17,655 research outputs found
Cyclic Statistics In Three Dimensions
While 2-dimensional quantum systems are known to exhibit non-permutation,
braid group statistics, it is widely expected that quantum statistics in
3-dimensions is solely determined by representations of the permutation group.
This expectation is false for certain 3-dimensional systems, as was shown by
the authors of ref. [1,2,3]. In this work we demonstrate the existence of
``cyclic'', or , {\it non-permutation group} statistics for a system of n
> 2 identical, unknotted rings embedded in . We make crucial use of a
theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch
relations for the automorphisms of the free product group on n elements.Comment: 13 pages, 1 figure, LaTex, minor page reformattin
Protected Qubits and Chern Simons theories in Josephson Junction Arrays
We present general symmetry arguments that show the appearance of doubly
denerate states protected from external perturbations in a wide class of
Hamiltonians. We construct the simplest spin Hamiltonian belonging to this
class and study its properties both analytically and numerically. We find that
this model generally has a number of low energy modes which might destroy the
protection in the thermodynamic limit. These modes are qualitatively different
from the usual gapless excitations as their number scales as the linear size
(instead of volume) of the system. We show that the Hamiltonians with this
symmetry can be physically implemented in Josephson junction arrays and that in
these arrays one can eliminate the low energy modes with a proper boundary
condition. We argue that these arrays provide fault tolerant quantum bits.
Further we show that the simplest spin model with this symmetry can be mapped
to a very special Z_2 Chern-Simons model on the square lattice. We argue that
appearance of the low energy modes and the protected degeneracy is a natural
property of lattice Chern-Simons theories. Finally, we discuss a general
formalism for the construction of discrete Chern-Simons theories on a lattice.Comment: 20 pages, 7 figure
Diffusive spin transport
Information to be stored and transported requires physical carriers. The
quantum bit of information (qubit) can for instance be realised as the spin 1/2
degree of freedom of a massive particle like an electron or as the spin 1
polarisation of a massless photon. In this lecture, I first use irreducible
representations of the rotation group to characterise the spin dynamics in a
least redundant manner. Specifically, I describe the decoherence dynamics of an
arbitrary spin S coupled to a randomly fluctuating magnetic field in the
Liouville space formalism. Secondly, I discuss the diffusive dynamics of the
particle's position in space due to the presence of randomly placed impurities.
Combining these two dynamics yields a coherent, unified picture of diffusive
spin transport, as applicable to mesoscopic electronic devices or photons
propagating in cold atomic clouds.Comment: Lecture notes, published in A. Buchleitner, C. Viviescas, and M.
Tiersch (Eds.), "Entanglement and Decoherence. Foundations and Modern
Trends", Lecture Notes in Physics 768, Springer, Berlin (2009
Calibration by correlation using metric embedding from non-metric similarities
This paper presents a new intrinsic calibration method that allows us to calibrate a generic single-view point camera just
by waving it around. From the video sequence obtained while the camera undergoes random motion, we compute the pairwise time
correlation of the luminance signal for a subset of the pixels. We show that, if the camera undergoes a random uniform motion, then
the pairwise correlation of any pixels pair is a function of the distance between the pixel directions on the visual sphere. This leads to
formalizing calibration as a problem of metric embedding from non-metric measurements: we want to find the disposition of pixels on
the visual sphere from similarities that are an unknown function of the distances. This problem is a generalization of multidimensional
scaling (MDS) that has so far resisted a comprehensive observability analysis (can we reconstruct a metrically accurate embedding?)
