771 research outputs found
Semiclassical trace formulae using coherent states
We derive semiclassical trace formulae including Gutzwiller's trace formula
using coherent states. This formulation has several advantages over the usual
coordinate-space formulation. Using a coherent-state basis makes it immediately
obvious that classical periodic orbits make separate contributions to the trace
of the quantum-mechanical time evolution operator. In addition, our approach is
manifestly canonically invariant at all stages, and leads to the simplest
possible derivation of Gutzwiller's formula.Comment: 19 pages, 1 figur
Statistical model for collisions and recollisions of inertial particles in mixing flows
Finding a quantitative description of the rate of collisions between small
particles suspended in mixing flows is a long-standing problem. Here we
investigate the validity of a parameterisation of the collision rate for
identical particles subject to Stokes force, based on results for relative
velocities of heavy particles that were recently obtained within a statistical
model for the dynamics of turbulent aerosols. This model represents the
turbulent velocity fluctuations by Gaussian random functions. We find that the
parameterisation gives quantitatively good results in the limit where the \lq
ghost-particle approximation' applies. The collision rate is a sum of two
contributions due to \lq caustics' and to \lq clustering'. Within the
statistical model we compare the relative importance of these two collision
mechanisms. The caustic formation rate is high when the particle inertia
becomes large, and we find that caustics dominate the collision rate as soon as
they form frequently. We compare the magnitude of the caustic contribution to
the collision rate to the formation rate of caustics.Comment: 9 pages, 4 figures, final version as publishe
Planet Formation by Concurrent Collapse
After reviewing the difficulties faced by the conventional theory of planet
formation (based upon the aggregation of microscopic dust particles), we
describe an alternative hypothesis. We propose that planets form by
gravitational collapse at the same time as the star about which they orbit.
This 'concurrent collapse' hypothesis avoids theoretical difficulties
associated with the conventional model and suggests satisfying explanations for
various poorly understood phenomena. We introduce new explanations for FU
Orionis outbursts seen in young stars, the discovery of exoplanets with
eccentric orbits and the existence of small rocky objects such as chondrules in
the solar system.Comment: 16 pages, no figures, extended and refined version of earlier
submissio
Precise asymptotics for a variable-range hopping model
For a system of localised electron states the DC conductivity vanishes at
zero temperature, but localised electrons can conduct at finite temperature.
Mott gave a theory for the low-temperature conductivity in terms of a
variable-range hopping model, which is hard to analyse. Here we give precise
asymptotic results for a modified variable-range hopping model proposed by S.
Alexander [Phys. Rev. B 26, 2956 (1982)].Comment: 7 pages, 2 figure
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