99 research outputs found
Phase space gaps and ergodicity breaking in systems with long range interactions
We study a generalized isotropic XY-model which includes both two-spin and
four-spin mean-field interactions. This model can be solved in the
microcanonical ensemble. It is shown that in certain parameter regions the
model exhibits gaps in the magnetization at fixed energy, resulting in
ergodicity breaking. This phenomenon has previously been reported in
anisotropic and discrete spin models. The entropy of the model is calculated
and the microcanonical phase diagram is derived, showing the existence of first
order phase transitions from the ferromagnetic to a paramagnetic disordered
phase. It is found that ergodicity breaking takes place both in the
ferromagnetic and the paramagnetic phases. As a consequence, the system can
exhibit a stable ferromagnetic phase within the paramagnetic region, and
conversely a disordered phase within the magnetically ordered region
Hyperbolic Kac Moody Algebras and Einstein Billiards
We identify the hyperbolic Kac Moody algebras for which there exists a
Lagrangian of gravity, dilatons and -forms which produces a billiard that
can be identified with their fundamental Weyl chamber. Because of the
invariance of the billiard upon toroidal dimensional reduction, the list of
admissible algebras is determined by the existence of a Lagrangian in three
space-time dimensions, where a systematic analysis can be carried out since
only zero-forms are involved. We provide all highest dimensional parent
Lagrangians with their full spectrum of -forms and dilaton couplings. We
confirm, in particular, that for the rank 10 hyperbolic algebra, , also known as the dual of , the
maximally oxidized Lagrangian is 9 dimensional and involves besides gravity, 2
dilatons, a 2-form, a 1-form and a 0-form.Comment: 33 page
Phase transitions of quasistationary states in the Hamiltonian Mean Field model
The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is
studied in presence of an externally imposed magnetic field h. Lynden-Bell's
theory of violent relaxation is revisited and shown to adequately capture the
system dynamics, as revealed by direct Vlasov based numerical simulations in
the limit of vanishing field. This includes the existence of an
out-of-equilibrium phase transition separating magnetized and non magnetized
phases. We also monitor the fluctuations in time of the magnetization, which
allows us to elaborate on the choice of the correct order parameter when
challenging the performance of Lynden-Bell's theory. The presence of the field
h removes the phase transition, as it happens at equilibrium. Moreover, regions
with negative susceptibility are numerically found to occur, in agreement with
the predictions of the theory.Comment: 6 pages, 7 figure
Long-Range Effects in Layered Spin Structures
We study theoretically layered spin systems where long-range dipolar
interactions play a relevant role. By choosing a specific sample shape, we are
able to reduce the complex Hamiltonian of the system to that of a much simpler
coupled rotator model with short-range and mean-field interactions. This latter
model has been studied in the past because of its interesting dynamical and
statistical properties related to exotic features of long-range interactions.
It is suggested that experiments could be conducted such that within a specific
temperature range the presence of long-range interactions crucially affect the
behavior of the system
E10 and SO(9,9) invariant supergravity
We show that (massive) D=10 type IIA supergravity possesses a hidden rigid
SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional
reduction to one (time-like) dimension. We explicitly construct the associated
locally supersymmetric Lagrangian in one dimension, and show that its bosonic
sector, including the mass term, can be equivalently described by a truncation
of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a
decomposition of E10 under its so(9,9) subalgebra. This decomposition is
presented up to level 10, and the even and odd level sectors are identified
tentatively with the Neveu--Schwarz and Ramond sectors, respectively. Further
truncation to the level \ell=0 sector yields a model related to the reduction
of D=10 type I supergravity. The hyperbolic Kac--Moody algebra DE10, associated
to the latter, is shown to be a proper subalgebra of E10, in accord with the
embedding of type I into type IIA supergravity. The corresponding decomposition
of DE10 under so(9,9) is presented up to level 5.Comment: 1+39 pages LaTeX2e, 2 figures, 2 tables, extended tables obtainable
by downloading sourc
Experimental perspectives for systems based on long-range interactions
The possibility of observing phenomena peculiar to long-range interactions,
and more specifically in the so-called Quasi-Stationary State (QSS) regime is
investigated within the framework of two devices, namely the Free-Electron
Laser (FEL) and the Collective Atomic Recoil Laser (CARL). The QSS dynamics has
been mostly studied using the Hamiltonian Mean-Field (HMF) toy model,
demonstrating in particular the presence of first versus second order phase
transitions from magnetized to unmagnetized regimes in the case of HMF. Here,
we give evidence of the strong connections between the HMF model and the
dynamics of the two mentioned devices, and we discuss the perspectives to
observe some specific QSS features experimentally. In particular, a dynamical
analog of the phase transition is present in the FEL and in the CARL in its
conservative regime. Regarding the dissipative CARL, a formal link is
established with the HMF model. For both FEL and CARL, calculations are
performed with reference to existing experimental devices, namely the
FERMI@Elettra FEL under construction at Sincrotrone Trieste (Italy) and the
CARL system at LENS in Florence (Italy)
On the effectiveness of mixing in violent relaxation
Relaxation processes in collisionless dynamics lead to peculiar behavior in
systems with long-range interactions such as self-gravitating systems,
non-neutral plasmas and wave-particle systems. These systems, adequately
described by the Vlasov equation, present quasi-stationary states (QSS), i.e.
