20,163 research outputs found
Non-autonomous Hamiltonian systems related to highest Hitchin integrals
We describe non-autonomous Hamiltonian systems coming from the Hitchin
integrable systems. The Hitchin integrals of motion depend on the W-structures
of the basic curve. The parameters of the W-structures play the role of times.
In particular, the quadratic integrals dependent on the complex structure
(W_2-structure) of the basic curve and times are coordinate on the Teichmuller
space. The corresponding flows are the monodromy preserving equations such as
the Schlesinger equations, the Painleve VI equation and their generalizations.
The equations corresponding to the highest integrals are monodromy preserving
conditions with respect to changing of the W_k-structures (k>2). They are
derived by the symplectic reduction from the gauge field theory on the basic
curve interacting with W_k-gravity. As by product we obtain the classical Ward
identities in this theory.Comment: 21 pages,Latex, Contribution in the Proceedings "International
Seminar on Integrable systems". In memoriam Mikail V. Saveliev. Bonn,
February, 199
Resolvent convergence of Sturm-Liouville operators with singular potentials
In this paper we consider the Sturm-Liuoville operator in the Hilbert space
with the singular complex potential of and two-point boundary
conditions. For this operator we give sufficient conditions for norm resolvent
approximation by the operators of the same class.Comment: 6 pages, to appear in Math. Note
Ground state structure and interactions between dimeric 2D Wigner crystals
We study the ground state ordering and interactions between two
two-dimensional Wigner crystals on neutralizing charged plates by means of
computer simulation. We consider crystals formed by (i) point-like charges and
(ii) charged dimers, which mimic the screening of charged surfaces by elongated
multivalent ions such as aspherical globular proteins, charged dendrimers or
short stiff polyelectrolytes. Both systems, with point-like and dimeric ions,
display five distinct crystalline phases on increasing the interlayer distance.
In addition to alteration of translational ordering within the bilayer, the
phase transitions in the dimeric system are characterized by alteration of
orientational ordering of the ions.Comment: Revised versio
Coulomb Glasses: A Comparison Between Mean Field and Monte Carlo Results
Recently a local mean field theory for both eqilibrium and transport
properties of the Coulomb glass was proposed [A. Amir et al., Phys. Rev. B 77,
165207 (2008); 80, 245214 (2009)]. We compare the predictions of this theory to
the results of dynamic Monte Carlo simulations. In a thermal equilibrium state
we compare the density of states and the occupation probabilities. We also
study the transition rates between different states and find that the mean
field rates underestimate a certain class of important transitions. We propose
modified rates to be used in the mean field approach which take into account
correlations at the minimal level in the sense that transitions are only to
take place from an occupied to an empty site. We show that this modification
accounts for most of the difference between the mean field and Monte Carlo
rates. The linear response conductance is shown to exhibit the Efros-Shklovskii
behaviour in both the mean field and Monte Carlo approaches, but the mean field
method strongly underestimates the current at low temperatures. When using the
modified rates better agreement is achieved
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Numerical modelling of microwave sintering of lunar simulants under near lunar atmospheric condition
Soft interaction model and the LHC data
Most models for soft interactions which were proposed prior to the
measurements at the LHC, are only marginally compatible with LHC data, our GLM
model has the same deficiency. In this paper we investigate possible causes of
the problem, by considering separate fits to the high energy (),
and low energy () data. Our new results are moderately higher
than our previous predictions. Our results for total and elastic cross sections
are systematically lower that the recent Totem and Alice published values,
while our results for the inelastic and forward slope agree with the data. If
with additional experimental data, the errors are reduced, while the central
cross section values remain unchanged, we will need to reconsider the physics
on which our model is built.Comment: 12 pp, 12 figures in .eps file
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