1,825 research outputs found
Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks
The aim of the study was to compare the epidemic spread on static and dynamic
small-world networks. The network was constructed as a 2-dimensional
Watts-Strogatz model (500x500 square lattice with additional shortcuts), and
the dynamics involved rewiring shortcuts in every time step of the epidemic
spread. The model of the epidemic is SIR with latency time of 3 time steps. The
behaviour of the epidemic was checked over the range of shortcut probability
per underlying bond 0-0.5. The quantity of interest was percolation threshold
for the epidemic spread, for which numerical results were checked against an
approximate analytical model. We find a significant lowering of percolation
thresholds for the dynamic network in the parameter range given. The result
shows that the behaviour of the epidemic on dynamic network is that of a static
small world with the number of shortcuts increased by 20.7 +/- 1.4%, while the
overall qualitative behaviour stays the same. We derive corrections to the
analytical model which account for the effect. For both dynamic and static
small-world we observe suppression of the average epidemic size dependence on
network size in comparison with finite-size scaling known for regular lattice.
We also study the effect of dynamics for several rewiring rates relative to
latency time of the disease.Comment: 13 pages, 6 figure
Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma
The two-dimensional one-component plasma (2dOCP) is a system of mobile
particles of the same charge on a surface with a neutralising background.
The Boltzmann factor of the 2dOCP at temperature can be expressed as a
Vandermonde determinant to the power . Recent advances in
the theory of symmetric and anti-symmetric Jack polymonials provide an
efficient way to expand this power of the Vandermonde in their monomial basis,
allowing the computation of several thermodynamic and structural properties of
the 2dOCP for values up to 14 and equal to 4, 6 and 8. In this
work, we explore two applications of this formalism to study the moments of the
pair correlation function of the 2dOCP on a sphere, and the distribution of
radial linear statistics of the 2dOCP in the plane
A planar diagram approach to the correlation problem
We transpose an idea of 't Hooft from its context of Yang and Mills' theory
of strongly interacting quarks to that of strongly correlated electrons in
transition metal oxides and show that a Hubbard model of N interacting electron
species reduces, to leading orders in N, to a sum of almost planar diagrams.
The resulting generating functional and integral equations are very similar to
those of the FLEX approximation of Bickers and Scalapino. This adds the Hubbard
model at large N to the list of solvable models of strongly correlated
electrons.
PACS Numbers: 71.27.+a 71.10.-w 71.10.FdComment: revtex, 5 pages, with 3 eps figure
Hamiltonian Theory of the FQHE: Conserving Approximation for Incompressible Fractions
A microscopic Hamiltonian theory of the FQHE developed by Shankar and the
present author based on the fermionic Chern-Simons approach has recently been
quite successful in calculating gaps and finite tempertature properties in
Fractional Quantum Hall states. Initially proposed as a small- theory, it
was subsequently extended by Shankar to form an algebraically consistent theory
for all in the lowest Landau level. Such a theory is amenable to a
conserving approximation in which the constraints have vanishing correlators
and decouple from physical response functions. Properties of the incompressible
fractions are explored in this conserving approximation, including the
magnetoexciton dispersions and the evolution of the small- structure factor
as \nu\to\half. Finally, a formalism capable of dealing with a nonuniform
ground state charge density is developed and used to show how the correct
fractional value of the quasiparticle charge emerges from the theory.Comment: 15 pages, 2 eps figure
Edge reconstructions in fractional quantum Hall systems
Two dimensional electron systems exhibiting the fractional quantum Hall
effects are characterized by a quantized Hall conductance and a dissipationless
bulk. The transport in these systems occurs only at the edges where gapless
excitations are present. We present a {\it microscopic} calculation of the edge
states in the fractional quantum Hall systems at various filling factors using
the extended Hamiltonian theory of the fractional quantum Hall effect. We find
that at the quantum Hall edge undergoes a reconstruction as the
background potential softens, whereas quantum Hall edges at higher filling
factors, such as , are robust against reconstruction. We present
the results for the dependence of the edge states on various system parameters
such as temperature, functional form and range of electron-electron
interactions, and the confining potential. Our results have implications for
the tunneling experiments into the edge of a fractional quantum Hall system.Comment: 11 pages, 9 figures; minor typos corrected; added 2 reference
Impurity scattering and transport of fractional Quantum Hall edge state
We study the effects of impurity scattering on the low energy edge state
dynamic s for a broad class of quantum Hall fluids at filling factor , for integer and even integer . When is positive all
of the edge modes are expected to move in the same direction, whereas for
negative one mode moves in a direction opposite to the other modes.
