20,203 research outputs found
Finite Controllability of Infinite-Dimensional Quantum Systems
Quantum phenomena of interest in connection with applications to computation
and communication almost always involve generating specific transfers between
eigenstates, and their linear superpositions. For some quantum systems, such as
spin systems, the quantum evolution equation (the Schr\"{o}dinger equation) is
finite-dimensional and old results on controllability of systems defined on on
Lie groups and quotient spaces provide most of what is needed insofar as
controllability of non-dissipative systems is concerned. However, in an
infinite-dimensional setting, controlling the evolution of quantum systems
often presents difficulties, both conceptual and technical. In this paper we
present a systematic approach to a class of such problems for which it is
possible to avoid some of the technical issues. In particular, we analyze
controllability for infinite-dimensional bilinear systems under assumptions
that make controllability possible using trajectories lying in a nested family
of pre-defined subspaces. This result, which we call the Finite Controllability
Theorem, provides a set of sufficient conditions for controllability in an
infinite-dimensional setting. We consider specific physical systems that are of
interest for quantum computing, and provide insights into the types of quantum
operations (gates) that may be developed.Comment: This is a much improved version of the paper first submitted to the
arxiv in 2006 that has been under review since 2005. A shortened version of
this paper has been conditionally accepted for publication in IEEE
Transactions in Automatic Control (2009
Detection of Spiral photons in Quantum Optics
We show that a new type of photon detector, sensitive to the gradients of
electromagnetic fields, should be a useful tool to characterize the quantum
properties of spatially-dependent optical fields. As a simple detector of such
a kind, we propose using magnetic dipole or electric quadrupole transitions in
atoms or molecules and apply it to the detection of spiral photons in
Laguerre-Gauss (LG) beams. We show that LG beams are not true hollow beams, due
to the presence of magnetic fields and gradients of electric fields on beam
axis. This approach paves the way to an analysis at the quantum level of the
spatial structure and angular momentum properties of singular light beams.Comment: 5 pages, 4 figure
Phase diagram and critical properties in the Polyakov--Nambu--Jona-Lasinio model
We investigate the phase diagram of the so-called
Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical
potential with three quark flavours. Chiral and deconfinement phase transitions
are discussed, and the relevant order-like parameters are analyzed. The results
are compared with simple thermodynamic expectations and lattice data. A special
attention is payed to the critical end point: as the strength of the
flavour-mixing interaction becomes weaker, the critical end point moves to low
temperatures and can even disappear.Comment: Talk given at the 9th International Conference on Quark Confinement
and the Hadron Spectrum - QCHS IX, Madrid, Spain, 30 August - September 201
K -> pi pi and a light scalar meson
We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi
transitions using a Dyson-Schwinger equation model. Exploiting the feature that
QCD penguin operators direct K^0_S transitions through 0^{++} intermediate
states, we find an explanation of the enhancement of I=0 K -> pi pi transitions
in the contribution of a light sigma-meson. This mechanism also affects
epsilon'/epsilon.Comment: 7 pages, REVTE
A new Bloch period for interacting cold atoms in 1D optical lattices
The paper studies Bloch oscillations of ultracold atoms in optical lattice in
the presence of atom-atom interaction. A new, interaction-induced Bloch period
is identified. The analytical results are corroborated by realistic numerical
calculations.Comment: revtex4, 4 pages, 4 figures, gzipped tar fil
Numerical cancellation of photon quadratic divergence in the study of the Schwinger-Dyson equations in Strong Coupling QED
The behaviour of the photon renormalization function in strong coupling QED
has been recently studied by Kondo, Mino and Nakatani. We find that the sharp
decrease in its behaviour at intermediate photon momenta is an artefact of the
method used to remove the quadratic divergence in the vacuum polarization. We
discuss how this can be avoided in numerical studies of the Schwinger-Dyson
equations.Comment: 9 pages, Latex, 5 figures. Complete postscript file available from:
ftp://cpt1.dur.ac.uk/pub/preprints/dtp94/dtp94100/dtp94100.p
- …