133 research outputs found
Quantum mechanics on non commutative spaces and squeezed states: a functional approach
We review here the quantum mechanics of some noncommutative theories in which
no state saturates simultaneously all the non trivial Heisenberg uncertainty
relations. We show how the difference of structure between the Poisson brackets
and the commutators in these theories generically leads to a harmonic
oscillator whose positions and momenta mean values are not strictly equal to
the ones predicted by classical mechanics.
This raises the question of the nature of quasi classical states in these
models. We propose an extension based on a variational principle. The action
considered is the sum of the absolute values of the expressions associated to
the non trivial Heisenberg uncertainty relations. We first verify that our
proposal works in the usual theory i.e we recover the known Gaussian functions.
Besides them, we find other states which can be expressed as products of
Gaussians with specific hyper geometrics.
We illustrate our construction in two models defined on a four dimensional
phase space: a model endowed with a minimal length uncertainty and the non
commutative plane. Our proposal leads to second order partial differential
equations. We find analytical solutions in specific cases. We briefly discuss
how our proposal may be applied to the fuzzy sphere and analyze its
shortcomings.Comment: 15 pages revtex. The title has been modified,the paper shortened and
misprints have been corrected. Version to appear in JHE
The critical end point in QCD
In this talk I present the logic behind, and examine the reliability of,
estimates of the critical end point (CEP) of QCD using the Taylor expansion
method.Comment: Plenary talk at SEWM 06 by S
Entanglement in quantum catastrophes
We classify entanglement singularities for various two-mode bosonic systems
in terms of catastrophe theory. Employing an abstract phase-space
representation, we obtain exact results in limiting cases for the entropy in
cusp, butterfly, and two-dimensional catastrophes. We furthermore use numerical
results to extract the scaling of the entropy with the non-linearity parameter,
and discuss the role of mixing entropies in more complex systems.Comment: 7 pages, 3 figure
Linear Statistics of Non-Hermitian Matrices Matching the Real or Complex Ginibre Ensemble to Four Moments
We prove that, for general test functions, the limiting behavior of the
linear statistic of an independent entry random matrix is determined only by
the first four moments of the entry distributions. This immediately generalizes
the known central limit theorem for independent entry matrices with complex
normal entries. We also establish two central limit theorems for matrices with
real normal entries, considering separately functions supported exclusively on
and exclusively away from the real line. In contrast to previously obtained
results in this area, we do not impose analyticity on test functions.Comment: Preliminary versio
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