Using a chiral-Luttinger model to describe the edge channels, we show that for
an ideal edge when is negative, a non-quantized and non-universal Hall
conductance is predicted. The non-quantized conductance is associated with an
absence of equilibration between the edge channels. To explain the robust
experimental Hall quantization, it is thus necessary to incorporate impurity
scattering into the model, to allow for edge equilibration. A perturbative
analysis reveals that edge impurity scattering is relevant and will modify the
low energy edge dynamics. We describe a non-perturbative solution for the
random channel edge, which reveals the existence of a new
disorder-dominated phase, characterized by a stable zero temperature
renormalization group fixed point. The phase consists of a single propagating
charge mode, which gives a quantized Hall conductance, and neutral modes.
The neutral modes all propagate at the same speed, and manifest an exact SU(n)
symmetry. At finite temperatures the SU(n) symmetry is broken and the neutral
modes decay with a finite rate which varies as at low temperatures.
Various experimental predictions and implications which follow from the exact
solution are described in detail, focusing on tunneling experiments through
point contacts.Comment: 19 pages (two column), 5 post script figures appended, 3.0 REVTE
Predictors of loneliness during the Covid-19 pandemic in people with dementia and their carers in England: findings from the DETERMIND-C19 study
Objectives
To identify factors that predict the risk of loneliness for people with dementia and carers during a pandemic.
Methods
People with dementia and their carers completed assessments before (July 2019–March 2020; 206 dyads) and after (July–October 2020) the first Covid-19 ‘lockdown’ in England. At follow-up, the analytic sample comprised 67 people with dementia and 108 carers. We built a longitudinal path model with loneliness as an observed outcome. Carer type and social contacts at both measurements were considered. Other social resources (quality of relationship, formal day activities), wellbeing (anxiety, psychological wellbeing) and cognitive impairment were measured with initial level and change using latent growth curves. We adjusted for socio-demographic factors and health at baseline.
Results
In carers, higher levels of loneliness were directly associated with non-spouse coresident carer type, level and increase of anxiety in carer, more formal day activities, and higher cognitive impairment in the person with dementia. In people with dementia, non-spouse coresident carer type, and higher initial levels of social resources, wellbeing, and cognitive impairment predicted the changes in these factors; this produced indirect effects on social contacts and loneliness.
Conclusion
Loneliness in the Covid-19 pandemic appears to be shaped by different mechanisms for people with dementia and their carers. The results suggest that carers of those with dementia may prioritize providing care that protects the person with dementia from loneliness at the cost of experiencing loneliness themselves. Directions for the promotion of adaptive social care during the Covid-19 pandemic and beyond are discussed
Charge and spin configurations in the coupled quantum dots with Coulomb correlations induced by tunneling current
We investigated the peculiarities of non-equilibrium charge states and spin
configurations in the system of two strongly coupled quantum dots (QDs) weakly
connected to the electrodes in the presence of Coulomb correlations. We
analyzed the modification of non-equilibrium charge states and different spin
configurations of the system in a wide range of applied bias voltage and
revealed well pronounced ranges of system parameters where negative tunneling
conductivity appears due to the Coulomb correlations.Comment: 10 pages, 6 figure
Conductance oscillations in strongly correlated fractional quantum Hall line junctions
We present a detailed theory of transport through line junctions formed by
counterpropagating single-branch fractional-quantum-Hall edge channels having
different filling factors. Intriguing transport properties are exhibited when
strong Coulomb interactions between electrons from the two edges are present.
Such strongly correlated line junctions can be classified according to the
value of an effective line-junction filling factor n that is the inverse of an
even integer. Interactions turn out to affect transport most importantly for
n=1/2 and n=1/4. A particularly interesting case is n=1/4 corresponding to,
e.g., a junction of edge channels having filling factor 1 and 1/5,
respectively. We predict its differential tunneling conductance to oscillate as
a function of voltage. This behavior directly reflects the existence of novel
Majorana-fermion quasiparticle excitations in this type of line junction.
Experimental accessibility of such systems in current cleaved-edge overgrown
samples enables direct testing of our theoretical predictions.Comment: 2 figures, 10 pages, RevTex4, v2: added second figure for clarit
Ring exchange, the Bose metal, and bosonization in two dimensions
Motivated by the high-T_c cuprates, we consider a model of bosonic Cooper
pairs moving on a square lattice via ring exchange. We show that this model
offers a natural middle ground between a conventional antiferromagnetic Mott
insulator and the fully deconfined fractionalized phase which underlies the
spin-charge separation scenario for high-T_c superconductivity. We show that
such ring models sustain a stable critical phase in two dimensions, the *Bose
metal*. The Bose metal is a compressible state, with gapless but uncondensed
boson and ``vortex'' excitations, power-law superconducting and charge-ordering
correlations, and broad spectral functions. We characterize the Bose metal with
the aid of an exact plaquette duality transformation, which motivates a
universal low energy description of the Bose metal. This description is in
terms of a pair of dual bosonic phase fields, and is a direct analog of the
well-known one-dimensional bosonization approach. We verify the validity of the
low energy description by numerical simulations of the ring model in its exact
dual form. The relevance to the high-T_c superconductors and a variety of
extensions to other systems are discussed, including the bosonization of a two
dimensional fermionic ring model
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