77 research outputs found
Nonhyperbolic step skew-products: Ergodic approximation
We study transitive step skew-product maps modeled over a complete shift of
, , symbols whose fiber maps are defined on the circle and have
intermingled contracting and expanding regions. These dynamics are genuinely
nonhyperbolic and exhibit simultaneously ergodic measures with positive,
negative, and zero exponents.
We introduce a set of axioms for the fiber maps and study the dynamics of the
resulting skew-product. These axioms turn out to capture the key mechanisms of
the dynamics of nonhyperbolic robustly transitive maps with compact central
leaves.
Focusing on the nonhyperbolic ergodic measures (with zero fiber exponent) of
these systems, we prove that such measures are approximated in the weak
topology and in entropy by hyperbolic ones. We also prove that they are in the
intersection of the convex hulls of the measures with positive fiber exponent
and with negative fiber exponent. Our methods also allow us to perturb
hyperbolic measures. We can perturb a measure with negative exponent directly
to a measure with positive exponent (and vice-versa), however we lose some
amount of entropy in this process. The loss of entropy is determined by the
difference between the Lyapunov exponents of the measures.Comment: 43 pages, 5 figure
The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results
After a brief discussion of the Bogoliubov inequality and possible
generalizations thereof, we present a complete review of results concerning the
Mermin-Wagner theorem for various many-body systems, geometries and order
parameters. We extend the method to cover magnetic phase transitions in the
periodic Anderson Model as well as certain superconducting pairing mechanisms
for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations
in many-body physics is discussed on a conceptual level.Comment: 33 pages; accepted for publication as a Topical Review in Journal of
Physics: Condensed Matte
Ferromagnetic Kondo-Lattice Model
We present a many-body approach to the electronic and magnetic properties of
the (multiband) Kondo-lattice model with ferromagnetic interband exchange. The
coupling between itinerant conduction electrons and localized magnetic moments
leads, on the one hand, to a distinct temperature-dependence of the electronic
quasiparticle spectrum and, on the other hand, to magnetic properties, as
e.~g.the Curie temperature T_C or the magnon dispersion, which are strongly
influenced by the band electron selfenergy and therewith in particular by the
carrier density. We present results for the single-band Kondo-lattice model in
terms of quasiparticle densities of states and quasiparticle band structures
and demonstrate the density-dependence of the self-consistently derived Curie
temperature. The transition from weak-coupling (RKKY) to strong-coupling
(double exchange) behaviour is worked out.
The multiband model is combined with a tight-binding-LMTO bandstructure
calculation to describe real magnetic materials. As an example we present
results for the archetypal ferromagnetic local-moment systems EuO and EuS. The
proposed method avoids the double counting of relevant interactions and takes
into account the correct symmetry of atomic orbitals.Comment: 15 pages, 10 figure
Exploring modularity in biological networks
Network theoretical approaches have shaped our understanding of many different kinds of biological modularity. This essay makes the case that to capture these contributions, it is useful to think about the role of network models in exploratory research. The overall point is that it is possible to provide a systematic analysis of the exploratory functions of network models in bioscientific research. Using two examples from molecular and developmental biology, I argue that often the same modelling approach can perform one or more exploratory functions, such as introducing new directions of research, offering a complementary set of concepts, methods and algorithms for individuating important features of natural phenomena, generating proofs of principle demonstrations and potential explanations for phenomena of interest and enlarging the scope of certain research agendas. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'
Thermodynamic formalism for contracting Lorenz flows
We study the expansion properties of the contracting Lorenz flow introduced
by Rovella via thermodynamic formalism. Specifically, we prove the existence of
an equilibrium state for the natural potential for the contracting Lorenz flow and for in an interval
containing . We also analyse the Lyapunov spectrum of the flow in terms
of the pressure
Kondo-lattice model: Application to the temperature-dependent electronic structure of EuO(100) films
We present calculations for the temperature-dependent electronic structure
and magnetic properties of thin ferromagnetic EuO films. The treatment is based
on a combination of a multiband-Kondo lattice model with first-principles
TB-LMTO band structure calculations. The method avoids the problem of
double-counting of relevant interactions and takes into account the correct
symmetry of the atomic orbitals. We discuss the temperature-dependent
electronic structures of EuO(100) films in terms of quasiparticle densities of
states and quasiparticle band structures. The Curie temperature T_C of the EuO
films turns out to be strongly thickness-dependent, starting from a very low
value = 15K for the monolayer and reaching the bulk value at about 25 layers
Physics of Neutron Star Crusts
The physics of neutron star crusts is vast, involving many different research
fields, from nuclear and condensed matter physics to general relativity. This
review summarizes the progress, which has been achieved over the last few
years, in modeling neutron star crusts, both at the microscopic and macroscopic
levels. The confrontation of these theoretical models with observations is also
briefly discussed.Comment: 182 pages, published version available at
<http://www.livingreviews.org/lrr-2008-10
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