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The Green's function for the radial Schramm-Loewner evolution
We prove the existence of the Green's function for radial SLE(k) for k<8.
Unlike the chordal case where an explicit formula for the Green's function is
known for all values of k<8, we give an explicit formula only for k=4. For
other values of k, we give a formula in terms of an expectation with respect to
SLE conditioned to go through a point.Comment: v1: 16 pages, 0 figure
Markovian versus non-Markovian stochastic quantization of a complex-action model
We analyze the Markovian and non-Markovian stochastic quantization methods
for a complex action quantum mechanical model analog to a Maxwell-Chern-Simons
eletrodynamics in Weyl gauge. We show through analytical methods convergence to
the correct equilibrium state for both methods. Introduction of a memory kernel
generates a non-Markovian process which has the effect of slowing down
oscillations that arise in the Langevin-time evolution toward equilibrium of
complex action problems. This feature of non-Markovian stochastic quantization
might be beneficial in large scale numerical simulations of complex action
field theories on a lattice.Comment: Accepted for publication in the International Journal of Modern
Physics
Scaling of the superconducting transition temperature in underdoped high-Tc cuprates with a pseudogap energy: Does this support the anyon model of their superfluidity?
In earlier work, we have been concerned with the scaling properties of some
classes of superconductors, specifically with heavy Fermion materials and with
five bcc transition metals of BCS character. Both of these classes of
superconductors were three-dimensional but here we are concerned solely with
quasi-two-dimensional high-Tc cuprates in the underdoped region of their phase
diagram. A characteristic feature of this part of the phase diagram is the
existence of a pseudogap (pg). We therefore build our approach around the
assumption that kB Tc / E_pg is the basic dimensionless ratio on which to
focus, where the energy E_pg introduced above is a measure of the pseudogap.
Since anyon fractional statistics apply to two-dimensional assemblies, we
expect the fractional statistics parameter allowing `interpolation' between
Fermi-Dirac and Bose-Einstein statistical distribution functions as limiting
cases to play a significant role in determining kB Tc / E_pg and experimental
data are analyzed with this in mind.Comment: Phys. Chem. Liquids, to be publishe
Riemann zeta zeros and prime number spectra in quantum field theory
The Riemann hypothesis states that all nontrivial zeros of the zeta function
lie in the critical line . Hilbert and P\'olya suggested that one
possible way to prove the Riemann hypothesis is to interpret the nontrivial
zeros in the light of spectral theory. Following this approach, we discuss a
necessary condition that such a sequence of numbers should obey in order to be
associated with the spectrum of a linear differential operator of a system with
countably infinite number of degrees of freedom described by quantum field
theory. The sequence of nontrivial zeros is zeta regularizable. Then,
functional integrals associated with hypothetical systems described by
self-adjoint operators whose spectra is given by this sequence can be
constructed. However, if one considers the same situation with primes numbers,
the associated functional integral cannot be constructed, due to the fact that
the sequence of prime numbers is not zeta regularizable. Finally, we extend
this result to sequences whose asymptotic distributions are not "far away" from
the asymptotic distribution of prime numbers.Comment: Revised version, 18 page
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