329 research outputs found
Cliffordization, Spin and Fermionic Star Products
Deformation quantization is a powerful tool for quantizing theories with
bosonic and fermionic degrees of freedom. The star products involved generate
the mathematical structures which have recently been used in attempts to
analyze the algebraic properties of quantum field theory. In the context of
quantum mechanics they provide a canonical quantization procedure for systems
with either bosonic of fermionic degrees of freedom. We illustrate this
procedure for a number a physical examples, including bosonic, fermionic and
supersymmetric oscillators. We show how non-relativistic and relativistic
particles with spin can be naturally described in this framework.Comment: 21 page
Foldy-Wouthuysen Transformation for a Spinning Particle with Anomalous Magnetic Moment
We study the Foldy-Wouthuysen transformation for a pseudoclassical particle
with anomalous magnetic moment in an external, stationary electromagnetic
field. We show that the transformation can be expressed in a closed form for
neutral particles in purely electrostatic fields and for neutral and charged
particles in external magnetostatic fields. The explicit expressions of the
diagonalized Hamiltonians are calculated.Comment: 10 page
A Phase transition in acoustic propagation in 2D random liquid media
Acoustic wave propagation in liquid media containing many parallel air-filled
cylinders is considered. A self-consistent method is used to compute rigorously
the propagation, incorporating all orders of multiple scattering. It is shown
that under proper conditions, multiple scattering leads to a peculiar phase
transition in acoustic propagation. When the phase transition occurs, a
collective behavior of the cylinders appears and the acoustic waves are
confined in a region of space in the neighborhood of the transmission source. A
novel phase diagram is used to describe such phase transition.
Originally submitted on April 6, 99.Comment: 5 pages, 5 color figure
Self-Binding Transition in Bose Condensates with Laser-Induced ``Gravitation''
In our recent publication (D. O'Dell, et al, Phys. Rev. Lett. 84, 5687
(2000)) we proposed a scheme for electromagnetically generating a self-bound
Bose-Einstein condensate with 1/r attractive interactions: the analog of a Bose
star. Here we focus upon the conditions neccessary to observe the transition
from external trapping to self-binding. This transition becomes manifest in a
sharp reduction of the condensate radius and its dependence on the laser
intensity rather that the trap potential.Comment: 5 pages, 2 figures: slightly enhanced text: more explanatio
Relativistic corrections in magnetic systems
We present a weak-relativistic limit comparison between the Kohn-Sham-Dirac
equation and its approximate form containing the exchange coupling, which is
used in almost all relativistic codes of density-functional theory. For these
two descriptions, an exact expression of the Dirac Green's function in terms of
the non-relativistic Green's function is first derived and then used to
calculate the effective Hamiltonian, i.e., Pauli Hamiltonian, and effective
velocity operator in the weak-relativistic limit. We point out that, besides
neglecting orbital magnetism effects, the approximate Kohn-Sham-Dirac equation
also gives relativistic corrections which differ from those of the exact
Kohn-Sham-Dirac equation. These differences have quite serious consequences: in
particular, the magnetocrystalline anisotropy of an uniaxial ferromagnet and
the anisotropic magnetoresistance of a cubic ferromagnet are found from the
approximate Kohn-Sham-Dirac equation to be of order , whereas the
correct results obtained from the exact Kohn-Sham-Dirac equation are of order
. We give a qualitative estimate of the order of magnitude of these
spurious terms
WKB analysis of relativistic Stern-Gerlach measurements
Spin is an important quantum degree of freedom in relativistic quantum
information theory. This paper provides a first-principles derivation of the
observable corresponding to a Stern-Gerlach measurement with relativistic
particle velocity. The specific mathematical form of the Stern-Gerlach operator
is established using the transformation properties of the electromagnetic
field. To confirm that this is indeed the correct operator we provide a
detailed analysis of the Stern-Gerlach measurement process. We do this by
applying a WKB approximation to the minimally coupled Dirac equation describing
an interaction between a massive fermion and an electromagnetic field. Making
use of the superposition principle we show that the +1 and -1 spin eigenstates
of the proposed spin operator are split into separate packets due to the
inhomogeneity of the Stern-Gerlach magnetic field. The operator we obtain is
dependent on the momentum between particle and Stern-Gerlach apparatus, and is
mathematically distinct from two other commonly used operators. The
consequences for quantum tomography are considered.Comment: 13 pages, no figures. Comments welcom
Improved Nonrelativistic QCD for Heavy Quark Physics
We construct an improved version of nonrelativistic QCD for use in lattice
simulations of heavy quark physics, with the goal of reducing systematic errors
from all sources to below 10\%. We develop power counting rules to assess the
importance of the various operators in the action and compute all leading order
corrections required by relativity and finite lattice spacing. We discuss
radiative corrections to tree level coupling constants, presenting a procedure
that effectively resums the largest such corrections to all orders in
perturbation theory. Finally, we comment on the size of nonperturbative
contributions to the coupling constants.Comment: 40 pages, 2 figures (not included), in LaTe
More on Symmetries in Heavy Quark Effective Theory
We present a general classification of all normal and ``chiral" symmetries of
heavy quark effective theories. Some peculiarities and conondrums associated
with the ``chiral" symmetries are discussed.Comment: 15 pages, preprint UR-1320, ER40685-77
Relativistic Hamiltonians in many-body theories
We discuss the description of a many-body nuclear system using Hamiltonians
that contain the nucleon relativistic kinetic energy and potentials with
relativistic corrections. Through the Foldy-Wouthuysen transformation, the
field theoretical problem of interacting nucleons and mesons is mapped to an
equivalent one in terms of relativistic potentials, which are then expanded at
some order in 1/m_N. The formalism is applied to the Hartree problem in nuclear
matter, showing how the results of the relativistic mean field theory can be
recovered over a wide range of densities.Comment: 14 pages, uses REVTeX and epsfig, 3 postscript figures; a postscript
version of the paper is available by anonymous ftp at
ftp://carmen.to.infn.it/pub/depace/papers/951
Are waves all localized in two dimensional random media?
It has been the dominant view for over two decades that all waves are
localized in two dimensions for any given amount of disorder. Here, I would
like to raise questions about this assertion. The discussion leads to the
conclusion that there is a lack of the conclusive and definite support of the
claim. Rather, the recent evidence tends to indicate that waves are not
necessarily always localized in two dimensional random systems. Reasons are
elaborated
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