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Example of a diffeomorphism for which the special ergodic theorem doesn't hold
In this work we present an example of C^\infty-diffeomorphism of a compact
4-manifold such that it admits a global SRB measure \mu but for which the
special ergodic theorem doesn't hold. Namely, for this transformation there
exist a continuous function \phi and a positive constant \alpha such that the
following holds: the set of the initial points for which the Birkhoff time
averages of the function \phi differ from its \mu--space average by at least
\alpha has zero Lebesgue measure but full Hausdorff dimension.Comment: 15 pages, 7 figure
Cluster model of glass transition in simple liquids
On the basis of microscopic statistical mechanics of simple liquids the
orientational interaction between clusters consisting of a particle and its
nearest neighbors is estimated. It is shown that there are ranges of density
and temperature where the interaction changes sign as a function of a radius of
a cluster. The model of interacting cubic and icosahedral clusters is proposed
and solved in mean-field replica symmetric approximation. It is shown that the
glass order parameter grows smoothly upon cooling, the transition temperature
being identified with the temperature of the replica symmetry breaking. It is
shown that upon cooling a Lennard-Jones system, cubic clusters freeze first.
The transition temperature for icosahedral clusters is about ten per cent
lower. So the local structure of Lennard-Jones glass in the vicinity of glass
transition should be most probably cubic.Comment: 4 pages, 3 figure
Neutron diffraction, magnetization and ESR studies of pseudocubic Nd(0.75)Ba(0.25)MnO3 and its unusual critical behavior above Tc
Results of structural neutron diffraction study, magnetization and ESR
measure-ments are presented for insulating Nd0.75Ba0.25MnO3, Tc = 129 K. The
crystal structure is refined in the range 4.2-300 K. The compound is found to
exhibit the Jahn-Teller (JT) transition at 250 K. The field cooled (FC)
magnetization data are in a reasonable agreement with the predictions for a 3D
isotropic ferromagnet above Tc. However, these measurements reveal a difference
between the FC and zero FC data in the paramagnetic region. ESR results are
also in a correspondence with behavior of a cubic ferromagnet above T* = 143 K.
It is shown that an anisotropic exchange coupling of the Mn and Nd magnetic
moments can give a substantial contribution in ESR linewidth masking its
critical enhan-cement. The different temperature treatments of the sample
reveal a temperature hysteresis of the ESR spectra below T* indicating an
anomalous response in the paramagnetic region. The study of phase transition in
this manganite suggests change in its character from the second to first order
at T*. The conventional free energy including the magnetization and magnetic
field is not found to describe the first order transition. This suggests that
the charge, orbital and JT phonon degrees of freedom, in addition to
magnetization, may be the critical variables, the unusual character of the
transition being determined by their coupling. Unconventional critical behavior
is attributed to orbital liquid metallic phase that coexists with the initial
orbital ordered phase below T*.Comment: 18 pages, 5 figures, submitted to Phys. Rev.
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