103 research outputs found
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
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
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
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
K(E10), Supergravity and Fermions
We study the fermionic extension of the E10/K(E10) coset model and its
relation to eleven-dimensional supergravity. Finite-dimensional spinor
representations of the compact subgroup K(E10) of E(10,R) are studied and the
supergravity equations are rewritten using the resulting algebraic variables.
The canonical bosonic and fermionic constraints are also analysed in this way,
and the compatibility of supersymmetry with local K(E10) is investigated. We
find that all structures involving A9 levels 0,1 and 2 nicely agree with
expectations, and provide many non-trivial consistency checks of the existence
of a supersymmetric extension of the E10/K(E10) coset model, as well as a new
derivation of the `bosonic dictionary' between supergravity and coset
variables. However, there are also definite discrepancies in some terms
involving level 3, which suggest the need for an extension of the model to
infinite-dimensional faithful representations of the fermionic degrees of
freedom.Comment: 50 page
Models with short and long-range interactions: phase diagram and reentrant phase
We study the phase diagram of two different Hamiltonians with competiting
local, nearest-neighbour, and mean-field couplings. The first example
corresponds to the HMF Hamiltonian with an additional short-range interaction.
The second example is a reduced Hamiltonian for dipolar layered spin
structures, with a new feature with respect to the first example, the presence
of anisotropies. The two examples are solved in both the canonical and the
microcanonical ensemble using a combination of the min-max method with the
transfer operator method. The phase diagrams present typical features of
systems with long-range interactions: ensemble inequivalence, negative specific
heat and temperature jumps. Moreover, in a given range of parameters, we report
the signature of phase reentrance. This can also be interpreted as the presence
of azeotropy with the creation of two first order phase transitions with
ensemble inequivalence, as one parameter is varied continuously
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
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)
Embeddings of hyperbolic Kac-Moody algebras into }
We show that the rank 10 hyperbolic Kac-Moody algebra contains every
simply laced hyperbolic Kac-Moody algebra as a Lie subalgebra. Our method is
based on an extension of earlier work of Feingold and Nicolai.Comment: 10 pages. to appear in Letters in Mathematical Physic
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