2,163 research outputs found
World Nematic Crystal Model of Gravity Explaining the Absence of Torsion
Assuming that at small distances space-time is equivalent to an elastic
medium which is isotropic in space and time directions, we demonstrate that the
quantum nematic liquid arising from this crystal by spontaneous proliferation
of dislocations corresponds with a medium which is merely carrying curvature
rigidity. This medium is at large distances indistinguishable from Einstein's
spacetime of general relativity. It does not support torsion and possesses
string-like curvature sources which in spacetime form world surfaces.Comment: 4 pages, submitted to Phys. Let. B: this is a polished version of
gr-qc/030703
Variational Perturbation Theory for Fokker-Planck Equation with Nonlinear Drift
We develop a recursive method for perturbative solutions of the Fokker-Planck
equation with nonlinear drift. The series expansion of the time-dependent
probability density in terms of powers of the coupling constant is obtained by
solving a set of first-order linear ordinary differential equations. Resumming
the series in the spirit of variational perturbation theory we are able to
determine the probability density for all values of the coupling constant.
Comparison with numerical results shows exponential convergence with increasing
order.Comment: Author Information under
http://www.theo-phys.uni-essen.de/tp/ags/pelster_dir
Modelling two-dimensional Crystals with Defects under Stress: Superelongation of Carbon Nanotubes at high Temperatures
We calculate analytically the phase diagram of a two-dimensional square
crystal and its wrapped version with defects under external homogeneous stress
as a function of temperature using a simple elastic lattice model that allows
for defect formation. The temperature dependence turns out to be very weak. The
results are relevant for recent stress experiments on carbon nanotubes. Under
increasing stress, we find a crossover regime which we identify with a cracking
transition that is almost independent of temperature. Furthermore, we find an
almost stress-independent melting point. In addition, we derive an enhanced
ductility with relative strains before cracking between 200-400%, in agreement
with carbon nanotube experiments. The specific values depend on the Poisson
ratio and the angle between the external force and the crystal axes. We give
arguments that the results for carbon nanotubes are not much different to the
wrapped square crystal.Comment: 12 pages, 6 eps figures, section VI added discussing the
modifications of our model when applied to tube
Brownian motion of Massive Particle in a Space with Curvature and Torsion and Crystals with Defects
We develop a theory of Brownian motion of a massive particle, including the
effects of inertia (Kramers' problem), in spaces with curvature and torsion.
This is done by invoking the recently discovered generalized equivalence
principle, according to which the equations of motion of a point particle in
such spaces can be obtained from the Newton equation in euclidean space by
means of a nonholonomic mapping. By this principle, the known Langevin equation
in euclidean space goes over into the correct Langevin equation in the Cartan
space. This, in turn, serves to derive the Kubo and Fokker-Planck equations
satisfied by the particle distribution as a function of time in such a space.
The theory can be applied to classical diffusion processes in crystals with
defects.Comment: LaTeX, http://www.physik.fu-berlin.de/kleinert.htm
Recursive Graphical Construction for Feynman Diagrams of Quantum Electrodynamics
We present a method for a recursive graphical construction of Feynman
diagrams with their correct multiplicities in quantum electrodynamics. The
method is first applied to find all diagrams contributing to the vacuum energy
from which all n-point functions are derived by functional differentiation with
respect to electron and photon propagators, and to the interaction. Basis for
our construction is a functional differential equation obeyed by the vacuum
energy when considered as a functional of the free propagators and the
interaction. Our method does not employ external sources in contrast to
traditional approaches.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/29
Interpretation of experimental data near lambda-transition point in liquid helium
The recently published experimental data for specific heat C_p of liquid
helium in zero gravity conditions very close to the lambda-transition have been
discussed. We have shown that these data allow different interpretations. They
can be well interpreted within the perturbative RG approach and within our
recently developed theory, as well. Allowing the logarithmic correction, the
corresponding fits lie almost on top of each other over the whole range of the
reduced temperatures t (for bin averaged data) 6.3 x 10^{-10} < t < 8.8 x
10^{-3}. However, the plot of the effective exponent alpha_eff(t) suggests that
the behaviour of C_p, probably, changes very close to the lambda-transition
temperature. To clarify this question, we need more accurate data for
t<10^{-7}. In addition, we show that the experimental data for superfluid
fraction of liquid helium close to the critical point within 3 x 10^{-7} < t <
10^{-4} can be better fit by our exponents nu=9/13, Delta=5/13 than by the RG
exponents (nu approximately 0.6705 and Delta about 0.5). The latter ones are
preferable to fit the whole measured range 3 x 10^{-7} < t < 10^{-2} where,
however, remarkable systematic deviations appear. Our estimated value 0.694 +/-
0.017 of the asymptotic exponent nu well agrees with the theoretical prediction
nu=9/13.Comment: 9 pages, 4 figures. The first version was a preliminary one. Now it
is substentially extended and coincides with the published pape
Autoparallels From a New Action Principle
We present a simpler and more powerful version of the recently-discovered
action principle for the motion of a spinless point particle in spacetimes with
curvature and torsion. The surprising feature of the new principle is that an
action involving only the metric can produce an equation of motion with a
torsion force, thus changing geodesics to autoparallels. This additional
torsion force arises from a noncommutativity of variations with parameter
derivatives of the paths due to the closure failure of parallelograms in the
presence of torsionComment: Paper in src. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Read paper directly
with Netscape under
http://www.physik.fu-berlin.de/~kleinert/kleiner_re243/preprint.htm
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