Fire is a worldwide phenomenon that appears in the geological record soon after the appearance of terrestrial plants. Fire influences global ecosystem patterns and processes, including vegetation distribution and structure, the carbon cycle, and climate. Although humans and fire have always coexisted, our capacity to manage fire remains imperfect and may become more difficult in the future as climate change alters fire regimes. This risk is difficult to assess, however, because fires are still poorly represented in global models. Here, we discuss some of the most important issues involved in developing a better understanding of the role of fire in the Earth system.

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Cazalilla and Marston Reply:The authors of the Comment [1] propose an improvement to our timedependent density-matrix renormalization group (TdDMRG) algorithm as described in our Letter [2], providing few details about the proposed extension. Luo, Xiang, and Wang (LXW) [1] then point out that the oscillations at late times (t > 18) shown in two of the lines plotted in Fig. 2 of our manuscript are an artifact of the truncation of the Hilbert space.LXW are correct that the oscillations we reported in the one case of V=w 1:1 are in fact spurious. We had systematically examined the errors induced by truncations of the Hilbert space in our Letter. However, we failed to notice that, for the case of V=w 1:1 when the leads are insulating, the eigenvalues of the reduced density matrices become so small so quickly (due to the gap to excitations) that our code discarded the same portion of the Hilbert space for truncations M 256 and 512. Thus we were left with the illusion that we had achieved convergence in this one case, when in fact we had not.Unfortunately the Comment [1] does not provide enough details regarding the construction of the (reduced) density matrix. As Eq. (1) of the Comment [1] shows, LXW's density matrix requires knowledge of the wave function at different times; but to obtain the timeevolved wave function, one needs the density matrix in the first place. Thus it seems that LXW use an iterative procedure: LXW apparently carry out repeated integrations forward in time for each chain size starting with the shortest chain, of length four sites. Once the density matrix is constructed for a chain of a given length, it is then lengthened by the addition of two sites via the usual (infinite-size) density-matrix renormalization group (DMRG) algorithm, and time integration is repeated again from the beginning. The process is then repeated until a sufficiently long chain is built up, tailored to the particular choice of applied bias. Thus the proposed modification of our TdDMRG algorithm is computationally intensive and time-consuming. We further point out

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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 d x 2 Ϫy 2ϩ id xy superconductor which we argue has a dimensionless spin Hall conductance equal to 2. A theory of the edge states of the d x 2 Ϫy 2ϩ id xy 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.

We develop and describe new approaches to the problem of interacting Fermions in spatial dimensions greater than one. 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. Despite this drastic approximation, the model exhibits physically reasonable behavior both at half-filling (where instabilities occur) and away from half-filling (where a Luttinger liquid arises). Next we implement the Bosonization of higher dimensional Fermi surfaces introduced by Luther and advocated most recently by Haldane. Bosonization incorporates the phase space and small-angle scattering processes neglected in our model (but does not, as yet, addressquestions of stability). The charge sector is equivalent to an exactly solvable Gaussian quantum field theory; the spin sector, however, must be solved semiclassically. Using the Luther-Haldane approach we recover the collective mode equation of Fermi-liquid theory and in three dimensions reproduce the T 3 ln(T ) contribution to the specific heat due to small angle scattering processes. We conclude with a discussion of our results and some speculation about future possibilities.

The ground state of the spin-i nearest-neighbor Heisenberg quantum antiferromagnet on the KagomC lattice probably lacks &in order; therefore, conventional spin-wave analysis breaks down. To ascertain the ground state, we instead use a systematic l/n expansion with .SU(n) fermions. Two distinct states occur in the large-n limit, depending on the size of the biquadratic interaction z When ?=O, there are an infinite number of degenerate. ground states consisting of disconnected dimers. At finite n, however, this degeneracy is broken by local resonance. In qontrast, a globally resonating chiral spin-liquid phase with no spin-Peierls modulation-is. the likely large-n ground state at sufficiently large f For intermediate values of J, a phase transition from the dimer state to the chiral phase occurs as the temperature &-eases. At a higher temperature, there is a second transition to a paramagnetic state. We comment on the possibility that these phases are experimentally realized by the nuclear magneti.q.motients of a second layer of 3He atoms lying on a graphite surface.

Topology sheds new light on the emergence of unidirectional edge waves in a variety of physical systems, from condensed matter to artificial lattices. Waves observed in geophysical flows are also robust to perturbations, which suggests a role for topology. We show a topological origin for two well-known equatorially trapped waves, the Kelvin and Yanai modes, owing to the breaking of time-reversal symmetry by Earth's rotation. The nontrivial structure of the bulk Poincaré wave modes encoded through the first Chern number of value 2 guarantees the existence of these waves. This invariant demonstrates that ocean and atmospheric waves share fundamental properties with topological insulators and that topology plays an unexpected role in Earth's climate system.