106 research outputs found
Time Evolution of Unstable Particle Decay Seen with Finite Resolution
Time evolution of the decay process of unstable particles is investigated in
field theory models. We first formulate how to renormalize the non-decay
amplitude beyond perturbation theory and then discuss short-time behavior of
very long-lived particles. Two different formalisms, one that does and one that
does not, assume existence of the asymptotic field of unstable particles are
considered. The non-decay amplitude is then calculated by introducing a finite
time resolution of measurement, which makes it possible to discuss both
renormalizable and non-renormalizable decay interaction including the nucleon
decay. In ordinary circumstances the onset of the exponential decay law starts
at times as early as at roughly the resolution time, but with an enhanced
amplitude which may be measurable. It is confirmed that the short-time formula
of the exponential decay law may be used to set limits on the
nucleon decay rate in underground experiments. On the other hand, an
exceptional example of S-wave decay of very small Q-value is found, which does
not have the exponential period at all.Comment: 26 pages, LATEX file with 8 PS figure
Faraday rotation in graphene
We study magneto--optical properties of monolayer graphene by means of
quantum field theory methods in the framework of the Dirac model. We reveal a
good agreement between the Dirac model and a recent experiment on giant Faraday
rotation in cyclotron resonance. We also predict other regimes when the effects
are well pronounced. The general dependence of the Faraday rotation and
absorption on various parameters of samples is revealed both for suspended and
epitaxial graphene.Comment: 10 pp; v2: typos corrected and references added, v3, v4: small
changes and more reference
Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
A recent conjecture regarding the average of the minimum eigenvalue of the
reduced density matrix of a random complex state is proved. In fact, the full
distribution of the minimum eigenvalue is derived exactly for both the cases of
a random real and a random complex state. Our results are relevant to the
entanglement properties of eigenvectors of the orthogonal and unitary ensembles
of random matrix theory and quantum chaotic systems. They also provide a rare
exactly solvable case for the distribution of the minimum of a set of N {\em
strongly correlated} random variables for all values of N (and not just for
large N).Comment: 13 pages, 2 figures included; typos corrected; to appear in J. Stat.
Phy
The relativistic Sagnac Effect: two derivations
The phase shift due to the Sagnac Effect, for relativistic matter and
electromagnetic beams, counter-propagating in a rotating interferometer, is
deduced using two different approaches. From one hand, we show that the
relativistic law of velocity addition leads to the well known Sagnac time
difference, which is the same independently of the physical nature of the
interfering beams, evidencing in this way the universality of the effect.
Another derivation is based on a formal analogy with the phase shift induced by
the magnetic potential for charged particles travelling in a region where a
constant vector potential is present: this is the so called Aharonov-Bohm
effect. Both derivations are carried out in a fully relativistic context, using
a suitable 1+3 splitting that allows us to recognize and define the space where
electromagnetic and matter waves propagate: this is an extended 3-space, which
we call "relative space". It is recognized as the only space having an actual
physical meaning from an operational point of view, and it is identified as the
'physical space of the rotating platform': the geometry of this space turns out
to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor
corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and
M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also
http://digilander.libero.it/solciclo
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