long lasting intermediate stages of the dynamics that occur after a short
significant evolution called "violent relaxation". The nature of the
relaxation, in the absence of collisions, is not yet fully understood. We
demonstrate in this article the occurrence of stretching and folding behavior
in numerical simulations of the Vlasov equation, providing a plausible
relaxation mechanism that brings the system from its initial condition into the
QSS regime. Area-preserving discrete-time maps with a mean-field coupling term
are found to display a similar behaviour in phase space as the Vlasov system.Comment: 10 pages, 11 figure
Describing general cosmological singularities in Iwasawa variables
Belinskii, Khalatnikov, and Lifshitz (BKL) conjectured that the description
of the asymptotic behavior of a generic solution of Einstein equations near a
spacelike singularity could be drastically simplified by considering that the
time derivatives of the metric asymptotically dominate (except at a sequence of
instants, in the `chaotic case') over the spatial derivatives. We present a
precise formulation of the BKL conjecture (in the chaotic case) that consists
of basically three elements: (i) we parametrize the spatial metric by
means of \it{Iwasawa variables} ); (ii) we define, at
each spatial point, a (chaotic) \it{asymptotic evolution system} made of
ordinary differential equations for the Iwasawa variables; and (iii) we
characterize the exact Einstein solutions whose asymptotic
behavior is described by a solution of the
previous evolution system by means of a `\it{generalized Fuchsian system}' for
the differenced variables , , and by requiring that and tend to zero on the singularity. We also show that, in spite of the
apparently chaotic infinite succession of `Kasner epochs' near the singularity,
there exists a well-defined \it{asymptotic geometrical structure} on the
singularity : it is described by a \it{partially framed flag}. Our treatment
encompasses Einstein-matter systems (comprising scalar and p-forms), and also
shows how the use of Iwasawa variables can simplify the usual (`asymptotically
velocity term dominated') description of non-chaotic systems.Comment: 50 pages, 4 figure
Pure type I supergravity and DE(10)
We establish a dynamical equivalence between the bosonic part of pure type I
supergravity in D=10 and a D=1 non-linear sigma-model on the Kac-Moody coset
space DE(10)/K(DE(10)) if both theories are suitably truncated. To this end we
make use of a decomposition of DE(10) under its regular SO(9,9) subgroup. Our
analysis also deals partly with the fermionic fields of the supergravity theory
and we define corresponding representations of the generalized spatial Lorentz
group K(DE(10)).Comment: 28 page
Solitons in Five Dimensional Minimal Supergravity: Local Charge, Exotic Ergoregions, and Violations of the BPS Bound
We describe a number of striking features of a class of smooth solitons in
gauged and ungauged minimal supergravity in five dimensions. The solitons are
globally asymptotically flat or asymptotically AdS without any Kaluza-Klein
directions but contain a minimal sphere formed when a cycle pinches off in the
interior of the spacetime. The solutions carry a local magnetic charge and many
have rather unusual ergosurfaces. Perhaps most strikingly, many of the solitons
have more electric charge or, in the asymptotically AdS case, more electric
charge and angular momentum than is allowed by the usual BPS bound. We comment
on, but do not resolve, the new puzzle this raises for AdS/CFT.Comment: 60 pages, 12 figures, 3 table
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