9,018 research outputs found
Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel
We use an exact transfer-matrix approach to compute the equilibrium
properties of a system of hard disks of diameter confined to a
two-dimensional channel of width at constant longitudinal
applied force. At this channel width, which is sufficient for
next-nearest-neighbor disks to interact, the system is known to have a great
many jammed states. Our calculations show that the longitudinal force
(pressure) extrapolates to infinity at a well-defined packing fraction
that is less than the maximum possible , the latter
corresponding to a buckled crystal. In this quasi-one-dimensional problem there
is no question of there being any \emph{real} divergence of the pressure at
. We give arguments that this avoided phase transition is a structural
feature -- the remnant in our narrow channel system of the hexatic to crystal
transition -- but that it has the phenomenology of the (avoided) ideal glass
transition. We identify a length scale as our equivalent of the
penetration length for amorphous order: In the channel system, it reaches a
maximum value of around at , which is larger than the
penetration lengths that have been reported for three dimensional systems. It
is argued that the -relaxation time would appear on extrapolation to
diverge in a Vogel-Fulcher manner as the packing fraction approaches .Comment: 17 pages, 16 figure
Absence of hyperuniformity in amorphous hard-sphere packings of nonvanishing complexity
We relate the structure factor in a system of
jammed hard spheres of number density to its complexity per particle
by the formula . We have verified this formula for
the case of jammed disks in a narrow channel, for which it is possible to find
and analytically. Hyperuniformity, which is the
vanishing of , will therefore not occur if the
complexity is nonzero. An example is given of a jammed state of hard disks in a
narrow channel which is hyperuniform when generated by dynamical rules that
produce a non-extensive complexity.Comment: 5 pages, 3 figure
Electromagnetic Wave Transmission Through a Subwavelength Nano-hole in a Two-dimensional Plasmonic Layer
An integral equation is formulated to describe electromagnetic wave
transmission through a sub-wavelength nano-hole in a thin plasmonic sheet in
terms of the dyadic Green's function for the associated Helmholtz problem.
Taking the subwavelength radius of the nano-hole to be the smallest length of
the system, we have obtained an exact solution of the integral equation for the
dyadic Green's function analytically and in closed form. This dyadic Green's
function is then employed in the numerical analysis of electromagnetic wave
transmission through the nano-hole for normal incidence of the incoming wave
train. The electromagnetic transmission involves two distinct contributions,
one emanating from the nano-hole and the other is directly transmitted through
the thin plasmonic layer itself (which would not occur in the case of a perfect
metal screen). The transmitted radiation exhibits interference fringes in the
vicinity of the nano-hole, and they tend to flatten as a function of increasing
lateral separation from the hole, reaching the uniform value of transmission
through the sheet alone at large separations.Comment: 14 pages, 24 individual figures organized in 9 captioned group
Transition state theory and the dynamics of hard disks
The dynamics of two and five disk systems confined in a square has been
studied using molecular dynamics simulations and compared with the predictions
of transition state theory. We determine the partition functions Z and
Z^\ddagger of transition state theory using a procedure first used by Salsburg
and Wood for the pressure. Our simulations show this procedure and transition
state theory are in excellent agreement with the simulations. A generalization
of the transition state theory to the case of a large number of disks N is made
and shown to be in full agreement with simulations of disks moving in a narrow
channel. The same procedure for hard spheres in three dimensions leads to the
Vogel-Fulcher-Tammann formula for their alpha relaxation time.Comment: 1 new author, new simulations and figures, less speculation. Now 6
pages, 6 figures, 1 animation. Animation may be viewed at
http://www.theory.physics.manchester.ac.uk/~godfrey/supplement/activated_dynamics2.htm
Carrier localization mechanisms in InGaN/GaN quantum wells
Localization lengths of the electrons and holes in InGaN/GaN quantum wells
have been calculated using numerical solutions of the effective mass
Schr\"odinger equation. We have treated the distribution of indium atoms as
random and found that the resultant fluctuations in alloy concentration can
localize the carriers. By using a locally varying indium concentration function
we have calculated the contribution to the potential energy of the carriers
from band gap fluctuations, the deformation potential and the spontaneous and
piezoelectric fields. We have considered the effect of well width fluctuations
and found that these contribute to electron localization, but not to hole
localization. We also simulate low temperature photoluminescence spectra and
find good agreement with experiment.Comment: 7 pages, 7 figure
Influence of reheating on the trispectrum and its scale dependence
We study the evolution of the non-linear curvature perturbation during perturbative reheating, and hence how observables evolve to their final values which we may compare against observations. Our study includes the evolution of the two trispectrum parameters, \gnl and \taunl, as well as the scale dependence of both \fnl and \taunl. In general the evolution is significant and must be taken into account, which means that models of multifield inflation cannot be compared to observations without specifying how the subsequent reheating takes place. If the trispectrum is large at the end of inflation, it normally remains large at the end of reheating. In the classes of models we study, it is very hard to generate \taunl\gg\fnl^2, regardless of the decay rates of the fields. Similarly, for the classes of models in which \gnl\simeq\taunl during slow--roll inflation, we find the relation typically remains valid during reheating. Therefore it is possible to observationally test such classes of models without specifying the parameters of reheating, even though the individual observables are sensitive to the details of reheating. It is hard to generate an observably large \gnl however. The runnings, \nfnl and \ntaunl, tend to satisfy a consistency relation \ntaunl=(3/2)\nfnl, but are in general too small to be observed for the class of models considered regardless of reheating timescale
The Effect of a Magnetic Field on the Acoustoelectric current in a Narrow Channel
The effect of a perpendicular magnetic field on the quantized current induced
by a surface acoustic wave in a quasi-1D channel is studied. The channel has
been produced experimentally in a GaAs heterostructure by shallow etching
techniques and by the application of a negative gate voltage to Schottky split
gates. Commensurability oscillations of the quantized current in this
constriction have been observed in the interval of current between quantized
plateaus. The results can be understood in terms of a moving quantum dot with
the electron in the dot tunneling into the adjacent two-dimensional region. The
goal is to explain qualitatively the mechanism for the steplike nature of the
acoustoelectric current as a function of gate voltage and the oscillations when
a magnetic field is applied. A transfer Hamiltonian formalism is employed.Comment: 5 pages, 2 figure
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