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Universal behavior of Ferromagnet at Quantum Critical Point
The heavy-fermion metal can be tuned from ferromagnetism
at to non-magnetic state at some critical concentration . The
non-Fermi liquid behavior (NFL) at is recognized by power low
dependence of the specific heat given by the electronic contribution,
magnetic susceptibility and volume expansion coefficient
at low temperatures: . We
also demonstrate that the behavior of normalized effective mass
observed in at agrees with that of
observed in paramagnetic and conclude that these alloys
exhibit the universal NFL thermodynamic behavior at their quantum critical
points. We show that the NFL behavior of can be accounted
for within frameworks of quasiparticle picture and fermion condensation quantum
phase transition, while this alloy exhibits a universal thermodynamic NFL
behavior which is independent of the characteristic features of the given alloy
such as its lattice structure, magnetic ground state, dimension etc.Comment: 5 pages, 3 figure
Correlation femtoscopy of small systems
The basic principles of the correlation femtoscopy, including its
correspondence to the Hanbury Brown and Twiss intensity interferometry, are
re-examined. The main subject of the paper is an analysis of the correlation
femtoscopy when the source size is as small as the order of the uncertainty
limit. It is about 1 fm for the current high energy experiments. Then the
standard femtoscopy model of random sources is inapplicable. The uncertainty
principle leads to the partial indistinguishability and coherence of closely
located emitters that affect the observed femtoscopy scales. In thermal systems
the role of corresponding coherent length is taken by the thermal de Broglie
wavelength that also defines the size of a single emitter. The formalism of
partially coherent phases in the amplitudes of closely located individual
emitters is used for the quantitative analysis. The general approach is
illustrated analytically for the case of the Gaussian approximation for
emitting sources. A reduction of the interferometry radii and a suppression of
the Bose-Einstein correlation functions for small sources due to the
uncertainty principle are found. There is a positive correlation between the
source size and the intercept of the correlation function. The peculiarities of
the non-femtoscopic correlations caused by minijets and fluctuations of the
initial states of the systems formed in and collisions are also
analyzed. The factorization property for the contributions of femtoscopic and
non-femtoscopic correlations into complete correlation function is observed in
numerical calculations in a wide range of the model parameters.Comment: 34 pages, 5 figures. In the version 4 some stylistic improvements
were made, some misprints were corrected. The results and conclusions are not
change
Different Facets of Chaos in Quantum Mechanics
Nowadays there is no universally accepted definition of quantum chaos. In
this paper we review and critically discuss different approaches to the
subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze
the problem of dynamical chaos and the time scales associated with chaos
suppression in quantum mechanics. Summary: 1. Introduction 2. Quantum Chaology
and Spectral Statistics 3. From Poisson to GOE Transition: Comparison with
Experimental Data 3.1 Atomic Nuclei 3.2 The Hydrogen Atom in the Strong
Magnetic Field 4. Quantum Chaos and Field Theory 5. Alternative Approaches to
Quantum Chaos 6. Dynamical Quantum Chaos and Time Scales 6.1 Mean-Field
Approximation and Dynamical Chaos 7. ConclusionsComment: RevTex, 25 pages, 7 postscript figures, to be published in Int. J.
Mod. Phys.
Star-Triangle Relation for a Three Dimensional Model
The solvable -chiral Potts model can be interpreted as a
three-dimensional lattice model with local interactions. To within a minor
modification of the boundary conditions it is an Ising type model on the body
centered cubic lattice with two- and three-spin interactions. The corresponding
local Boltzmann weights obey a number of simple relations, including a
restricted star-triangle relation, which is a modified version of the
well-known star-triangle relation appearing in two-dimensional models. We show
that these relations lead to remarkable symmetry properties of the Boltzmann
weight function of an elementary cube of the lattice, related to spatial
symmetry group of the cubic lattice. These symmetry properties allow one to
prove the commutativity of the row-to-row transfer matrices, bypassing the
tetrahedron relation. The partition function per site for the infinite lattice
is calculated exactly.Comment: 20 pages, plain TeX, 3 figures, SMS-079-92/MRR-020-92. (corrupted
figures replaced
The vertex formulation of the Bazhanov-Baxter Model
In this paper we formulate an integrable model on the simple cubic lattice.
The -- valued spin variables of the model belong to edges of the lattice.
The Boltzmann weights of the model obey the vertex type Tetrahedron Equation.
In the thermodynamic limit our model is equivalent to the Bazhanov -- Baxter
Model. In the case when we reproduce the Korepanov's and Hietarinta's
solutions of the Tetrahedron equation as some special cases.Comment: 20 pages, LaTeX fil
Nonperiodic Orbit Sums in Weyl's Expansion for Billiards
Weyl's expansion for the asymptotic mode density of billiards consists of the
area, length, curvature and corner terms. The area term has been associated
with the so-called zero-length orbits. Here closed nonperiodic paths
corresponding to the length and corner terms are constructed.Comment: 8 pages, 2 figure
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