What happened to risk dispersion?

The turbulence in credit and funding markets in the second half of 2007 is disturbing evidence that risk dispersion in financial markets has been less effective than expected. Investors appear to have acquired risks that they did not understand. Much more worrisome, however, is the evidence that major financial firms did not succeed in shedding risks so much as in transferring them among their own business lines, resulting in an unintended concentration of risks on their own balance sheets. In order to restore confidence in the near term, and to put credit creation on a more sustainable path in the future, supervisory authorities, central banks and governments will first need to understand why the much-vaunted dispersion of risk fell so far short of expectations. The “reluctance to lend” which underlies these strains in money markets was widely attributed to concerns about the financial condition of borrowers, as a consequence of uncertainty about the value of assets on the borrowers’ balance sheets, and also to insuffi cient attention to liquidity management by financial firms. But the focus on uncertainty about borrowers ignores the awkward fact that the major financial intermediaries are both lenders and borrowers themselves and their reluctance to lend significantly reflects a defensive reaction to their own uncertainties about their own balance sheets. Better stress testing for liquidity as well as solvency would certainly be beneficial. Yet a major cause of the strains in credit and funding markets has been the apparent inability of many firms to anticipate the interaction of their various on- and off-balance sheet exposures and, particularly, to understand the velocity of their off-balance sheet activities and how these affected their overall exposures. In considering potential remedies to the credit market’s turbulence and to the apparent failure of risk dispersion, the authorities should first reflect on their own role in the trend of pushing risks off of bank balance sheets.

Cluster approach study of intersite electron correlations in pyrochlore and checkerboard lattices

To treat effects of electron correlations in geometrically frustrated pyrochlore and checkerboard lattices, an extended single-orbital Hubbard model with nearest neighbor hopping $\sim t$ and Coulomb repulsion $\sim V$ is applied. Infinite on-site repulsion, $U\to\infty$, is assumed, thus double occupancies of sites are forbidden completely in the present study. A variational Gutzwiller type approach is extended to examine correlations due to short-range $V-$interaction and a cluster approximation is developed to evaluate a variational ground state energy of the system. Obtained analytically in a special case of quarter band filling appropriate to LiV$_2$O$_4$, the resulting simple expression describes the ground state energy in the regime of intermediate and strong coupling $V$. Like in the Brinkman-Rice theory based on the standard Gutzwiller approach to the Hubbard model, the mean value of the kinetic energy is shown to be reduced strongly as the coupling $V$ approaches a critical value $V_{c}$. This finding may contribute to explaining the observed heavy fermion behavior in LiV$_2$O$_4$

Partial breakdown of quantum thermalization in a Hubbard-like model

We study the possible breakdown of quantum thermalization in a model of itinerant electrons on a one-dimensional chain without disorder, with both spin and charge degrees of freedom. The eigenstates of this model exhibit peculiar properties in the entanglement entropy, the apparent scaling of which is modified from a "volume law" to an "area law" after performing a partial, site-wise measurement on the system. These properties and others suggest that this model realizes a new, non-thermal phase of matter, known as a quantum disentangled liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.Comment: As accepted to PR

Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip

Recent experiments on triangular lattice organic Mott insulators have found evidence for a 2D spin liquid in proximity to the metal-insulator transition. A Gutzwiller wavefunction study of the triangular lattice Heisenberg model with appropriate four-spin ring exchanges has found that the projected spinon Fermi sea state has a low variational energy. This wavefunction, together with a slave particle gauge theory, suggests that such spin liquid possesses spin correlations that are singular along surfaces in momentum space ("Bose surfaces"). Signatures of this state, which we refer to as a "Spin Bose-Metal" (SBM), are expected to be manifest in quasi-1D ladder systems: The discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg strip (zigzag chain). Using DMRG, variational wavefunctions, and a Bosonization analysis, we map out the full phase diagram. Without ring exchange the model is equivalent to the J_1 - J_2 Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess particular singular wavevectors and allow us to identify this phase as the hoped for quasi-1D descendant SBM state. We derive a low energy theory and find three gapless modes and one Luttinger parameter controlling all power laws. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 VBS or a period-4 Chirality order, which we discover in the DMRG; we also find an interesting SBM state with partial ferromagnetism.Comment: 30 pages, 23 figure

Weakly versus highly nonlinear dynamics in 1D systems

We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order parameter, or a concentration profile. We show that two types of dynamics occur around the transition: weakly nonlinear dynamics, or highly nonlinear dynamics. The conditions under which highly nonlinear evolution equations appear are determined, and their generic form is derived. Finally, examples are discussed.Comment: to be published in Europhys. Let

The Pairwise Peculiar Velocity Dispersion of Galaxies: Effects of the Infall

We study the reliability of the reconstruction method which uses a modelling of the redshift distortions of the two-point correlation function to estimate the pairwise peculiar velocity dispersion of galaxies. In particular, the dependence of this quantity on different models for the infall velocity is examined for the Las Campanas Redshift Survey. We make extensive use of numerical simulations and of mock catalogs derived from them to discuss the effect of a self-similar infall model, of zero infall, and of the real infall taken from the simulation. The implications for two recent discrepant determinations of the pairwise velocity dispersion for this survey are discussed.Comment: minor changes in the discussion; accepted for publication in ApJ; 8 pages with 2 figures include

Universal transport signatures of Majorana fermions in superconductor-Luttinger liquid junctions

One of the most promising proposals for engineering topological superconductivity and Majorana fermions employs a spin-orbit coupled nanowire subjected to a magnetic field and proximate to an s-wave superconductor. When only part of the wire's length contacts to the superconductor, the remaining conducting portion serves as a natural lead that can be used to probe these Majorana modes via tunneling. The enhanced role of interactions in one dimension dictates that this configuration should be viewed as a superconductor-Luttinger liquid junction. We investigate such junctions between both helical and spinful Luttinger liquids, and topological as well as non-topological superconductors. We determine the phase diagram for each case and show that universal low-energy transport in these systems is governed by fixed points describing either perfect normal reflection or perfect Andreev reflection. In addition to capturing (in some instances) the familiar Majorana-mediated `zero-bias anomaly' in a new framework, we show that interactions yield dramatic consequences in certain regimes. Indeed, we establish that strong repulsion removes this conductance anomaly altogether while strong attraction produces dynamically generated effective Majorana modes even in a junction with a trivial superconductor. Interactions further lead to striking signatures in the local density of states and the line-shape of the conductance peak at finite voltage, and also are essential for establishing smoking-gun transport signatures of Majorana fermions in spinful Luttinger liquid junctions.Comment: 25 pages, 6 figures, v

Can crack front waves explain the roughness of cracks ?

We review recent theoretical progress on the dynamics of brittle crack fronts and its relationship to the roughness of fracture surfaces. We discuss the possibility that the intermediate scale roughness of cracks, which is characterized by a roughness exponent approximately equal to 0.5, could be caused by the generation, during local instabilities by depinning, of diffusively broadened corrugation waves, which have recently been observed to propagate elastically along moving crack fronts. We find that the theory agrees plausibly with the orders of magnitude observed. Various consequences and limitations, as well as alternative explanations, are discussed. We argue that another mechanism, possibly related to damage cavity coalescence, is needed to account for the observed large scale roughness of cracks that is characterized by a roughness exponent approximately equal to 0.8Comment: 26 pages, 3 .eps figure. Submitted to J. Mech. Phys. Solid