and a solid generic solution (how to do so?). We show that the observability depends both on the local geometric properties (curvature)
as well as on the global topological properties (connectedness) of the target manifold. We show that, in contrast to the Euclidean case,
on the sphere we can recover the scale of the points distribution, therefore obtaining a metrically accurate solution from non-metric
measurements. We describe an algorithm that is robust across manifolds and can recover a metrically accurate solution when the metric
information is observable. We demonstrate the performance of the algorithm for several cameras (pin-hole, fish-eye, omnidirectional),
and we obtain results comparable to calibration using classical methods. Additional synthetic benchmarks show that the algorithm
performs as theoretically predicted for all corner cases of the observability analysis
Light-front representation of chiral dynamics in peripheral transverse densities
The nucleon's electromagnetic form factors are expressed in terms of the
transverse densities of charge and magnetization at fixed light-front time. At
peripheral transverse distances the densities are governed
by chiral dynamics and can be calculated model-independently using chiral
effective field theory (EFT). We represent the leading-order chiral EFT results
for the peripheral transverse densities as overlap integrals of chiral
light-front wave functions, describing the transition of the initial nucleon to
soft pion-nucleon intermediate states and back. The new representation (a)
explains the parametric order of the peripheral transverse densities; (b)
establishes an inequality between the spin-independent and -dependent
densities; (c) exposes the role of pion orbital angular momentum in chiral
dynamics; (d) reveals a large left-right asymmetry of the current in a
transversely polarized nucleon and suggests a simple interpretation. The
light-front representation enables a first-quantized, quantum-mechanical view
of chiral dynamics that is fully relativistic and exactly equivalent to the
second-quantized, field-theoretical formulation. It relates the charge and
magnetization densities measured in low-energy elastic scattering to the
generalized parton distributions probed in peripheral high-energy scattering
processes. The method can be applied to nucleon form factors of other
operators, e.g. the energy-momentum tensor.Comment: 28 pages, 9 figure
Stationary correlations for a far-from-equilibrium spin chain
A kinetic one-dimensional Ising model on a ring evolves according to a
generalization of Glauber rates, such that spins at even (odd) lattice sites
experience a temperature (). Detailed balance is violated so
that the spin chain settles into a non-equilibrium stationary state,
characterized by multiple interactions of increasing range and spin order. We
derive the equations of motion for arbitrary correlation functions and solve
them to obtain an exact representation of the steady state. Two nontrivial
amplitudes reflect the sublattice symmetries; otherwise, correlations decay
exponentially, modulo the periodicity of the ring. In the long chain limit,
they factorize into products of two-point functions, in precise analogy to the
equilibrium Ising chain. The exact solution confirms the expectation, based on
simulations and renormalization group arguments, that the long-time,
long-distance behavior of this two-temperature model is Ising-like, in spite of
the apparent complexity of the stationary distribution.Comment: 9 page
The Light-Cone Fock Expansion in Quantum Chromodynamics
A fundamental question in QCD is the non-perturbative structure of hadrons at
the amplitude level--not just the single-particle flavor, momentum, and
helicity distributions of the quark constituents, but also the multi-quark,
gluonic, and hidden-color correlations intrinsic to hadronic and nuclear
wavefunctions. The light-cone Fock-state representation of QCD encodes the
properties of a hadrons in terms of frame-independent wavefunctions. A number
of applications are discussed, including semileptonic B decays, deeply virtual
Compton scattering, and dynamical higher twist effects in inclusive reactions.
A new type of jet production reaction, "self-resolving diffractive
interactions" can provide direct information on the light-cone wavefunctions of
hadrons in terms of their quark and gluon degrees of freedom as well as the
composition of nuclei in terms of their nucleon and mesonic degrees of freedom.
The relation of the intrinsic sea to the light-cone wavefunctions is discussed.
The physics of light-cone wavefunctions is illustrated for the quantum
fluctuations of an electron.Comment: Presented at VII Hadron Physics 2000, Caraguatatuba, Sao Paulo,
Brazil, April 10-15, 200
Time reversal in classical electromagnetism
Richard Feynman has claimed that anti-particles are nothing but particles `propagating backwards in time'; that time reversing a particle state always turns it into the corresponding anti-particle state. According to standard quantum eld theory textbooks this is not so: time reversal does not turn particles into anti-particles. Feynman's view is interesting because, in particular, it suggests a nonstandard, and possibly illuminating, interpretation of the CPT theorem. In this paper, we explore a classical analog of Feynman's view, in the context of the recent debate between David Albert and David Malament over time reversal in classical electromagnetism
Discussion on spin-flip synchrotron radiation
Quantum spin-flip transitions are of great importance in the synchrotron
radiation theory. For better understanding of the nature of this phenomenon, it
is necessary to except the effects connected with the electric charge radiation
from observation. This fact explains the suggested choice of the spin-flip
radiation model in the form of radiation of the electric neutral Dirac-Pauli
particle moving in the homogeneous magnetic field. It is known that in this
case, the total radiation in the quantum theory is conditioned by spin-flip
transitions. The idea is that spin-flip radiation is represented as a
nonstationary process connected with spin precession. We shall shown how to
construct a solution of the classical equation of the spin precession in the
BMT theory having the exact solution of the Dirac-Pauli equation.Thus, one will
find the connection of the quantum spin-flip transitions with classical spin
precession.Comment: 4 pages, LATE
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