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 $N$ mobile particles of the same charge $q$ on a surface with a neutralising background. The Boltzmann factor of the 2dOCP at temperature $T$ can be expressed as a Vandermonde determinant to the power $\Gamma=q^{2}/(k_B T)$. 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 $N$ values up to 14 and $\Gamma$ 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-$q$ theory, it was subsequently extended by Shankar to form an algebraically consistent theory for all $q$ 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-$q$ 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 $\nu=1/3$ the quantum Hall edge undergoes a reconstruction as the background potential softens, whereas quantum Hall edges at higher filling factors, such as $\nu=2/5, 3/7$, 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 $\nu =n/(np+1)$, for integer $n$ and even integer $p$. When $p$ is positive all $n$ of the edge modes are expected to move in the same direction, whereas for negative $p$ one mode moves in a direction opposite to the other $n-1$ modes. Using a chiral-Luttinger model to describe the edge channels, we show that for an ideal edge when $p$ 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 $n$ 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 $n-$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 $n-1$ 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 $T^2$ 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

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

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

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