5,375 research outputs found
Interferometry versus projective measurement of anyons
The distinct methods for measuring topological charge in a non-abelian
anyonic system have been discussed in the literature: projective measurement of
a single point-like quasiparticle and interferometric measurement of the total
topological charge of a group of quasiparticles. Projective measurement by
definition is only applied near a point and will project to a topological
charge sector near that point. Thus, if it is to be applied to a \emph{group}
of anyons to project to a \emph{total} charge, then the anyons must first be
fused one by one to obtain a single anyon carrying the collective charge. We
show that interferometric measurement is strictly stronger: Any protocol
involving projective measurement can be simulated at low overhead by another
protocol involving only interferometric measurement.Comment: 6 pages, 7 figure
Three flavour Quark matter in chiral colour dielectric model
We investigate the properties of quark matter at finite density and
temperature using the nonlinear chiral extension of Colour Dielectric Model
(CCM). Assuming that the square of the meson fields devlop non- zero vacuum
expectation value, the thermodynamic potential for interacting three flavour
matter has been calculated. It is found that remain zero
in the medium whereas changes in the medium. As a result, and
quark masses decrease monotonically as the temperature and density of the quark
matter is increased.In the present model, the deconfinement density and
temperature is found to be lower compared to lattice results. We also study the
behaviour of pressure and energy density above critical temperature.Comment: Latex file. 5 figures available on request. To appear in Phys. Rev.
Hamiltonian lattice QCD at finite chemical potential
At sufficiently high temperature and density, quantum chromodynamics (QCD) is
expected to undergo a phase transition from the confined phase to the
quark-gluon plasma phase. In the Lagrangian lattice formulation the Monte Carlo
method works well for QCD at finite temperature, however, it breaks down at
finite chemical potential. We develop a Hamiltonian approach to lattice QCD at
finite chemical potential and solve it in the case of free quarks and in the
strong coupling limit. At zero temperature, we calculate the vacuum energy,
chiral condensate, quark number density and its susceptibility, as well as mass
of the pseudoscalar, vector mesons and nucleon. We find that the chiral phase
transition is of first order, and the critical chemical potential is (dynamical quark mass at ). This is consistent with
(where is the nucleon mass at ).Comment: Final version appeared in Phys. Rev.
Quantum Fluctuations of Radiation Pressure
Quantum fluctuations of electromagnetic radiation pressure are discussed. We
use an approach based on the quantum stress tensor to calculate the
fluctuations in velocity and position of a mirror subjected to electromagnetic
radiation. Our approach reveals that radiation pressure fluctuations are due to
a cross term between vacuum and state dependent terms in a stress tensor
operator product. Thus observation of these fluctuations would entail
experimental confirmation of this cross term. We first analyze the pressure
fluctuations on a single, perfectly reflecting mirror, and then study the case
of an interferometer. This involves a study of the effects of multiple bounces
in one arm, as well as the correlations of the pressure fluctuations between
arms of the interferometer. In all cases, our results are consistent with those
previously obtained by Caves using different mehods.Comment: 23 pages, 3 figures, RevTe
Quantum Knitting
We analyze the connections between the mathematical theory of knots and
quantum physics by addressing a number of algorithmic questions related to both
knots and braid groups.
Knots can be distinguished by means of `knot invariants', among which the
Jones polynomial plays a prominent role, since it can be associated with
observables in topological quantum field theory.
Although the problem of computing the Jones polynomial is intractable in the
framework of classical complexity theory, it has been recently recognized that
a quantum computer is capable of approximating it in an efficient way. The
quantum algorithms discussed here represent a breakthrough for quantum
computation, since approximating the Jones polynomial is actually a `universal
problem', namely the hardest problem that a quantum computer can efficiently
handle.Comment: 29 pages, 5 figures; to appear in Laser Journa
Holographic Coulomb branch vevs
We compute holographically the vevs of all chiral primary operators for
supergravity solutions corresponding to the Coulomb branch of N=4 SYM and find
exact agreement with the corresponding field theory computation. Using the
dictionary between 10d geometries and field theory developed to extract these
vevs, we propose a gravity dual of a half supersymmetric deformation of N=4 SYM
by certain irrelevant operators.Comment: 16 pages, v2 corrections in appendi
On the stability of two-chunk file-sharing systems
We consider five different peer-to-peer file sharing systems with two chunks,
with the aim of finding chunk selection algorithms that have provably stable
performance with any input rate and assuming non-altruistic peers who leave the
system immediately after downloading the second chunk. We show that many
algorithms that first looked promising lead to unstable or oscillating
behavior. However, we end up with a system with desirable properties. Most of
our rigorous results concern the corresponding deterministic large system
limits, but in two simplest cases we provide proofs for the stochastic systems
also.Comment: 19 pages, 7 figure
The Non-Trapping Degree of Scattering
We consider classical potential scattering. If no orbit is trapped at energy
E, the Hamiltonian dynamics defines an integer-valued topological degree. This
can be calculated explicitly and be used for symbolic dynamics of
multi-obstacle scattering.
If the potential is bounded, then in the non-trapping case the boundary of
Hill's Region is empty or homeomorphic to a sphere.
We consider classical potential scattering. If at energy E no orbit is
trapped, the Hamiltonian dynamics defines an integer-valued topological degree
deg(E) < 2. This is calculated explicitly for all potentials, and exactly the
integers < 2 are shown to occur for suitable potentials.
The non-trapping condition is restrictive in the sense that for a bounded
potential it is shown to imply that the boundary of Hill's Region in
configuration space is either empty or homeomorphic to a sphere.
However, in many situations one can decompose a potential into a sum of
non-trapping potentials with non-trivial degree and embed symbolic dynamics of
multi-obstacle scattering. This comprises a large number of earlier results,
obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more
detailed proofs and remark
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