1,177 research outputs found
Multiscalar amplitudes to all orders in perturbation theory
A method for calculating loop amplitudes at the multiboson threshold is
presented, based on Feynman-diagram techniques. We explicitly calculate the
one-loop amplitudes in both -symmetric and broken symmetry cases, using
dimensional regularization. We argue that, to all orders in the perturbation
expansion, the unitarity-violating behaviour of the tree-order amplitudes
persists.Comment: 7 pages, Latex, CERN-TH.6852/9
On Relativistic Material Reference Systems
This work closes certain gaps in the literature on material reference systems
in general relativity. It is shown that perfect fluids are a special case of
DeWitt's relativistic elastic media and that the velocity--potential formalism
for perfect fluids can be interpreted as describing a perfect fluid coupled to
a fleet of clocks. A Hamiltonian analysis of the elastic media with clocks is
carried out and the constraints that arise when the system is coupled to
gravity are studied. When the Hamiltonian constraint is resolved with respect
to the clock momentum, the resulting true Hamiltonian is found to be a
functional only of the gravitational variables. The true Hamiltonian is
explicitly displayed when the medium is dust, and is shown to depend on the
detailed construction of the clocks.Comment: 18 pages, ReVTe
GTI-space : the space of generalized topological indices
A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given
Generation of Porous Particle Structures using the Void Expansion Method
The newly developed "void expansion method" allows for an efficient
generation of porous packings of spherical particles over a wide range of
volume fractions using the discrete element method. Particles are randomly
placed under addition of much smaller "void-particles". Then, the void-particle
radius is increased repeatedly, thereby rearranging the structural particles
until formation of a dense particle packing.
The structural particles' mean coordination number was used to characterize
the evolving microstructures. At some void radius, a transition from an
initially low to a higher mean coordination number is found, which was used to
characterize the influence of the various simulation parameters. For structural
and void-particle stiffnesses of the same order of magnitude, the transition is
found at constant total volume fraction slightly below the random close packing
limit. For decreasing void-particle stiffness the transition is shifted towards
a smaller void-particle radius and becomes smoother.Comment: 9 pages, 8 figure
Exact quantum states of a general time-dependent quadratic system from classical action
A generalization of driven harmonic oscillator with time-dependent mass and
frequency, by adding total time-derivative terms to the Lagrangian, is
considered. The generalization which gives a general quadratic Hamiltonian
system does not change the classical equation of motion. Based on the
observation by Feynman and Hibbs, the propagators (kernels) of the systems are
calculated from the classical action, in terms of solutions of the classical
equation of motion: two homogeneous and one particular solutions. The kernels
are then used to find wave functions which satisfy the Schr\"{o}dinger
equation. One of the wave functions is shown to be that of a Gaussian pure
state. In every case considered, we prove that the kernel does not depend on
the way of choosing the classical solutions, while the wave functions depend on
the choice. The generalization which gives a rather complicated quadratic
Hamiltonian is simply interpreted as acting an unitary transformation to the
driven harmonic oscillator system in the Hamiltonian formulation.Comment: Submitted to Phys. Rev.
Spatial Degrees of Freedom in Everett Quantum Mechanics
Stapp claims that, when spatial degrees of freedom are taken into account,
Everett quantum mechanics is ambiguous due to a "core basis problem." To
examine an aspect of this claim I generalize the ideal measurement model to
include translational degrees of freedom for both the measured system and the
measuring apparatus. Analysis of this generalized model using the Everett
interpretation in the Heisenberg picture shows that it makes unambiguous
predictions for the possible results of measurements and their respective
probabilities. The presence of translational degrees of freedom for the
measuring apparatus affects the probabilities of measurement outcomes in the
same way that a mixed state for the measured system would. Examination of a
measurement scenario involving several observers illustrates the consistency of
the model with perceived spatial localization of the measuring apparatus.Comment: 34 pp., no figs. Introduction, discussion revised. Material
tangential to main point remove
Fermi-edge singularities in linear and non-linear ultrafast spectroscopy
We discuss Fermi-edge singularity effects on the linear and nonlinear
transient response of an electron gas in a doped semiconductor. We use a
bosonization scheme to describe the low energy excitations, which allows to
compute the time and temperature dependence of the response functions. Coherent
control of the energy absorption at resonance is analyzed in the linear regime.
It is shown that a phase-shift appears in the coherent control oscillations,
which is not present in the excitonic case. The nonlinear response is
calculated analytically and used to predict that four wave-mixing experiments
would present a Fermi-edge singularity when the exciting energy is varied. A
new dephasing mechanism is predicted in doped samples that depends linearly on
temperature and is produced by the low-energy bosonic excitations in the
conduction band.Comment: long version; 9 pages, 4 figure
Influence of confinement on the orientational phase transitions in the lamellar phase of a block copolymer melt under shear flow
In this work we incorporate some real-system effects into the theory of
orientational phase transitions under shear flow (M. E. Cates and S. T. Milner,
Phys. Rev. Lett. v.62, p.1856 (1989) and G. H. Fredrickson, J. Rheol. v.38,
p.1045 (1994)). In particular, we study the influence of the shear-cell
boundaries on the orientation of the lamellar phase. We predict that at low
shear rates the parallel orientation appears to be stable. We show that there
is a critical value of the shear rate at which the parallel orientation loses
its stability and the perpendicular one appears immediately below the spinodal.
We associate this transition with a crossover from the fluctuation to the
mean-field behaviour. At lower temperatures the stability of the parallel
orientation is restored. We find that the region of stability of the
perpendicular orientation rapidly decreases as shear rate increases. This
behaviour might be misinterpreted as an additional perpendicular to parallel
transition recently discussed in literature.Comment: 25 pages, 4 figures, submitted to Phys. Rev.
Self-consistent description of nuclear compressional modes
Isoscalar monopole and dipole compressional modes are computed for a variety
of closed-shell nuclei in a relativistic random-phase approximation to three
different parametrizations of the Walecka model with scalar self-interactions.
Particular emphasis is placed on the role of self-consistency which by itself,
and with little else, guarantees the decoupling of the spurious
isoscalar-dipole strength from the physical response and the conservation of
the vector current. A powerful new relation is introduced to quantify the
violation of the vector current in terms of various ground-state form-factors.
For the isoscalar-dipole mode two distinct regions are clearly identified: (i)
a high-energy component that is sensitive to the size of the nucleus and scales
with the compressibility of the model and (ii) a low-energy component that is
insensitivity to the nuclear compressibility. A fairly good description of both
compressional modes is obtained by using a ``soft'' parametrization having a
compression modulus of K=224 MeV.Comment: 28 pages and 10 figures; submitted to PR
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