2,967 research outputs found
Quantum Algorithm for Triangle Finding in Sparse Graphs
This paper presents a quantum algorithm for triangle finding over sparse
graphs that improves over the previous best quantum algorithm for this task by
Buhrman et al. [SIAM Journal on Computing, 2005]. Our algorithm is based on the
recent -query algorithm given by Le Gall [FOCS 2014] for
triangle finding over dense graphs (here denotes the number of vertices in
the graph). We show in particular that triangle finding can be solved with
queries for some constant whenever the graph
has at most edges for some constant .Comment: 13 page
A dusty pinwheel nebula around the massive star WR 104
Wolf-Rayet (WR) stars are luminous massive blue stars thought to be immediate
precursors to the supernova terminating their brief lives. The existence of
dust shells around such stars has been enigmatic since their discovery some 30
years ago; the intense radiation field from the star should be inimical to dust
survival. Although dust-creation models, including those involving interacting
stellar winds from a companion star, have been put forward, high-resolution
observations are required to understand this phenomena. Here we present
resolved images of the dust outflow around Wolf-Rayet WR 104, obtained with
novel imaging techniques, revealing detail on scales corresponding to about 40
AU at the star. Our maps show that the dust forms a spatially confined stream
following precisely a linear (or Archimedian) spiral trajectory. Images taken
at two separate epochs show a clear rotation with a period of 220 +/- 30 days.
Taken together, these findings prove that a binary star is responsible for the
creation of the circumstellar dust, while the spiral plume makes WR 104 the
prototype of a new class of circumstellar nebulae unique to interacting wind
systems.Comment: 7 pages, 2 figures, Appearing in Nature (1999 April 08
Gate-controlled Guiding of Electrons in Graphene
Ballistic semiconductor structures have allowed the realization of
optics-like phenomena in electronics, including magnetic focusing and lensing.
An extension that appears unique to graphene is to use both n and p carrier
types to create electronic analogs of optical devices having both positive and
negative indices of refraction. Here, we use gate-controlled density with both
p and n carrier types to demonstrate the analog of the fiber-optic guiding in
graphene. Two basic effects are investigated: (1) bipolar p-n junction guiding,
based on the principle of angle-selective transmission though the graphene p-n
interface, and (2) unipolar fiber-optic guiding, using total internal
reflection controlled by carrier density. Modulation of guiding efficiency
through gating is demonstrated and compared to numerical simulations, which
indicates that interface roughness limits guiding performance, with
few-nanometer effective roughness extracted. The development of p-n and
fiber-optic guiding in graphene may lead to electrically reconfigurable wiring
in high-mobility devices.Comment: supplementary materal at
http://marcuslab.harvard.edu/papers/OG_SI.pd
Quantum interference and Klein tunneling in graphene heterojunctions
The observation of quantum conductance oscillations in mesoscopic systems has
traditionally required the confinement of the carriers to a phase space of
reduced dimensionality. While electron optics such as lensing and focusing have
been demonstrated experimentally, building a collimated electron interferometer
in two unconfined dimensions has remained a challenge due to the difficulty of
creating electrostatic barriers that are sharp on the order of the electron
wavelength. Here, we report the observation of conductance oscillations in
extremely narrow graphene heterostructures where a resonant cavity is formed
between two electrostatically created bipolar junctions. Analysis of the
oscillations confirms that p-n junctions have a collimating effect on
ballistically transmitted carriers. The phase shift observed in the conductance
fringes at low magnetic fields is a signature of the perfect transmission of
carriers normally incident on the junctions and thus constitutes a direct
experimental observation of ``Klein Tunneling.''Comment: 13 pages and 6 figures including supplementary information. The paper
has been modified in light of new theoretical results available at
arXiv:0808.048
Wigner Crystallization in a Quasi-3D Electronic System
When a strong magnetic field is applied perpendicularly (along z) to a sheet
confining electrons to two dimensions (x-y), highly correlated states emerge as
a result of the interplay between electron-electron interactions, confinement
and disorder. These so-called fractional quantum Hall (FQH) liquids form a
series of states which ultimately give way to a periodic electron solid that
crystallizes at high magnetic fields. This quantum phase of electrons has been
identified previously as a disorder-pinned two-dimensional Wigner crystal with
broken translational symmetry in the x-y plane. Here, we report our discovery
of a new insulating quantum phase of electrons when a very high magnetic field,
up to 45T, is applied in a geometry parallel (y-direction) to the
