82 research outputs found
Self-propulsion through symmetry breaking
In addition to self-propulsion by phoretic mechanisms that arises from an
asymmetric distribution of reactive species around a catalytic motor, spherical
particles with a uniform distribution of catalytic activity may also propel
themselves under suitable conditions. Reactive fluctuation-induced asymmetry
can give rise to transient concentration gradients which may persist under
certain conditions, giving rise to a bifurcation to self-propulsion. The nature
of this phenomenon is analyzed in detail, and particle-level simulations are
carried out to demonstrate its existence.Comment: 6 pages, 3 figures. Appeared in EPL (Europhysics Letters
Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point
Chiral gravity admits asymptotically AdS3 solutions that are not locally
equivalent to AdS3; meaning that solutions do exist which, while obeying the
strong boundary conditions usually imposed in General Relativity, happen not to
be Einstein spaces. In Topologically Massive Gravity (TMG), the existence of
non-Einstein solutions is particularly connected to the question about the role
played by complex saddle points in the Euclidean path integral. Consequently,
studying (the existence of) non-locally AdS3 solutions to chiral gravity is
relevant to understand the quantum theory. Here, we discuss a special family of
non-locally AdS3 solutions to chiral gravity. In particular, we show that such
solutions persist when one deforms the theory by adding the higher-curvature
terms of the so-called New Massive Gravity (NMG). Moreover, the addition of
higher-curvature terms to the gravity action introduces new non-locally AdS3
solutions that have no analogues in TMG. Both stationary and time-dependent,
axially symmetric solutions that asymptote AdS3 space without being locally
equivalent to it appear. Defining the boundary stress-tensor for the full
theory, we show that these non-Einstein geometries have associated vanishing
conserved charges.Comment: 8 pages. v2 minor typos correcte
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
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)
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
Non-Einstein geometries in Chiral Gravity
We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive
Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on
non-Einstein metrics. A class of such solutions admits curvature singularities
in the interior which are reflected as singularities or infinite bulk energy of
the corresponding linear solutions. A non-linear solution is found exactly. The
back-reaction induces a repulsion of geodesics and a shielding of the
singularity by an event horizon but also introduces closed timelike curves.Comment: 11 pages, 3 figures. v2: references and comments on linear stability
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