3,717 research outputs found
Cluster synchronization in an ensemble of neurons interacting through chemical synapses
In networks of periodically firing spiking neurons that are interconnected
with chemical synapses, we analyze cluster state, where an ensemble of neurons
are subdivided into a few clusters, in each of which neurons exhibit perfect
synchronization. To clarify stability of cluster state, we decompose linear
stability of the solution into two types of stabilities: stability of mean
state and stabilities of clusters. Computing Floquet matrices for these
stabilities, we clarify the total stability of cluster state for any types of
neurons and any strength of interactions even if the size of networks is
infinitely large. First, we apply this stability analysis to investigating
synchronization in the large ensemble of integrate-and-fire (IF) neurons. In
one-cluster state we find the change of stability of a cluster, which
elucidates that in-phase synchronization of IF neurons occurs with only
inhibitory synapses. Then, we investigate entrainment of two clusters of IF
neurons with different excitability. IF neurons with fast decaying synapses
show the low entrainment capability, which is explained by a pitchfork
bifurcation appearing in two-cluster state with change of synapse decay time
constant. Second, we analyze one-cluster state of Hodgkin-Huxley (HH) neurons
and discuss the difference in synchronization properties between IF neurons and
HH neurons.Comment: Notation for Jacobi matrix is changed. Accepted for publication in
Phys. Rev.
Consequences of a possible adiabatic transition between \nu=1/3 and \nu=1 quantum Hall states in a narrow wire
We consider the possibility of creating an adiabatic transition through a
narrow neck, or point contact, between two different quantized Hall states that
have the same number of edge modes, such as \nu=1 and \nu=1/3. We apply both
the composite fermion and the Luttinger liquid formalism to analyze the
transition. We suggest that using such adiabatic junctions one could build a DC
step-up transformer, where the output voltage is higher than the input.
Difficulties standing in the way of an experimental implementation of the
adiabatic junction are addressed.Comment: 4 pages RevTex, includes 2 eps figures, Submitted to Phys. Rev. Let
Relativistic Hall Effect
We consider the relativistic deformation of quantum waves and mechanical
bodies carrying intrinsic angular momentum (AM). When observed in a moving
reference frame, the centroid of the object undergoes an AM-dependent
transverse shift. This is the relativistic analogue of the spin Hall effect,
which occurs in free space without any external fields. Remarkably, the shifts
of the geometric and energy centroids differ by a factor of 2, and both
centroids are crucial for the correct Lorentz transformations of the AM tensor.
We examine manifestations of the relativistic Hall effect in quantum vortices,
and mechanical flywheels, and also discuss various fundamental aspects of this
phenomenon. The perfect agreement of quantum and relativistic approaches allows
applications at strikingly different scales: from elementary spinning
particles, through classical light, to rotating black-holes.Comment: 5 pages, 3 figures, to appear in Phys. Rev. Let
Localized matter-waves patterns with attractive interaction in rotating potentials
We consider a two-dimensional (2D) model of a rotating attractive
Bose-Einstein condensate (BEC), trapped in an external potential. First, an
harmonic potential with the critical strength is considered, which generates
quasi-solitons at the lowest Landau level (LLL). We describe a family of the
LLL quasi-solitons using both numerical method and a variational approximation
(VA), which are in good agreement with each other. We demonstrate that kicking
the LLL mode or applying a ramp potential sets it in the Larmor (cyclotron)
motion, that can also be accurately modeled by the VA.Comment: 13 pages, 11 figure
Temperature dependence of the conductivity of the electronic crystal
We study the temperature dependence of the conductivity of the 2D electronic
solid. In realistic samples, a domain structure forms in the solid and each
domain randomly orients in the absence of the in-plane field. At higher
temperature, the electron transport is governed by thermal activation form of
. The impurities will localize the
electron states along the edges of the crystal domains. At sufficient low
temperature, another transport mechanism called Mott's variable range hopping
mechanism, similar to that in a disorder insulator takes effect. We show that
as the temperature decreases, a crossover from the fixed range hopping of the
transport to the variable range hopping of transport in the 2D electron system
may be experimentally observed.Comment: 4 pages,1 figure
Structural properties of electrons in quantum dots in high magnetic fields: Crystalline character of cusp states and excitation spectra
The crystalline or liquid character of the downward cusp states in N-electron
parabolic quantum dots (QD's) at high magnetic fields is investigated using
conditional probability distributions obtained from exact diagonalization.
