J. B. Marston

Spin quantum Hall effect in unconventional superconductors

We study the properties of the ‘‘spin quantum Hall fluid’’—a spin phase with quantized spin Hall conductance that is potentially realizable in superconducting systems with unconventional pairing symmetry. A simple realization is provided by a dx22y 21idxy superconductor which we argue has a dimensionless spin Hall conductance equal to 2. A theory of the edge states of the dx22y 21idxy superconductor is developed. The properties of the transition to a phase with vanishing spin Hall conductance induced by disorder are considered. We construct a description of this transition in terms of a supersymmetric spin chain, and use it to numerically determine universal properties of the transition. We discuss various possible experimental probes of this quantum Hall physics. @S0163-1829~99!00426-9#

Bosonization and fermion liquids in dimensions greater than one

We develop and describe new approaches to the problem of interacting fermions in spatial dimensions greater than 1. These approaches are based on generalizations of powerful tools previously applied to problems in one spatial dimension. We begin with a review of one-dimensional interacting fermions. We then introduce a simplified model in two spatial dimensions to study the role that spin and perfect nesting play in destabilizing fermion liquids. The complicated functional renormalization-group equations of the full problem are made tractable in our model by replacing the continuum of points that make up the closed Fermi line with four Fermi points

Statistics of an Unstable Barotropic Jet from a Cumulant Expansion

Low-order equal-time statistics of a barotropic flow on a rotating sphere are investigated. The flow is driven by linear relaxation toward an unstable zonal jet. For relatively short relaxation times, the flow is dominated by critical-layer waves. For sufficiently long relaxation times, the flow is turbulent. Statistics obtained from a second-order cumulant expansion are compared to those accumulated in direct numerical simulations, revealing the strengths and limitations of the expansion for different relaxation times.

Charge ordering and antiferromagnetic exchange in layered molecular crystals of the theta type

We consider the electronic properties of layered molecular crystals of the type theta -D(2)A where A is an anion and D is a donor molecule such as bis-(ethylenedithia-tetrathiafulvalene) (BEDT-TTF), which is arranged in the theta -type pattern within the layers. We argue that the simplest strongly correlated electron model that can describe the rich phase diagram of these materials is the extended Hubbard model on the square lattice at one-quarter filling. In the limit where the Coulomb repulsion on a single site is large, the nearest-neighbor Coulomb repulsion V plays a crucial role. When V is much larger than the intermolecular hopping integral t the ground state is an insulator with charge ordering. In this phase antiferromagnetism arises due to a novel fourth-order superexchange process around a plaquette on the square lattice. We argue that the charge ordered phase is destroyed below a critical nonzero value V, of the order of t. Slave-boson theory is used to explicitly demonstrate this for the SU(N) generalization of the model, in the large-N limit. We also discuss the relevance of the model to the all-organic family beta-(BEDT-TTF)(2)SF5YSO3 where Y=CH2CF2, CH2, CHF.

ASTROPHYSICAL FLUID DYNAMICS VIA DIRECT STATISTICAL SIMULATION

In this paper, we introduce the concept of direct statistical simulation for astrophysical flows. This technique may be appropriate for problems in astrophysical fluids where the instantaneous dynamics of the flows are of secondary importance to their statistical properties. We give examples of such problems including mixing and transport in planets, stars, and disks. The method is described for a general set of evolution equations, before we consider the specific case of a spectral method optimized for problems on a spherical surface. The method is illustrated for the simplest non-trivial example of hydrodynamics and magnetohydrodynamics on a rotating spherical surface. We then discuss possible extensions of the method both in terms of computational methods and the range of astrophysical problems that are of interest.

Feedbacks and landscape-level vegetation dynamics

Alternative stable-state theory (ASS) is widely accepted as explaining landscape-level vegetation dynamics, such as switches between forest and grassland. This theory argues that webs of feedbacks stabilise vegetation composition and structure, and that abrupt state shifts can occur if stabilising feedbacks are weakened. However, it is difficult to identify stabilising feedback loops and the disturbance thresholds beyond which state changes occur. Here, we argue that doing this requires a synthetic approach blending observation, experimentation, simulation, conceptual models, and narratives. Using forest boundaries and large mammal extinctions, we illustrate how a multifaceted research program can advance understanding of feedback-driven ecosystem change. Our integrative approach has applicability to other complex macroecological systems controlled by numerous feedbacks where controlled experimentation is impossible.

Direct statistical simulation of out-of-equilibrium jets.

We present direct statistical simulation of jet formation on a β plane, solving for the statistics of a fluid flow via an expansion in cumulants. Here we compare an expansion truncated at second order (CE2) to statistics accumulated by direct numerical simulations. We show that, for jets near equilibrium, CE2 is capable of reproducing the jet structure (although some differences remain in the second cumulant). However, as the degree of departure from equilibrium is increased (as measured by the zonostrophy parameter), the jets meander more and CE2 becomes less accurate. We discuss a possible remedy by inclusion of higher cumulants.

Broken Time-Reversal Symmetry in Strongly Correlated Ladder Structures

We provide, for the first time, in a doped strongly correlated system (two-leg ladder), a controlled theoretical demonstration of the existence of a state in which long-range ordered orbital currents are arranged in a staggered pattern, coexisting with a charge density wave. The method used is the highly accurate density-matrix renormalization group technique. This brings us closer to recent proposals that this order is realized in the enigmatic pseudogap phase of the cuprate high temperature superconductors.

Quantum phases of the Shastry-Sutherland antiferromagnet: Application to SrCu 2 ( BO 3 ) 2

We study possible paramagnetic phases of antiferromagnets on the Shastry-Sutherland lattice by a gauge-theoretic analysis of fluctuations in a theory with

The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

\mathrm{Sp}(2N)