5,559 research outputs found
Bounds on three- and higher-distance sets
A finite set X in a metric space M is called an s-distance set if the set of
distances between any two distinct points of X has size s. The main problem for
s-distance sets is to determine the maximum cardinality of s-distance sets for
fixed s and M. In this paper, we improve the known upper bound for s-distance
sets in n-sphere for s=3,4. In particular, we determine the maximum
cardinalities of three-distance sets for n=7 and 21. We also give the maximum
cardinalities of s-distance sets in the Hamming space and the Johnson space for
several s and dimensions.Comment: 12 page
Quantum Quench and Scaling of Entanglement Entropy
Global quantum quench with a finite quench rate which crosses critical points
is known to lead to universal scaling of correlation functions as functions of
the quench rate. In this work, we explore scaling properties of the
entanglement entropy of a subsystem in a harmonic chain during a mass quench
which asymptotes to finite constant values at early and late times and for
which the dynamics is exactly solvable. When the initial state is the ground
state, we find that for large enough subsystem sizes the entanglement entropy
becomes independent of size. This is consistent with Kibble-Zurek scaling for
slow quenches, and with recently discussed "fast quench scaling" for quenches
fast compared to physical scales, but slow compared to UV cutoff scales.Comment: 6 pages, 5 figures; Major revision which affects the main result
Direct observation of a hydrophobic bond in loop-closure of a capped (-OCH2CH2-)n oligomer in water
The small r variation of the probability density P(r) for end-to-end
separations of a -CH2CH3 capped (-OCH2CH2-)n oligomer in water is computed to
be closely similar to the CH4 ... CH4 potential of mean force under the same
circumstances. Since the aqueous solution CH4 ... CH4 potential of mean force
is the natural physical definition of a primitive hydrophobic bond, the present
result identifies an experimentally accessible circumstance for direct
observation of a hydrophobic bond which has not been observed previously
because of the low solubility of CH4 in water. The physical picture is that the
soluble chain molecule carries the capping groups into aqueous solution, and
permits them to find one another with reasonable frequency. Comparison with the
corresponding results without the solvent shows that hydration of the solute
oxygen atoms swells the chain molecule globule. This supports the view that the
chain molecule globule might have a secondary effect on the hydrophobic
interaction which is of first interest here. The volume of the chain molecule
globule is important for comparing the probabilities with and without solvent
because it characterizes the local concentration of capping groups. Study of
other capping groups to enable X-ray and neutron diffraction measurements of
P(r) is discussed.Comment: 4 pages, 3 figure
Control of quantum interference in molecular junctions: Understanding the origin of Fano and anti- resonances
We investigate within a coarse-grained model the conditions leading to the
appearance of Fano resonances or anti-resonances in the conductance spectrum of
a generic molecular junction with a side group (T-junction). By introducing a
simple graphical representation (parabolic diagram), we can easily visualize
the relation between the different electronic parameters determining the
regimes where Fano resonances or anti-resonances in the low-energy conductance
spectrum can be expected. The results obtained within the coarse-grained model
are validated using density-functional based quantum transport calculations in
realistic T-shaped molecular junctions.Comment: 5 pages, 5 figure
Crossover behavior and multi-step relaxation in a schematic model of the cut-off glass transition
We study a schematic mode-coupling model in which the ideal glass transition
is cut off by a decay of the quadratic coupling constant in the memory
function. (Such a decay, on a time scale tau_I, has been suggested as the
likely consequence of activated processes.) If this decay is complete, so that
only a linear coupling remains at late times, then the alpha relaxation shows a
temporal crossover from a relaxation typical of the unmodified schematic model
to a final strongly slower-than-exponential relaxation. This crossover, which
differs somewhat in form from previous schematic models of the cut-off glass
transition, resembles light-scattering experiments on colloidal systems, and
can exhibit a `slower-than-alpha' relaxation feature hinted at there. We also
consider what happens when a similar but incomplete decay occurs, so that a
significant level of quadratic coupling remains for t>>tau_I. In this case the
correlator acquires a third, weaker relaxation mode at intermediate times. This
empirically resembles the beta process seen in many molecular glass formers. It
disappears when the initial as well as the final quadratic coupling lies on the
liquid side of the glass transition, but remains present even when the final
coupling is only just inside the liquid (so that the alpha relaxation time is
finite, but too long to measure). Our results are suggestive of how, in a
cut-off glass, the underlying `ideal' glass transition predicted by
mode-coupling theory can remain detectable through qualitative features in
dynamics.Comment: 14 pages revtex inc 10 figs; submitted to pr
Derivation of Amplitude Equations by Renormalization Group Method
A proper formulation in the perturbative renormalization group method is
presented to deduce amplitude equations. The formulation makes it possible not
only avoiding a serious difficulty in the previous reduction to amplitude
equations by eliminating all of the secular terms but also consistent
derivation of higher-order correction to amplitude equations.Comment: 6 page, revte
A Noise Removal of the Penumbral Images by the Kernel Principal Component Analysis and its Evaluation
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