374 research outputs found
Arguments towards the construction of a matrix model groundstate
We discuss the existence and uniqueness of wavefunctions for inhomogenoeus
boundary value problems associated to x^2y^2-type matrix model on a bounded
domain of R^2. Both properties involve a combination of the Cauchy-Kovalewski
Theorem and a explicit calculations.Comment: 3 pages, Latex Proceedings for the XIX Simposio Chileno de Fisica,
SOCHIFI 2014 Conference, 26-28 November 2014, held at Concepcion U., Chil
On the groundstate of octonionic matrix models in a ball
In this work we examine the existence and uniqueness of the groundstate of a
SU(N)x G2 octonionic matrix model on a bounded domain of R^N. The existence and
uniqueness argument of the groundstate wavefunction follows from the
Lax-Milgram theorem. Uniqueness is shown by means of an explicit argument which
is drafted in some detail.Comment: Latex, 6 page
The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition
The spectrum of the bosonic sector of the D=11 supermembrane with central
charges is shown to be discrete and with finite multiplicities, hence
containing a mass gap. The result extends to the exact theory our previous
proof of the similar property for the SU(N) regularised model and strongly
suggest discreteness of the spectrum for the complete Hamiltonian of the
supermembrane with central charges. This theory is a quantum equivalent to a
symplectic non-commutative super-Yang-Mills in 2+1 dimensions, where the
space-like sector is a Riemann surface of positive genus. In this context, it
is argued how the theory in 4D exhibits confinement in the N=1 supermembrane
with central charges phase and how the theory enters in the quark-gluon plasma
phase through the spontaneous breaking of the centre. This phase is interpreted
in terms of the compactified supermembrane without central charges.Comment: 33 pages, Latex. In this new version, several changes have been made
and various typos were correcte
Massless ground state for a compact SU(2) matrix model in 4D
We show the existence and uniqueness of a massless supersymmetric ground
state wavefunction of a SU(2) matrix model in a bounded smooth domain with
Dirichlet boundary conditions. This is a gauge system and we provide a new
framework to analyze the quantum spectral properties of this class of
supersymmetric matrix models subject to constraints which can be generalized
for arbitrary number of colors.Comment: 12 pages, Latex. Somme clarifications. Minor changes. Version to
appear at NP
The ground state of the D=11 supermembrane and matrix models on compact regions
We establish a general framework for the analysis of boundary value problems
of matrix models at zero energy on compact regions. We derive existence and
uniqueness of ground state wavefunctions for the mass operator of the
regularized supermembrane theory, that is the supersymmetric
matrix model, on balls of finite radius. Our results rely on the
structure of the associated Dirichlet form and a factorization in terms of the
supersymmetric charges. They also rely on the polynomial structure of the
potential and various other supersymmetric properties of the system.Comment: Latex, 26 pages. We have added some comments at the introduction in
order to make it easier for the reader. Results of the paper unchange
On the spectrum of a matrix model for the D=11 supermembrane compactified on a torus with non-trivial winding
The spectrum of the Hamiltonian of the double compactified D=11 supermembrane
with non-trivial central charge or equivalently the non-commutative symplectic
super Maxwell theory is analyzed. In distinction to what occurs for the D=11
supermembrane in Minkowski target space where the bosonic potential presents
string-like spikes which render the spectrum of the supersymmetric model
continuous, we prove that the potential of the bosonic compactified membrane
with non-trivial central charge is strictly positive definite and becomes
infinity in all directions when the norm of the configuration space goes to
infinity. This ensures that the resolvent of the bosonic Hamiltonian is
compact. We find an upper bound for the asymptotic distribution of the
eigenvalues.Comment: 11 pages, LaTe
Intrinsic Moment of Inertia of Membranes as bounds for the mass gap of Yang-Mills Theories
We obtain the precise condition on the potentials of Yang-Mills theories in
0+1 dimensions and D0 brane quantum mechanics ensuring the discretness of the
spectrum. It is given in terms of a moment of inertia of the membrane. From it
we obtain a bound for the mass gap of any D+1 Yang-Mills theory in the
slow-mode regime. In particular we analyze the physical case D=3. The quantum
mechanical behavior of the theories, concerning its spectrum, is determined by
harmonic oscillators with frequencies given by the inertial tensor of the
membrane. We find a class of quantum mechanic potential polynomials of any
degree, with classical instabilities that at quantum level have purely discrete
spectrum.Comment: 12pages, Latex, minor changes, more explanatory comment
A minor-merger origin for inner disks and rings in early-type galaxies
Nuclear disks and rings are frequent galaxy substructures, for a wide range
of morphological types (from S0 to Sc). We have investigated the possible
minor-merger origin of inner disks and rings in spiral galaxies through
collisionless N-body simulations. The models confirm that minor mergers can
drive the formation of thin, kinematically-cold structures in the center of
galaxies out of satellite material, without requiring the previous formation of
a bar. Satellite core particles tend to be deposited in circular orbits in the
central potential, due to the strong circularization experienced by the
satellite orbit through dynamical friction. The material of the satellite core
reaches the remnant center if satellites are dense or massive, building up a
thin inner disk; whereas it is fully disrupted before reaching the center in
the case of low-mass satellites, creating an inner ring instead.Comment: 2 pages, 2 figures, Proceedings of the conference "Hunting for the
Dark: The Hidden Side of Galaxy Formation", held in Malta, 19-23 Oct. 2009,
ed. V. Debattista and C. C. Popescu, AIP Conf. Ser., in pres
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