Quantum mechanics on the noncommutative plane and sphere

We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density of states becomes infinite, for the value of the magnetic field equal to the inverse of the noncommutativity parameter. The Landau problem on the noncommutative two-sphere is also solved and compared to the plane problem.Comment: 12 pages, no figures; references adde

Identification of circles from datapoints using Gaussian sums

We present a pattern recognition method which use datapoints on a plane and estimates the parameters of a circle. MC data are generated in order to test the method's efficiency over noise hits, uncertainty in the hits positions and number of datapoints. The scenario were the hits from a quadrant of the circle are missing is also considered. The method proposed is proven to be robust, accurate and very efficient.Comment: 4 pages, 5 figure

Two-dimensional Born-Infeld gauge theory: spectrum, string picture and large-N phase transition

We analyze U(N) Born-Infeld gauge theory in two spacetime dimensions. We derive the exact energy spectrum on the circle and show that it reduces to N relativistic fermions on a dual space. This contrasts to the Yang-Mills case that reduces to nonrelativistic fermions. The theory admits a string theory interpretation, analogous to the one for ordinary Yang-Mills, but with higher order string interactions. We also demonstrate that the partition function on the sphere exhibits a large-N phase transition in the area and calculate the critical area. The limit in which the dimensionless coupling of the theory goes to zero corresponds to massless fermions, admits a perturbatively exact free string interpretation and exhibits no phase transition.Comment: 19 page

On the Lieb-Liniger model in the infinite coupling constant limit

We consider the one-dimensional Lieb-Liniger model (bosons interacting via 2-body delta potentials) in the infinite coupling constant limit (the so-called Tonks-Girardeau model). This model might be relevant as a description of atomic Bose gases confined in a one-dimensional geometry. It is known to have a fermionic spectrum since the N-body wavefunctions have to vanish at coinciding points, and therefore be symmetrizations of fermionic Slater wavefunctions. We argue that in the infinite coupling constant limit the model is indistinguishable from free fermions, i.e., all physically accessible observables are the same as those of free fermions. Therefore, Bose-Einstein condensate experiments at finite energy that preserve the one-dimensional geometry cannot test any bosonic characteristic of such a model

On Level Quantization for the Noncommutative Chern-Simons Theory

We show that the coefficient of the three-dimensional Chern-Simons action on the noncommutative plane must be quantized. Similar considerations apply in other dimensions as well.Comment: 6 pages, Latex, no figure

Fuzzy spaces and new random matrix ensembles

We analyze the expectation value of observables in a scalar theory on the fuzzy two sphere, represented as a generalized hermitian matrix model. We calculate explicitly the form of the expectation values in the large-N limit and demonstrate that, for any single kind of field (matrix), the distribution of its eigenvalues is still a Wigner semicircle but with a renormalized radius. For observables involving more than one type of matrix we obtain a new distribution corresponding to correlated Wigner semicircles.Comment: 12 pages, 1 figure; version to appear in Phys. Rev.

A spark-resistant bulk-micromegas chamber for high-rate applications

We report on the design and performance of a spark-resistant bulk-micromegas chamber. The principle of this design lends itself to the construction of large-area muon chambers for the upgrade of the detectors at the Large Hadron Collider at CERN for luminosities in excess of 10**34/cm2/s or other high-rate applications.Comment: 12 pages, 13 figure

Inhomogeneous Condensates in Planar QED

We study the formation of vacuum condensates in $2+1$ dimensional QED in the presence of inhomogeneous background magnetic fields. For a large class of magnetic fields, the condensate is shown to be proportional to the inhomogeneous magnetic field, in the large flux limit. This may be viewed as a {\it local} form of the {\it integrated} degeneracy-flux relation of Aharonov and Casher.Comment: 13 pp, LaTeX, no figures; to appear in Phys. Rev.