These states are of crystalline character for fractional fillings covering both
low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in
remarkable agreement with the rotating-Wigner-molecule ones [Phys. Rev. B 66,
115315 (2002)]. The crystalline arrangement consists of concentric polygonal
rings that rotate independently of each other, with the electrons on each ring
rotating coherently. We show that the rotation stabilizes the Wigner molecule
relative to the static one defined by the broken-symmetry
unrestricted-Hartree-Fock solution. We discuss the non-rigid behavior of the
rotating Wigner molecule and pertinent features of the excitation spectrum,
including the occurrence of a gap between the ground and first excited states
that underlies the incompressibility of the system. This leads us to conjecture
that the rotating crystal (and not the static one) remains the relevant ground
state for low fractional fillings even at the thermodynamic limit.Comment: Published version. Typos corrected. REVTEX4. 10 pages with 8
postscript figures (5 in color). For related papers, see
http://www.prism.gatech.edu/~ph274cy
Stability of the compressible quantum Hall state around the half-filled Landau level
We study the compressible states in the quantum Hall system using a mean
field theory on the von Neumann lattice. In the lowest Landau level, a kinetic
energy is generated dynamically from Coulomb interaction. The compressibility
of the state is calculated as a function of the filling factor and the
width of the spacer between the charge carrier layer and dopants. The
compressibility becomes negative below a critical value of and the state
becomes unstable at . Within a finite range around , the
stable compressible state exists above the critical value of .Comment: 4 pages, 4 Postscript figures, RevTe
Spin phase diagram of the nu_e=4/11 composite fermion liquid
Spin polarization of the "second generation" nu_e=4/11 fractional quantum
Hall state (corresponding to an incompressible liquid in a one-third-filled
composite fermion Landau level) is studied by exact diagonalization. Spin phase
diagram is determined for GaAs structures of different width and electron
concentration. Transition between the polarized and partially unpolarized
states with distinct composite fermion correlations is predicted for realistic
parameters.Comment: 5 pages, 3 figure
Quantum Hall effect in exfoliated graphene affected by charged impurities: metrological measurements
Metrological investigations of the quantum Hall effect (QHE) completed by
transport measurements at low magnetic field are carried out in
a-few--wide Hall bars made of monolayer (ML) or bilayer (BL)
exfoliated graphene transferred on substrate. From the
charge carrier density dependence of the conductivity and from the measurement
of the quantum corrections at low magnetic field, we deduce that transport
properties in these devices are mainly governed by the Coulomb interaction of
carriers with a large concentration of charged impurities. In the QHE regime,
at high magnetic field and low temperature (), the Hall
resistance is measured by comparison with a GaAs based quantum resistance
standard using a cryogenic current comparator. In the low dissipation limit, it
is found quantized within 5 parts in (one standard deviation, ) at the expected rational fractions of the von Klitzing constant,
respectively and in the ML and BL
devices. These results constitute the most accurate QHE quantization tests to
date in monolayer and bilayer exfoliated graphene. It turns out that a main
limitation to the quantization accuracy, which is found well above the
accuracy usually achieved in GaAs, is the low value of the QHE
breakdown current being no more than . The current dependence
of the longitudinal conductivity investigated in the BL Hall bar shows that
dissipation occurs through quasi-elastic inter-Landau level scattering,
assisted by large local electric fields. We propose that charged impurities are
responsible for an enhancement of such inter-Landau level transition rate and
cause small breakdown currents.Comment: 14 pages, 9 figure
Effect of a tilted magnetic field on the orientation of Wigner crystals
We study the effect of a tilted magnetic field on the orientation of Wigner
crystals by taking account of the width of a quantum well in the -direction.
It is found that the cohesive energy of the electronic crystal is always lower
for the direction parallel to the in-plane field. In a realistic
sample, a domain structure forms in the electronic solid and each domain
orients randomly when the magnetic field is normal to the quantum well. As the
field is tilted an angle, the electronic crystal favors to align along a
preferred direction which is determined by the in-plane magnetic field. The
orientation stabilization is strengthened for wider quantum wells as well as
for larger tilted angles. Possible consequence of the tilted field on the
transport property in the electronic solid is discussed
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