839 research outputs found
Cluster Approximation for the Farey Fraction Spin Chain
We consider the Farey fraction spin chain in an external field . Utilising
ideas from dynamical systems, the free energy of the model is derived by means
of an effective cluster energy approximation. This approximation is valid for
divergent cluster sizes, and hence appropriate for the discussion of the
magnetizing transition. We calculate the phase boundaries and the scaling of
the free energy. At we reproduce the rigorously known asymptotic
temperature dependence of the free energy. For , our results are
largely consistent with those found previously using mean field theory and
renormalization group arguments.Comment: 17 pages, 3 figure
The Non-Trapping Degree of Scattering
We consider classical potential scattering. If no orbit is trapped at energy
E, the Hamiltonian dynamics defines an integer-valued topological degree. This
can be calculated explicitly and be used for symbolic dynamics of
multi-obstacle scattering.
If the potential is bounded, then in the non-trapping case the boundary of
Hill's Region is empty or homeomorphic to a sphere.
We consider classical potential scattering. If at energy E no orbit is
trapped, the Hamiltonian dynamics defines an integer-valued topological degree
deg(E) < 2. This is calculated explicitly for all potentials, and exactly the
integers < 2 are shown to occur for suitable potentials.
The non-trapping condition is restrictive in the sense that for a bounded
potential it is shown to imply that the boundary of Hill's Region in
configuration space is either empty or homeomorphic to a sphere.
However, in many situations one can decompose a potential into a sum of
non-trapping potentials with non-trivial degree and embed symbolic dynamics of
multi-obstacle scattering. This comprises a large number of earlier results,
obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more
detailed proofs and remark
Symbolic dynamics for the -centre problem at negative energies
We consider the planar -centre problem, with homogeneous potentials of
degree -\a<0, \a \in [1,2). We prove the existence of infinitely many
collisions-free periodic solutions with negative and small energy, for any
distribution of the centres inside a compact set. The proof is based upon
topological, variational and geometric arguments. The existence result allows
to characterize the associated dynamical system with a symbolic dynamics, where
the symbols are the partitions of the centres in two non-empty sets
YBCO-buffered NdBCO film with higher thermal stability in seeding REBCO Growth
In this work, we report a strengthened superheating effect caused by a
buffering YBa2Cu3Oy (Y123 or YBCO) layer in the Nd1+xBa2-xCu3O7-y (Nd123 or
NdBCO) thin film with MgO substrate (i.e., NdBCO/YBCO/MgO thin film). In the
cold-seeding melt-textured (MT) growth, the NdBCO/YBCO/MgO film presented an
even higher superheating level, about 20 {\deg}C higher than that of
non-buffered NdBCO film (i.e., NdBCO/MgO film). Using this NdBCO/YBCO/MgO film
as seeds and undergoing a maximum processing temperature (Tmax) up to 1120
{\deg}C, we succeeded in growing various RE1+xBa2-xCu3O7-y (REBCO, RE=rare
elements) bulk superconductors, including Gd1+xBa2-xCu3O7-y (GdBCO),
Sm1+xBa2-xCu3O7-y (SmBCO) and NdBCO that have high peritectic temperatures
(Tp). The pole figure (X-Ray \phi-scan) measurement reveals that the
NdBCO/YBCO/MgO film has better in-plane alignment than the NdBCO/MgO film,
indicating that the induced intermediate layer improves the crystallinity of
the NdBCO film, which could be the main origin of the enhanced thermal
stability. In short, possessing higher thermal stability and enduring a higher
Tmax in the MT process, the NdBCO/YBCO/MgO film is beneficial to the growth of
bulk superconductors in two aspects: (1) broad application for high-Tp REBCO
materials; (2) effective suppression against heterogeneous nucleation, which is
of great assistance in growing large and high-performance REBCO crystals.Comment: 9 pages, 4 figure
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
This paper deals with the problem of analytically computing the largest
Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is
succesfully reached within a theoretical framework that makes use of a
geometrization of newtonian dynamics in the language of Riemannian geometry. A
new point of view about the origin of chaos in these systems is obtained
independently of homoclinic intersections. Chaos is here related to curvature
fluctuations of the manifolds whose geodesics are natural motions and is
described by means of Jacobi equation for geodesic spread. Under general
conditions ane effective stability equation is derived; an analytic formula for
the growth-rate of its solutions is worked out and applied to the
Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent
agreement is found the theoretical prediction and the values of the Lyapunov
exponent obtained by numerical simulations for both models.Comment: RevTex, 40 pages, 8 PostScript figures, to be published in Phys. Rev.
E (scheduled for November 1996
Conifolds and Geometric Transitions
Conifold geometries have recieved a lot of attention in string theory and
string-inspired cosmology recently, in particular the Klebanov-Strassler
background that is known as the "warped throat". It is our intention in this
article to give a pedagogical explanation for the singularity resolution in
this geometry and emphasise its connection to geometric transitions. The first
part focuses on the gauge theory dual to the Klebanov-Strassler background,
which we also explain from a T-dual intersecting branes scenario. We then make
the connection to the Gopakumar-Vafa conjecture for open/closed string duality
and summarise a series of papers verifying this model on the supergravity
level.
An appendix provides extensive background material about conifold geometries.
We pay special attention to their complex structures and re-evaluate the
supersymmetry conditions on the background flux in constructions with
fractional D3-branes on the singular (Klebanov-Tseytlin) and resolved (Pando
Zayas-Tseytlin) conifolds. We agree with earlier results that only the singular
solution allows a supersymmetric flux, but point out the importance of using
the correct complex structure to reach this conclusion.Comment: 37 pages, v3: accepted for publication in Reviews of Modern Physic
Hamiltonian dynamics of the two-dimensional lattice phi^4 model
The Hamiltonian dynamics of the classical model on a two-dimensional
square lattice is investigated by means of numerical simulations. The
macroscopic observables are computed as time averages. The results clearly
reveal the presence of the continuous phase transition at a finite energy
density and are consistent both qualitatively and quantitatively with the
predictions of equilibrium statistical mechanics. The Hamiltonian microscopic
dynamics also exhibits critical slowing down close to the transition. Moreover,
the relationship between chaos and the phase transition is considered, and
interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure
Linear Sigma Models with Torsion
Gauged linear sigma models with (0,2) supersymmetry allow a larger choice of
couplings than models with (2,2) supersymmetry. We use this freedom to find a
fully linear construction of torsional heterotic compactifications, including
models with branes. As a non-compact example, we describe a family of metrics
which correspond to deformations of the heterotic conifold by turning on
H-flux. We then describe compact models which are gauge-invariant only at the
quantum level. Our construction gives a generalization of symplectic reduction.
The resulting spaces are non-Kahler analogues of familiar toric spaces like
complex projective space. Perturbatively conformal models can be constructed by
considering intersections.Comment: 40 pages, LaTeX, 1 figure; references added; a new section on
supersymmetry added; quantization condition revisite
Beyond the periodic orbit theory
The global constraints on chaotic dynamics induced by the analyticity of
smooth flows are used to dispense with individual periodic orbits and derive
infinite families of exact sum rules for several simple dynamical systems. The
associated Fredholm determinants are of particularly simple polynomial form.
The theory developed suggests an alternative to the conventional periodic orbit
theory approach to determining eigenspectra of transfer operators.Comment: 29 pages Latex2
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