81 research outputs found
An alternative approach to the construction of Schur-Weyl transform
We propose an alternative approach for the construction of the unitary matrix
which performs generalized unitary rotations of the system consisting of
independent identical subsystems (for example spin system). This matrix, when
applied to the system, results in a change of degrees of freedom, uncovering
the information hidden in non-local degrees of freedom. This information can be
used, inter alia, to study the structure of entangled states, their
classification and may be useful for construction of quantum algorithms.Comment: 6 page
Light-Front Quantisation as an Initial-Boundary Value Problem
In the light front quantisation scheme initial conditions are usually
provided on a single lightlike hyperplane. This, however, is insufficient to
yield a unique solution of the field equations. We investigate under which
additional conditions the problem of solving the field equations becomes well
posed. The consequences for quantisation are studied within a Hamiltonian
formulation by using the method of Faddeev and Jackiw for dealing with
first-order Lagrangians. For the prototype field theory of massive scalar
fields in 1+1 dimensions, we find that initial conditions for fixed light cone
time {\sl and} boundary conditions in the spatial variable are sufficient to
yield a consistent commutator algebra. Data on a second lightlike hyperplane
are not necessary. Hamiltonian and Euler-Lagrange equations of motion become
equivalent; the description of the dynamics remains canonical and simple. In
this way we justify the approach of discretised light cone quantisation.Comment: 26 pages (including figure), tex, figure in latex, TPR 93-
An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics
A general method for deriving closed reduced models of Hamiltonian dynamical
systems is developed using techniques from optimization and statistical
estimation. As in standard projection operator methods, a set of resolved
variables is selected to capture the slow, macroscopic behavior of the system,
and the family of quasi-equilibrium probability densities on phase space
corresponding to these resolved variables is employed as a statistical model.
The macroscopic dynamics of the mean resolved variables is determined by
optimizing over paths of these probability densities. Specifically, a cost
function is introduced that quantifies the lack-of-fit of such paths to the
underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of
the residual that results from submitting a path of trial densities to the
Liouville equation. The evolution of the macrostate is estimated by minimizing
the time integral of the cost function. The value function for this
optimization satisfies the associated Hamilton-Jacobi equation, and it
determines the optimal relation between the statistical parameters and the
irreversible fluxes of the resolved variables, thereby closing the reduced
dynamics. The resulting equations for the macroscopic variables have the
generic form of governing equations for nonequilibrium thermodynamics, and they
furnish a rational extension of the classical equations of linear irreversible
thermodynamics beyond the near-equilibrium regime. In particular, the value
function is a thermodynamic potential that extends the classical dissipation
function and supplies the nonlinear relation between thermodynamics forces and
fluxes
Higher spin quaternion waves in the Klein-Gordon theory
Electromagnetic interactions are discussed in the context of the Klein-Gordon
fermion equation. The Mott scattering amplitude is derived in leading order
perturbation theory and the result of the Dirac theory is reproduced except for
an overall factor of sixteen. The discrepancy is not resolved as the study
points into another direction. The vertex structures involved in the scattering
calculations indicate the relevance of a modified Klein-Gordon equation, which
takes into account the number of polarization states of the considered quantum
field. In this equation the d'Alembertian is acting on quaternion-like plane
waves, which can be generalized to representations of arbitrary spin. The
method provides the same relation between mass and spin that has been found
previously by Majorana, Gelfand, and Yaglom in infinite spin theories
On the connectedness structure of the Coulomb S -matrix
The forward direction singularity of the non-relativistic Coulomb S -matrix is examined and discussed. The relativistic Coulomb S -matrix to order α is shown to have a similar singularity.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46508/1/220_2005_Article_BF01646192.pd
Pulsar-wind nebulae and magnetar outflows: observations at radio, X-ray, and gamma-ray wavelengths
We review observations of several classes of neutron-star-powered outflows:
pulsar-wind nebulae (PWNe) inside shell supernova remnants (SNRs), PWNe
interacting directly with interstellar medium (ISM), and magnetar-powered
outflows. We describe radio, X-ray, and gamma-ray observations of PWNe,
focusing first on integrated spectral-energy distributions (SEDs) and global
spectral properties. High-resolution X-ray imaging of PWNe shows a bewildering
array of morphologies, with jets, trails, and other structures. Several of the
23 so far identified magnetars show evidence for continuous or sporadic
emission of material, sometimes associated with giant flares, and a few
possible "magnetar-wind nebulae" have been recently identified.Comment: 61 pages, 44 figures (reduced in quality for size reasons). Published
in Space Science Reviews, "Jets and Winds in Pulsar Wind Nebulae, Gamma-ray
Bursts and Blazars: Physics of Extreme Energy Release
Magnetic fields in supernova remnants and pulsar-wind nebulae
