2,752 research outputs found
The saga of the Ising susceptibility
We review developments made since 1959 in the search for a closed form for
the susceptibility of the Ising model. The expressions for the form factors in
terms of the nome and the modulus are compared and contrasted. The
generalized correlations are defined and explicitly
computed in terms of theta functions for .Comment: 19 pages, 1 figur
Self-Interacting Electromagnetic Fields and a Classical Discussion on the Stability of the Electric Charge
The present work proposes a discussion on the self-energy of charged
particles in the framework of nonlinear electrodynamics. We seek magnet- ically
stable solutions generated by purely electric charges whose electric and
magnetic fields are computed as solutions to the Born-Infeld equa- tions. The
approach yields rich internal structures that can be described in terms of the
physical fields with explicit analytic solutions. This suggests that the
anomalous field probably originates from a magnetic excitation in the vacuum
due to the presence of the very intense electric field. In addition, the
magnetic contribution has been found to exert a negative pressure on the
charge. This, in turn, balances the electric repulsion, in such a way that the
self-interaction of the field appears as a simple and natural classical
mechanism that is able to account for the stability of the electron charge.Comment: 8 pages, 1 figur
Non-Hermitian Hamiltonians of Lie algebraic type
We analyse a class of non-Hermitian Hamiltonians, which can be expressed
bilinearly in terms of generators of a sl(2,R)-Lie algebra or their isomorphic
su(1,1)-counterparts. The Hamlitonians are prototypes for solvable models of
Lie algebraic type. Demanding a real spectrum and the existence of a well
defined metric, we systematically investigate the constraints these
requirements impose on the coupling constants of the model and the parameters
in the metric operator. We compute isospectral Hermitian counterparts for some
of the original non-Hermitian Hamiltonian. Alternatively we employ a
generalized Bogoliubov transformation, which allows to compute explicitly real
energy eigenvalue spectra for these type of Hamiltonians, together with their
eigenstates. We compare the two approaches.Comment: 27 page
Thermofield Dynamics for Twisted Poincare-Invariant Field Theories: Wick Theorem and S-matrix
Poincare invariant quantum field theories can be formulated on
non-commutative planes if the statistics of fields is twisted. This is
equivalent to state that the coproduct on the Poincare group is suitably
twisted. In the present work we present a twisted Poincare invariant quantum
field theory at finite temperature. For that we use the formalism of
Thermofield Dynamics (TFD). This TFD formalism is extend to incorporate
interacting fields. This is a non trivial step, since the separation in
positive and negative frequency terms is no longer valid in TFD. In particular,
we prove the validity of Wick's theorem for twisted scalar quantum field at
finite temperature.Comment: v1: 25 pages, no figure v2: references added; typos corrected; typo
in title correcte
Antilinear deformations of Coxeter groups, an application to Calogero models
We construct complex root spaces remaining invariant under antilinear
involutions related to all Coxeter groups. We provide two alternative
constructions: One is based on deformations of factors of the Coxeter element
and the other based on the deformation of the longest element of the Coxeter
group. Motivated by the fact that non-Hermitian Hamiltonians admitting an
antilinear symmetry may be used to define consistent quantum mechanical systems
with real discrete energy spectra, we subsequently employ our constructions to
formulate deformations of Coxeter models remaining invariant under these
extended Coxeter groups. We provide explicit and generic solutions for the
Schroedinger equation of these models for the eigenenergies and corresponding
wavefunctions. A new feature of these novel models is that when compared with
the undeformed case their solutions are usually no longer singular for an
exchange of an amount of particles less than the dimension of the
representation space of the roots. The simultaneous scattering of all particles
in the model leads to anyonic exchange factors for processes which have no
analogue in the undeformed case.Comment: 32 page
Anatomia funcional de Lucina pectinata (Gmelin, 1791) Lucinidae - Bivalvia
A anatomia funcional de Lucina pectinata (Gmelin, 1791) foi estudada neste trabalho tendo sido dada atenção especial à formação do tubo inalante anterior, ao funcionamento do pé, manto, brânquias do manto, ctenídios, palpos labiais e estômago. Observações do comportamento do bivalve e o funcionamento destes órgãos permitiram verificar as adaptações relacionadas à vida em ambientes lodosos de enseadas sem arrebentação, onde existe pequena quantidade de alimento e pouco oxigênio em dissolução. Foiam analisadas a motilidade e atuação do pé, o tamanho dos palpos, ciliação do manto, do músculo adutor anterior, dos ctenídios e a estrutura e funcionamento do estomago. Os sifões são do tipo A (Yonge, 1948), os ctenídios pertencem a um novo tipo: G1, a relação entre os palpos e ctenídios é da categoria m (Stasek, 1963) e o estômago do tipo IV (Purchon, 1958)
PT-symmetry breaking in complex nonlinear wave equations and their deformations
We investigate complex versions of the Korteweg-deVries equations and an Ito
type nonlinear system with two coupled nonlinear fields. We systematically
construct rational, trigonometric/hyperbolic, elliptic and soliton solutions
for these models and focus in particular on physically feasible systems, that
is those with real energies. The reality of the energy is usually attributed to
different realisations of an antilinear symmetry, as for instance PT-symmetry.
It is shown that the symmetry can be spontaneously broken in two alternative
ways either by specific choices of the domain or by manipulating the parameters
in the solutions of the model, thus leading to complex energies. Surprisingly
the reality of the energies can be regained in some cases by a further breaking
of the symmetry on the level of the Hamiltonian. In many examples some of the
fixed points in the complex solution for the field undergo a Hopf bifurcation
in the PT-symmetry breaking process. By employing several different variants of
the symmetries we propose many classes of new invariant extensions of these
models and study their properties. The reduction of some of these models yields
complex quantum mechanical models previously studied.Comment: 50 pages, 39 figures (compressed in order to comply with arXiv
policy; higher resolutions maybe obtained from the authors upon request
- …