two-dimensional electron sheet. Our data point towards this new quantum phase
being an electron solid in a "quasi-3D" configuration induced by orbital
coupling with the parallel field
Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding
The motion of massless Dirac-electrons in graphene mimics the propagation of
photons. This makes it possible to control the charge-carriers with components
based on geometrical-optics and has led to proposals for an all-graphene
electron-optics platform. An open question arising from the possibility of
reducing the component-size to the nanometer-scale is how to access and
understand the transition from optical-transport to quantum-confinement. Here
we report on the realization of a circular p-n junction that can be
continuously tuned from the nanometer-scale, where quantum effects are
dominant, to the micrometer scale where optical-guiding takes over. We find
that in the nanometer-scale junction electrons are trapped in states that
resemble atomic-collapse at a supercritical charge. As the junction-size
increases, the transition to optical-guiding is signaled by the emergence of
whispering-gallery modes and Fabry-Perot interference. The creation of tunable
junctions that straddle the crossover between quantum-confinement and
optical-guiding, paves the way to novel design-architectures for controlling
electronic transport.Comment: 16 pages, 4 figure
Quantum and classical confinement of resonant states in a trilayer graphene Fabry-Pérot interferometer
The advent of few-layer graphene has given rise to a new family of two-dimensional systems with emergent electronic properties governed by relativistic quantum mechanics. The multiple carbon sublattices endow the electronic wavefunctions with pseudospin, a lattice analogue of the relativistic electron spin, whereas the multilayer structure leads to electric-field-effect tunable electronic bands. Here we use these properties to realize giant conductance oscillations in ballistic trilayer graphene Fabry-Pérot interferometers, which result from phase coherent transport through resonant bound states beneath an electrostatic barrier. We confine these states by selectively decoupling them from the leads, resulting in transport via non-resonant states and suppression of the giant oscillations. The confinement is achieved both classically, by manipulating quasiparticle momenta with a magnetic field, and quantum mechanically, by locally varying the pseudospin character of the carrier wavefunctions. Our results illustrate the unique potential of trilayer graphene as a versatile platform for electron optics and pseudospintronics.United States. Office of Naval Research (GATE MURI)National Science Foundation (U.S.) (Career Award DMR-0845287)Conselho Nacional de Pesquisas (Brazil
Quantum and classical confinement of resonant states in a trilayer graphene Fabry-Pérot interferometer
The advent of few-layer graphene has given rise to a new family of two-dimensional systems with emergent electronic properties governed by relativistic quantum mechanics. The multiple carbon sublattices endow the electronic wavefunctions with pseudospin, a lattice analogue of the relativistic electron spin, whereas the multilayer structure leads to electric-field-effect tunable electronic bands. Here we use these properties to realize giant conductance oscillations in ballistic trilayer graphene Fabry-Pérot interferometers, which result from phase coherent transport through resonant bound states beneath an electrostatic barrier. We confine these states by selectively decoupling them from the leads, resulting in transport via non-resonant states and suppression of the giant oscillations. The confinement is achieved both classically, by manipulating quasiparticle momenta with a magnetic field, and quantum mechanically, by locally varying the pseudospin character of the carrier wavefunctions. Our results illustrate the unique potential of trilayer graphene as a versatile platform for electron optics and pseudospintronics.United States. Office of Naval Research (GATE MURI)National Science Foundation (U.S.) (Career Award DMR-0845287)Conselho Nacional de Pesquisas (Brazil
Type Ia Supernova Explosion Models
Because calibrated light curves of Type Ia supernovae have become a major
tool to determine the local expansion rate of the Universe and also its
geometrical structure, considerable attention has been given to models of these
events over the past couple of years. There are good reasons to believe that
perhaps most Type Ia supernovae are the explosions of white dwarfs that have
approached the Chandrasekhar mass, M_ch ~ 1.39 M_sun, and are disrupted by
thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such
accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent
progress in modeling Type Ia supernovae as well as several of the still open
questions are addressed in this review. Although the main emphasis will be on
studies of the explosion mechanism itself and on the related physical
processes, including the physics of turbulent nuclear combustion in degenerate
stars, we also discuss observational constraints.Comment: 38 pages, 4 figures, Annual Review of Astronomy and Astrophysics, in
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