1,196 research outputs found
Lyapunov exponents from geodesic spread in configuration space
The exact form of the Jacobi -- Levi-Civita (JLC) equation for geodesic
spread is here explicitly worked out at arbitrary dimension for the
configuration space manifold M_E = {q in R^N | V(q) < E} of a standard
Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric g_J. As
the Hamiltonian flow corresponds to a geodesic flow on (M_E,g_J), the JLC
equation can be used to study the degree of instability of the Hamiltonian
flow. It is found that the solutions of the JLC equation are closely resembling
the solutions of the standard tangent dynamics equation which is used to
compute Lyapunov exponents. Therefore the instability exponents obtained
through the JLC equation are in perfect quantitative agreement with usual
Lyapunov exponents. This work completes a previous investigation that was
limited only to two-degrees of freedom systems.Comment: REVTEX file, 10 pages, 2 figure
Dynamic hysteresis from zigzag domain walls
We investigate dynamic hysteresis in ferromagnetic thin films with zigzag
domain walls. We introduce a discrete model describing the motion of a wall in
a disordered ferromagnet with in-plane magnetization, driven by an external
magnetic field, considering the effects of dipolar interactions and anisotropy.
We analyze the effects of external field frequency and temperature on the
coercive field by Monte Carlo simulations, and find a good agreement with the
experimental data reported in literature for Fe/GaAs films. This implies that
dynamic hysteresis in this case can be explained by a single propagating domain
wall model without invoking domain nucleation.Comment: 10 pages, 13 figures; minor modifications and two figures adde
Phase transitions as topology changes in configuration space: an exact result
The phase transition in the mean-field XY model is shown analytically to be
related to a topological change in its configuration space. Such a topology
change is completely described by means of Morse theory allowing a computation
of the Euler characteristic--of suitable submanifolds of configuration
space--which shows a sharp discontinuity at the phase transition point, also at
finite N. The present analytic result provides, with previous work, a new key
to a possible connection of topological changes in configuration space as the
origin of phase transitions in a variety of systems.Comment: REVTeX file, 5 pages, 1 PostScript figur
Topological aspects of geometrical signatures of phase transitions
Certain geometric properties of submanifolds of configuration space are
numerically investigated for classical lattice phi^4 models in one and two
dimensions. Peculiar behaviors of the computed geometric quantities are found
only in the two-dimensional case, when a phase transition is present. The
observed phenomenology strongly supports, though in an indirect way, a recently
proposed topological conjecture about a topology change of the configuration
space submanifolds as counterpart of a phase transition.Comment: REVTEX file, 4 pages, 5 figure
Hamiltonian dynamics and geometry of phase transitions in classical XY models
The Hamiltonian dynamics associated to classical, planar, Heisenberg XY
models is investigated for two- and three-dimensional lattices. Besides the
conventional signatures of phase transitions, here obtained through time
averages of thermodynamical observables in place of ensemble averages,
qualitatively new information is derived from the temperature dependence of
Lyapunov exponents. A Riemannian geometrization of newtonian dynamics suggests
to consider other observables of geometric meaning tightly related with the
largest Lyapunov exponent. The numerical computation of these observables -
unusual in the study of phase transitions - sheds a new light on the
microscopic dynamical counterpart of thermodynamics also pointing to the
existence of some major change in the geometry of the mechanical manifolds at
the thermodynamical transition. Through the microcanonical definition of the
entropy, a relationship between thermodynamics and the extrinsic geometry of
the constant energy surfaces of phase space can be naturally
established. In this framework, an approximate formula is worked out,
determining a highly non-trivial relationship between temperature and topology
of the . Whence it can be understood that the appearance of a phase
transition must be tightly related to a suitable major topology change of the
. This contributes to the understanding of the origin of phase
transitions in the microcanonical ensemble.Comment: in press on Physical Review E, 43 pages, LaTeX (uses revtex), 22
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