179 research outputs found
Comment on the equivalence of Bakamjian-Thomas mass operators in different forms of dynamics
We discuss the scattering equivalence of the generalized Bakamjian-Thomas
construction of dynamical representations of the Poincar\'e group in all of
Dirac's forms of dynamics. The equivalence was established by Sokolov in the
context of proving that the equivalence holds for models that satisfy cluster
separability. The generalized Bakamjian Thomas construction is used in most
applications, even though it only satisfies cluster properties for systems of
less than four particles. Different forms of dynamics are related by unitary
transformations that remove interactions from some infinitesimal generators and
introduce them to other generators. These unitary transformation must be
interaction dependent, because they can be applied to a non-interacting
generator and produce an interacting generator. This suggests that these
transformations can generate complex many-body forces when used in many-body
problems. It turns out that this is not the case. In all cases of interest the
result of applying the unitary scattering equivalence results in
representations that have simple relations, even though the unitary
transformations are dynamical. This applies to many-body models as well as
models with particle production. In all cases no new many-body operators are
generated by the unitary scattering equivalences relating the different forms
of dynamics. This makes it clear that the various calculations used in
applications that emphasize one form of the dynamics over another are
equivalent. Furthermore, explicit representations of the equivalent dynamical
models in any form of dynamics are easily constructed. Where differences do
appear is when electromagnetic probes are treated in the one-photon exchange
approximation. This approximation is different in each of Dirac's forms of
dynamics.Comment: 6 pages, no figure
Notions of Infinity in Quantum Physics
In this article we will review some notions of infiniteness that appear in
Hilbert space operators and operator algebras. These include proper
infiniteness, Murray von Neumann's classification into type I and type III
factors and the class of F{/o} lner C*-algebras that capture some aspects of
amenability. We will also mention how these notions reappear in the description
of certain mathematical aspects of quantum mechanics, quantum field theory and
the theory of superselection sectors. We also show that the algebra of the
canonical anti-commutation relations (CAR-algebra) is in the class of F{/o}
lner C*-algebras.Comment: 11 page
Entanglement, Haag-duality and type properties of infinite quantum spin chains
We consider an infinite spin chain as a bipartite system consisting of the
left and right half-chain and analyze entanglement properties of pure states
with respect to this splitting. In this context we show that the amount of
entanglement contained in a given state is deeply related to the von Neumann
type of the observable algebras associated to the half-chains. Only the type I
case belongs to the usual entanglement theory which deals with density
operators on tensor product Hilbert spaces, and only in this situation
separable normal states exist. In all other cases the corresponding state is
infinitely entangled in the sense that one copy of the system in such a state
is sufficient to distill an infinite amount of maximally entangled qubit pairs.
We apply this results to the critical XY model and show that its unique ground
state provides a particular example for this type of entanglement.Comment: LaTeX2e, 34 pages, 1 figure (pstricks
Relativity and the low energy nd Ay puzzle
We solve the Faddeev equation in an exactly Poincare invariant formulation of
the three-nucleon problem. The dynamical input is a relativistic
nucleon-nucleon interaction that is exactly on-shell equivalent to the high
precision CDBonn NN interaction. S-matrix cluster properties dictate how the
two-body dynamics is embedded in the three-nucleon mass operator. We find that
for neutron laboratory energies above 20 MeV relativistic effects on Ay are
negligible. For energies below 20 MeV dynamical effects lower the nucleon
analyzing power maximum slightly by 2% and Wigner rotations lower it further up
to 10 % increasing thus disagreement between data and theory. This indicates
that three-nucleon forces must provide an even larger increase of the Ay
maximum than expected up to now.Comment: 29 pages, 2 ps figure
Semicausal operations are semilocalizable
We prove a conjecture by DiVincenzo, which in the terminology of Preskill et
al. [quant-ph/0102043] states that ``semicausal operations are
semilocalizable''. That is, we show that any operation on the combined system
of Alice and Bob, which does not allow Bob to send messages to Alice, can be
represented as an operation by Alice, transmitting a quantum particle to Bob,
and a local operation by Bob. The proof is based on the uniqueness of the
Stinespring representation for a completely positive map. We sketch some of the
problems in transferring these concepts to the context of relativistic quantum
field theory.Comment: 4 pages, 1 figure, revte
First Order Relativistic Three-Body Scattering
Relativistic Faddeev equations for three-body scattering at arbitrary
energies are formulated in momentum space and in first order in the two-body
transition-operator directly solved in terms of momentum vectors without
employing a partial wave decomposition. Relativistic invariance is incorporated
within the framework of Poincare invariant quantum mechanics, and presented in
some detail.
Based on a Malfliet-Tjon type interaction, observables for elastic and
break-up scattering are calculated up to projectile energies of 1 GeV. The
influence of kinematic and dynamic relativistic effects on those observables is
systematically studied. Approximations to the two-body interaction embedded in
the three-particle space are compared to the exact treatment.Comment: 26 pages, 13 figure
Adsorption site and orientation of pyridine on Cu{110} determined by photoelectron diffraction
The local adsorption geometry of pyridine on Cu{110} has been determined quantitatively using photoelectron diffraction in the scanned-energy mode. At high coverages the molecule adsorbs nearly atop a Cu atom in the close-packed rows with a N–Cu bond length of 2.00 Å. Moreover, the Cu–N axis and the molecular (C2) axis are inclined by 8° and 20°, respectively, to the surface normal. The result shows that not only the adsorption site of the emitter (in this case the N atom) but also the position of relatively light scatterers (the C atoms) can be determined by photoelectron diffraction
Shell Corrections for Finite-Depth Deformed Potentials: Green's Function Oscillator Expansion Method
Shell corrections of the finite deformed Woods-Saxon potential are calculated
using the Green's function method and the generalized Strutinsky smoothing
procedure. They are compared with the results of the standard prescription
which are affected by the spurious contribution from the unphysical particle
gas. In the new method, the shell correction approaches the exact limit
provided that the dimension of the single-particle (harmonic oscillator) basis
is sufficiently large. For spherical potentials, the present method is faster
than the exact one in which the contribution from the particle continuum states
is explicitly calculated. For deformed potentials, the Green's function method
offers a practical and reliable way of calculating shell corrections for weakly
bound nuclei.Comment: submitted to Phys. Rev. C, 12 pages, 7 figure
Local adsorption geometry of acetylene on Si(100)(2×1)
Using C 1s scanned-energy-mode photoelectron diffraction the local adsorption geometry of acetylene on the Si(100)(2x1) surface has been determined and the results are compared with those of a similar study of ethylene adsorption on this surface. Both molecules bond to the surface along the Si-Si dimers with the C-C bonds parallel to the surface such that the C atoms are in off-atop sites relative to the Si dimer atoms. In both cases the Si-Si bond length (2.36±0.21 Å for ethylene and 2.44±0.58 Å for acetylene) is compatible only with the dimer remaining intact after adsorption and not with the Si-Si distance of an ideally terminated undimerized Si(100) surface (3.84 Å)
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