725 research outputs found
The price of anarchy in basketball
Optimizing the performance of a basketball offense may be viewed as a network
problem, wherein each play represents a "pathway" through which the ball and
players may move from origin (the in-bounds pass) to goal (the basket).
Effective field goal percentages from the resulting shot attempts can be used
to characterize the efficiency of each pathway. Inspired by recent discussions
of the "price of anarchy" in traffic networks, this paper makes a formal
analogy between a basketball offense and a simplified traffic network. The
analysis suggests that there may be a significant difference between taking the
highest-percentage shot each time down the court and playing the most efficient
possible game. There may also be an analogue of Braess's Paradox in basketball,
such that removing a key player from a team can result in the improvement of
the team's offensive efficiency.Comment: 9 pages, 6 figures; extra example and some discussion added;
formatting errors fixed; typo in Sec. IIID fixe
Chemical potential and compressibility of quantum Hall bilayer excitons
This paper considers a system of two parallel quantum Hall layers with total
filling factor or . When the distance between the layers is small
enough, electrons and holes in opposite layers form inter-layer excitons, which
have a finite effective mass and interact via a dipole-dipole potential.
Results are presented for the chemical potential of the resulting bosonic
system as a function of the exciton concentration and the interlayer
separation . Both and the interlayer capacitance have an unusual
nonmonotonic dependence on , owing to the interplay between an increasing
dipole moment and an increasing effective mass with increasing . A phase
transition between superfluid and Wigner crystal phases is shown to occur at . Results are derived first via simple intuitive arguments,
and then verified with more careful analytic derivations and numeric
calculations.Comment: 7 pages, 5 figures; improved discussion and references; published
versio
Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites
Variable-range hopping conductivity has long been understood in terms of a
canonical prescription for relating the single-particle density of states to
the temperature-dependent conductivity. Here we demonstrate that this
prescription breaks down in situations where a large and long-ranged random
potential develops. In particular, we examine a canonical model of a completely
compensated semiconductor, and we show that at low temperatures hopping
proceeds along self-organized, low-dimensional subspaces having fractal
dimension . We derive and study numerically the spatial structure of
these subspaces, as well as the conductivity and density of states that result
from them. One of our prominent findings is that fractal ordering of low energy
sites greatly enhances the hopping conductivity, and allows Efros-Shklovskii
type conductivity to persist up to unexpectedly high temperatures.Comment: 9 pages, 6 figures; published version with added references and
discussio
Large, nonsaturating thermopower in a quantizing magnetic field
The thermoelectric effect is the generation of an electrical voltage from a
temperature gradient in a solid material due to the diffusion of free charge
carriers from hot to cold. Identifying materials with large thermoelectric
response is crucial for the development of novel electric generators and
coolers. In this paper we consider theoretically the thermopower of Dirac/Weyl
semimetals subjected to a quantizing magnetic field. We contrast their
thermoelectric properties with those of traditional heavily-doped
semiconductors and we show that, under a sufficiently large magnetic field, the
thermopower of Dirac/Weyl semimetals grows linearly with the field without
saturation and can reach extremely high values. Our results suggest an
immediate pathway for achieving record-high thermopower and thermoelectric
figure of merit, and they compare well with a recent experiment on
PbSnSe.Comment: 6+3 pages, 4 figures; update discussion of experiments and device
performanc
Thermoelectric Hall conductivity and figure of merit in Dirac/Weyl materials
We calculate the thermoelectric response coefficients of three-dimensional
Dirac or Weyl semimetals as a function of magnetic field, temperature, and
Fermi energy. We focus in particular on the thermoelectric Hall coefficient
and the Seebeck coefficient , which are well-defined even
in the dissipationless limit. We contrast the behaviors of and
with those of traditional Schr\"{o}dinger particle systems, such as
doped semiconductors. Strikingly, we find that for Dirac materials
acquires a constant, quantized value at sufficiently large
magnetic field, which is independent of the magnetic field or the Fermi energy,
and this leads to unprecedented growth in the thermopower and the
thermoelectric figure of merit. We further show that even relatively small
fields, such that (where is the cyclotron
frequency and is the scattering time), are sufficient to produce a more
than increase in the figure of merit.Comment: 10 pages, 5 figure
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