We review the observations of supernova remnants (SNRs) and pulsar-wind
nebulae (PWNe) that give information on the strength and orientation of
magnetic fields. Radio polarimetry gives the degree of order of magnetic
fields, and the orientation of the ordered component. Many young shell
supernova remnants show evidence for synchrotron X-ray emission. The spatial
analysis of this emission suggests that magnetic fields are amplified by one to
two orders of magnitude in strong shocks. Detection of several remnants in TeV
gamma rays implies a lower limit on the magnetic-field strength (or a
measurement, if the emission process is inverse-Compton upscattering of cosmic
microwave background photons). Upper limits to GeV emission similarly provide
lower limits on magnetic-field strengths. In the historical shell remnants,
lower limits on B range from 25 to 1000 microGauss. Two remnants show
variability of synchrotron X-ray emission with a timescale of years. If this
timescale is the electron-acceleration or radiative loss timescale, magnetic
fields of order 1 mG are also implied. In pulsar-wind nebulae, equipartition
arguments and dynamical modeling can be used to infer magnetic-field strengths
anywhere from about 5 microGauss to 1 mG. Polarized fractions are considerably
higher than in SNRs, ranging to 50 or 60% in some cases; magnetic-field
geometries often suggest a toroidal structure around the pulsar, but this is
not universal. Viewing-angle effects undoubtedly play a role. MHD models of
radio emission in shell SNRs show that different orientations of upstream
magnetic field, and different assumptions about electron acceleration, predict
different radio morphology. In the remnant of SN 1006, such comparisons imply a
magnetic-field orientation connecting the bright limbs, with a non-negligible
gradient of its strength across the remnant.Comment: 20 pages, 24 figures; to be published in SpSciRev. Minor wording
change in Abstrac
Sum rules and dualities for generalized parton distributions: is there a holographic principle?
To leading order approximation, the physical content of generalized parton
distributions (GPDs) that is accessible in deep virtual electroproduction of
photons or mesons is contained in their value on the cross-over trajectory.
This trajectory separates the t-channel and s-channel dominated GPD regions.
The underlying Lorentz covariance implies correspondence between these two
regions through their relation to GPDs on the cross-over trajectory. This point
of view leads to a family of GPD sum rules which are a quark analogue of finite
energy sum rules and it guides us to a new phenomenological GPD concept. As an
example, we discuss the constraints from the JLab/Hall A data on the dominant
u-quark GPD H. The question arises whether GPDs are governed by some kind of
holographic principle.Comment: 45 pages, 4 figures, Sect. 2 reorganized for clarity. Typos in Eq.
(20) corrected. 4 new refs. Matches published versio
Quantum magnetism in two dimensions: From semi-classical N\'eel order to magnetic disorder
This is a review of ground-state features of the s=1/2 Heisenberg
antiferromagnet on two-dimensional lattices. A central issue is the interplay
of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor
bonds, geometric frustration) and quantum fluctuations and their impact on
possible long-range order. This article presents a unified summary of all 11
two-dimensional uniform Archimedean lattices which include e.g. the square,
triangular and kagome lattice. We find that the ground state of the spin-1/2
Heisenberg antiferromagnet is likely to be semi-classically ordered in most
cases. However, the interplay of geometric frustration and quantum fluctuations
gives rise to a quantum paramagnetic ground state without semi-classical
long-range order on two lattices which are precisely those among the 11 uniform
Archimedean lattices with a highly degenerate ground state in the classical
limit. The first one is the famous kagome lattice where many low-lying singlet
excitations are known to arise in the spin gap. The second lattice is called
star lattice and has a clear gap to all excitations.
Modification of certain bonds leads to quantum phase transitions which are
also discussed briefly. Furthermore, we discuss the magnetization process of
the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on
anomalies like plateaus and a magnetization jump just below the saturation
field. As an illustration we discuss the two-dimensional Shastry-Sutherland
model which is used to describe SrCu2(BO3)2.Comment: This is now the complete 72-page preprint version of the 2004 review
article. This version corrects two further typographic errors (three total
with respect to the published version), see page 2 for detail
Metastability Driven by Soft Quantum Fluctuation Modes
The semiclassical Euclidean path integral method is applied to compute the
low temperature quantum decay rate for a particle placed in the metastable
minimum of a cubic potential in a {\it finite} time theory. The classical path,
which makes a saddle for the action, is derived in terms of Jacobian elliptic
functions whose periodicity establishes the one-to-one correspondence between
energy of the classical motion and temperature (inverse imaginary time) of the
system. The quantum fluctuation contribution has been computed through the
theory of the functional determinants for periodic boundary conditions. The
decay rate shows a peculiar temperature dependence mainly due to the softening
of the low lying quantum fluctuation eigenvalues. The latter are determined by
solving the Lam\`{e} equation which governs the fluctuation spectrum around the
time dependent classical bounce.Comment: Journal of Low Temperature Physics (2008) Publisher: Springer
Netherland
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