3,974 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
Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals
We show that the generalized diffusion coefficient of a subdiffusive
intermittent map is a fractal function of control parameters. A modified
continuous time random walk theory yields its coarse functional form and
correctly describes a dynamical phase transition from normal to anomalous
diffusion marked by strong suppression of diffusion. Similarly, the probability
density of moving particles is governed by a time-fractional diffusion equation
on coarse scales while exhibiting a specific fine structure. Approximations
beyond stochastic theory are derived from a generalized Taylor-Green-Kubo
formula.Comment: 4 pages, 3 eps figure
Hand-Modelled Composite Prostheses after Resection of Peri-Acetabular Bone Malignancies
Purpose: To improve function after pelvic resection involving the acetabulum, using an anatomic composite implant built with screws and cement
Phase transitions in open quantum systems
We consider the behaviour of open quantum systems in dependence on the
coupling to one decay channel by introducing the coupling parameter
being proportional to the average degree of overlapping. Under critical
conditions, a reorganization of the spectrum takes place which creates a
bifurcation of the time scales with respect to the lifetimes of the resonance
states. We derive analytically the conditions under which the reorganization
process can be understood as a second-order phase transition and illustrate our
results by numerical investigations. The conditions are fulfilled e.g. for a
picket fence with equal coupling of the states to the continuum. Energy
dependencies within the system are included. We consider also the generic case
of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the
reorganization of the spectrum occurs at the critical value of
the control parameter globally over the whole energy range of the spectrum. All
states act cooperatively.Comment: 28 pages, 22 Postscript figure
Magneto-Optical Trap for Thulium Atoms
Thulium atoms are trapped in a magneto-optical trap using a strong transition
at 410 nm with a small branching ratio. We trap up to atoms at
a temperature of 0.8(2) mK after deceleration in a 40 cm long Zeeman slower.
Optical leaks from the cooling cycle influence the lifetime of atoms in the MOT
which varies between 0.3 -1.5 s in our experiments. The lower limit for the
leaking rate from the upper cooling level is measured to be 22(6) s. The
repumping laser transferring the atomic population out of the F=3 hyperfine
ground-state sublevel gives a 30% increase for the lifetime and the number of
atoms in the trap.Comment: 4 pages, 6 figure
Anharmonicity of BaTiO_3 single crystals
By analyzing the dielectric non-linearity with the Landau thermodynamic
expansion, we find a simple and direct way to assess the importance of the
eighth order term. Following this approach, it is demonstrated that the eighth
order term is essential for the adequate description of the para/ferroelectric
phase transition of BaTiO_3. The temperature dependence of the quartic
coefficient \beta is accordingly reconsidered and is strongly evidenced by the
change of its sign above 165 C. All these findings attest to the strong
polarization anharmonicity of this material, which is unexpected for classical
displacive ferroelectrics.Comment: 4 figures, to be published in Phys. Rev.
Structure and intramolecular mobility of N-(phosphoryl)-or N-(thiophosphoryl)amides and -thioamides: VIII. Structure of N-(thiophosphoryl)-S-organylbenzimidothioates by NMR spectroscopy
N-(Diisopropoxythiophosphoryl)-and N-(diisopropoxyphosphoryl)-S-organylbenzimidothioates, which contain one and two imidothiol fragments, are structurally homogeneous in solutions. Cis arrangement of the Ph and P(X)(OPr-i)2 substituents about the C=N bond (E isomer) was deduced from the 3JPNCC constants
Integrable matrix equations related to pairs of compatible associative algebras
We study associative multiplications in semi-simple associative algebras over
C compatible with the usual one. An interesting class of such multiplications
is related to the affine Dynkin diagrams of A, D, E-type. In this paper we
investigate in details the multiplications of the A-type and integrable matrix
ODEs and PDEs generated by them.Comment: 12 pages, Late
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