853 research outputs found
Asymptotics and local constancy of characters of p-adic groups
In this paper we study quantitative aspects of trace characters
of reductive -adic groups when the representation varies. Our approach
is based on the local constancy of characters and we survey some other related
results. We formulate a conjecture on the behavior of relative to
the formal degree of , which we are able to prove in the case where
is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the
structure of Moy-Prasad subgroups.Comment: Proceedings of Simons symposium on the trace formul
Gravitational anomalies in a dispersive approach
The gravitational anomalies in two dimensions, specifically the Einstein
anomaly and the Weyl anomaly, are fully determined by means of dispersion
relations. In this approach the anomalies originate from the peculiar infrared
feature of the imaginary part of the relevant formfactor which approaches a
-function singularity at zero momentum squared when .Comment: 10 page
Decoherence of entangled kaons and its connection to entanglement measures
We study the time evolution of the entangled kaon system by considering the
Liouville - von Neumann equation with an additional term which allows for
decoherence. We choose as generators of decoherence the projectors to the
2-particle eigenstates of the Hamiltonian. Then we compare this model with the
data of the CPLEAR experiment and find in this way an upper bound on the
strength of the decoherence. We also relate to an effective
decoherence parameter considered previously in literature. Finally we
discuss our model in the light of different measures of entanglement, i.e. the
von Neumann entropy , the entanglement of formation and the concurrence
, and we relate the decoherence parameter to the loss of
entanglement: .Comment: comments and references added, 18 pages, 1 figur
Heisenberg's Uncertainty Relation and Bell Inequalities in High Energy Physics
An effective formalism is developed to handle decaying two-state systems.
Herewith, observables of such systems can be described by a single operator in
the Heisenberg picture. This allows for using the usual framework in quantum
information theory and, hence, to enlighten the quantum feature of such systems
compared to non-decaying systems. We apply it to systems in high energy
physics, i.e. to oscillating meson-antimeson systems. In particular, we discuss
the entropic Heisenberg uncertainty relation for observables measured at
different times at accelerator facilities including the effect of CP violation,
i.e. the imbalance of matter and antimatter. An operator-form of Bell
inequalities for systems in high energy physics is presented, i.e. a
Bell-witness operator, which allows for simple analysis of unstable systems.Comment: 17 page
Dissipation in a 2-dimensional Hilbert space: Various forms of complete positivity
We consider the time evolution of the density matrix in a
2-dimensional complex Hilbert space. We allow for dissipation by adding to the
von Neumann equation a term , which is of Lindblad type in order to
assure complete positivity of the time evolution. We present five equivalent
forms of . In particular, we connect the familiar dissipation matrix
with a geometric version of , where consists of a positive sum
of projectors onto planes in . We also study the minimal number
of Lindblad terms needed to describe the most general case of . All
proofs are worked out comprehensively, as they present at the same time a
practical procedure how to determine explicitly the different forms of
. Finally, we perform a general discussion of the asymptotic behaviour
of the density matrix and we relate the two types of asymptotic
behaviour with our geometric version of .Comment: 11 pages, LaTeX, no figures. Further aspects of complete positivity
worked out and references added; version accepted for publication in Phys.
Lett.
Search for the decay in the momentum region
We have searched for the decay in the kinematic
region with pion momentum below the peak. One event was
observed, consistent with the background estimate of . This
implies an upper limit on
(90% C.L.), consistent with the recently measured branching ratio of
, obtained using the standard model
spectrum and the kinematic region above the peak. The
same data were used to search for , where is a weakly
interacting neutral particle or system of particles with .Comment: 4 pages, 2 figure
The effect of spontaneous collapses on neutrino oscillations
We compute the effect of collapse models on neutrino oscillations. The effect
of the collapse is to modify the evolution of the `spatial' part of the wave
function, which indirectly amounts to a change on the flavor components. In
many respects, this phenomenon is similar to neutrino propagation through
matter. For the analysis we use the mass proportional CSL model, and perform
the calculation to second order perturbation theory. As we will show, the CSL
prediction is very small - mainly due to the very small mass of neutrinos - and
practically undetectable.Comment: 24 pages, RevTeX. Updated versio
New nonrenormalization theorems for anomalous three point functions
Nonrenormalization theorems involving the transverse, i.e. non anomalous,
part of the correlator in perturbative QCD are proven. Some of their
consequences and questions they raise are discussed.Comment: 14 pages. People added in the acknowledgements. Minor changes to
match version to appear in journa
Chiral Symmetry and Diffractive Neutral Pion Photo- and Electroproduction
We show that diffractive production of a single neutral pion in
photon-induced reactions at high energy is dynamically suppressed due to the
approximate chiral symmetry of QCD. These reactions have been proposed as a
test of the odderon exchange mechanism. We show that the odderon contribution
to the amplitude for such reactions vanishes exactly in the chiral limit. This
result is obtained in a nonperturbative framework and by using PCAC relations
between the amplitudes for neutral pion and axial vector current production.Comment: 22 pages, 7 figure
Entanglement, Bell Inequalities and Decoherence in Particle Physics
We demonstrate the relevance of entanglement, Bell inequalities and
decoherence in particle physics. In particular, we study in detail the features
of the ``strange'' system as an example of entangled
meson--antimeson systems. The analogies and differences to entangled spin--1/2
or photon systems are worked, the effects of a unitary time evolution of the
meson system is demonstrated explicitly. After an introduction we present
several types of Bell inequalities and show a remarkable connection to CP
violation. We investigate the stability of entangled quantum systems pursuing
the question how possible decoherence might arise due to the interaction of the
system with its ``environment''. The decoherence is strikingly connected to the
entanglement loss of common entanglement measures. Finally, some outlook of the
field is presented.Comment: Lectures given at Quantum Coherence in Matter: from Quarks to Solids,
42. Internationale Universit\"atswochen f\"ur Theoretische Physik,
Schladming, Austria, Feb. 28 -- March 6, 2004, submitted to Lecture Notes in
Physics, Springer Verlag, 45 page
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