
4d Simplicial Quantum Gravity Interacting with Gauge Matter Fields
The effect of coupling non-compact gauge fields to four dimensional
simplicial quantum gravity is studied using strong coupling expansions and
Monte Carlo simulations. For one gauge field the back-reaction of the matter on
the geometry is weak. This changes, however, as more matter fields are
introduced. For more than two gauge fields the degeneracy of random manifolds
into branched polymers does not occur, and the branched polymer phase seems to
be replaced by a new phase with a negative string susceptibility exponent
and fractal dimension .Comment: latex2e, 10 pages incorporating 2 tables and 3 figures (using epsf
Analytical theory of finite-size effects in mechanical desorption
We discuss a unique system that allows exact analytical investigation of first- and second-order transitions with finite-size effects: mechanical desorption of an ideal lattice polymer chain grafted with one end to a solid substrate with a pulling force applied to the other end. We exploit the analogy with a continuum model and use accurate mapping between the parameters in continuum and lattice descriptions, which leads to a fully analytical partition function as a function of chain length, temperature (or adsorption strength), and pulling force. The adsorption-desorption phase diagram, which gives the critical force as a function of temperature, is nonmonotonic and gives rise to re-entrance. We analyze the chain length dependence of several chain properties (bound fraction, chain extension, and heat capacity) for different cross sections of the phase diagram. Close to the transition a single parameter (the product of the chain length N and the deviation from the transition point) describes all thermodynamic properties. We discuss finite-size effects at the second-order transition (adsorption without force) and at the first-order transition (mechanical desorption). The first-order transition has some unusual features: The heat capacity in the transition region increases anomalously with temperature as a power law, metastable states are completely absent, and instead of a bimodal distribution there is a flat region that becomes more pronounced with increasing chain length. The reason for this anomaly is the absence of an excess surface energy for the boundary between adsorbed and stretched coexisting phases (this boundary is one segment only): The two states strongly fluctuate in the transition point. The relation between mechanical desorption and mechanical unzipping of DNA is discusse
Anomalous Expansion of Attractively Interacting Fermionic Atoms in an Optical Lattice
Strong correlations can dramatically modify the thermodynamics of a quantum
many-particle system. Especially intriguing behaviour can appear when the
system adiabatically enters a strongly correlated regime, for the interplay
between entropy and strong interactions can lead to counterintuitive effects. A
well known example is the so-called Pomeranchuk effect, occurring when liquid
3He is adiabatically compressed towards its crystalline phase. Here, we report
on a novel anomalous, isentropic effect in a spin mixture of attractively
interacting fermionic atoms in an optical lattice. As we adiabatically increase
the attraction between the atoms we observe that the gas, instead of
contracting, anomalously expands. This expansion results from the combination
of two effects induced by pair formation in a lattice potential: the
suppression of quantum fluctuations as the attraction increases, which leads to
a dominant role of entropy, and the progressive loss of the spin degree of
freedom, which forces the gas to excite additional orbital degrees of freedom
and expand to outer regions of the trap in order to maintain the entropy. The
unexpected thermodynamics we observe reveal fundamentally distinctive features
of pairing in the fermionic Hubbard model.Comment: 6 pages (plus appendix), 6 figure
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