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J. B. Marston

Publications and source records attributed to J. B. Marston.

At least 55 records · Page 3Linked to original sources
arXiv2014

Hyperviscosity and statistical equilibria of Euler turbulence on the torus and the sphere

Coherent structures such as jets and vortices appear in two-dimensional (2D) turbulence. To gain insight into both numerical simulation and equilibrium statistical mechanical descriptions of 2D Euler flows, the Euler equation with added hyperviscosity is integrated forward in time on the square torus and on the sphere. Coherent structures that form are compared against a hierarchy of truncated Miller-Robert-Sommeria equilibria. The energy-circulation-enstrophy MRS-2 description produces a complete condensation of energy to the largest scales, and in the absence of rotation correctly predicts the number and polarity of coherent vortices. Perturbative imposition of the quartic Casimir constraint improves agreement with numerical simulation by sharpening the cores and transferring some energy to smaller-scale modes. MRS-2 cannot explain qualitative changes due to rotation, but descriptions that conserve higher Casimirs beyond enstrophy have the potential to do so. The result is in agreement with the somewhat paradoxical observation that hyperviscosity helps to remedy the non-conservation of the third and higher Casimirs in numerical simulation. For a rotating sphere, numerical simulation also demonstrates that coherent structures found at late times depend on initial conditions, limiting the usefulness of statistical mechanics.

physics.flu-dyn↗
arXiv2012

Rectification by Doped Mott-Insulator Junctions

Junctions of doped Mott insulators offer a route to rectification at frequencies beyond the terahertz range. Mott insulators have strong electronic correlations and therefore short timescales for electron-electron scattering. It is this short time scale that allows for the possibility of rectification at frequencies higher than those of semiconductor devices that are limited by the slow diffusion of charge carriers. We model a junction by a one dimensional chain of electrons with p- and n-doping on the two halves of the chain. Two types of systems are investigated: spin polarized electrons with nearest-neighbor interaction, and spin-half electrons that interact via on-site repulsion (the Hubbard model). For short chains the many-body Schrodinger equation can be integrated numerically exactly, and when driven by an oscillating electromagnetic field such idealized junctions rectify, showing a preferred direction for charge transfer. Longer chains are studied by the time-dependent density-matrix renormalization-group method, and also shown to rectify.

cond-mat.str-el↗
arXiv2011

Planetary Atmospheres as Non-Equilibrium Condensed Matter

Planetary atmospheres, and models of them, are discussed from the viewpoint of condensed matter physics. Atmospheres are a form of condensed matter, and many interesting phenomena of condensed matter systems are realized by them. The essential physics of the general circulation is illustrated with idealized 2-layer and 1-layer models of the atmosphere. Equilibrium and non-equilibrium statistical mechanics are used to directly ascertain the statistics of these models.

cond-mat.stat-mech↗
arXiv2011

Strong Correlations in Actinide Redox Reactions

Reduction-oxidation (redox) reactions of the redox couples An(VI)/An(V), An(V)/An(IV), and An(IV)/An(III), where An is an element in the family of early actinides (U, Np, and Pu), as well as Am(VI)/Am(V) and Am(V)/Am(III), are modeled by combining density functional theory with a generalized Anderson impurity model that accounts for the strong correlations between the 5f electrons. Diagonalization of the Anderson impurity model yields improved estimates for the redox potentials and the propensity of the actinide complexes to disproportionate.

cond-mat.str-el↗
arXiv2010

Astrophysical Fluid Dynamics via Direct Statistical Simulation

In this paper we introduce the concept of Direct Statistical Simulation (DSS) 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 optimised for problems on a spherical surface. The method is illustrated for the simplest non-trivial example of hydrodynamics and MHD 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.

astro-ph.SR↗
arXiv2010

Statistics of the General Circulation from Cumulant Expansions

Large-scale atmospheric flows may not be so nonlinear as to preclude their statistical description by systematic expansions in cumulants. I extend previous work by examining a two-layer baroclinic model of the general circulation. The fixed point of the cumulant expansion describes the statistically steady state of the out-of-equilibrium model. Equal-time statistics so obtained agree well with those accumulated by direct numerical simulation.

physics.ao-ph↗
arXiv2008

Weak Ferromagnetic Exchange and Anomalous Specific Heat in ZnCu3(OH)6Cl2

Experimental evidence for a plethora of low energy spin excitations in the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2 may be understandable in terms of an extended Fermi surface of spinons coupled to a U(1) gauge field. We carry out variational calculations to examine the possibility that such a state may be energetically viable. A Gutzwiller-projected wavefunction reproduces the dimerization of a kagome strip found previously by DMRG. Application to the full kagome lattice shows that the inclusion of a small ferromagnetic next-nearest-neighbor interaction favors a ground state with a spinon Fermi surface.

cond-mat.str-el↗
arXiv2007

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.

physics.flu-dyn↗
arXiv2007

SU(N) quantum spin models: A variational wavefunction study

The study of SU(N) quantum spin models is relevant to a variety of physical systems including ultracold atoms in optical lattices, and also leads to insights into novel quantum phases and phase transitions of SU(2) spin models. We use Gutzwiller projected fermionic variational wavefunctions to explore the phase diagram and correlation functions of SU(N) spin models in the self-conjugate representation, with Heisenberg bilinear and biquadratic interactions. In 1D, the variational phase diagram of the SU(4) spin chain is constructed by examining instabilities of the Gutzwiller projected free fermion ground state to various broken symmetries, and it agrees well with exact results.The spin and dimer correlations of the Gutzwiller projected free fermion state with N flavors of fermions are also in good agreement with exact and 1/N calculations for the critical points of SU(N) spin chains. In 2D, the variational phase diagram on the square lattice is obtained by studying instabilities of the Gutzwiller projected pi-flux state. The variational ground state of the pure Heisenberg model is found to exhibit long range Neel order for N=2,4 and spin Peierls order for N > 4. For N=4 and 6, biquadratic interactions lead to a complex phase diagram which includes an extended valence bond crystal in both cases, as well as a stable pi-flux phase for N=6. The spin correlations of the projected pi-flux state at N=4 are in good agreement with 1/N calculations. We find that this state also shows strongly enhanced dimer correlations, in qualitative accord with the large-N results. We compare our results with a recent QMC study of the SU(4) Heisenberg model.

cond-mat.str-el↗
arXiv2005

Phase diagram of the three band half-filled Cu-O two-leg ladder

We determine the phase diagram of the half-filled two-leg ladder both at weak and strong coupling, taking into account the Cu d_{x^2-y^2} and the O p_x and p_y orbitals. At weak coupling, renormalization group flows are interpreted with the use of bosonization. Two different models with and without outer oxygen orbitals are examined. For physical parameters, and in the absence of the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears when the outer oxygen atoms are included. We show that the circulating current phase that preserves translational symmetry does not appear at weak coupling. In the opposite strong-coupling atomic limit the model is purely electrostatic and the ground states may be found by simple energy minimization. The phase diagram so obtained is compared to the weak-coupling one.

cond-mat.str-el↗
arXiv2005

Rectification in one--dimensional electronic systems

Asymmetric current--voltage ($I(V)$) curves, known as the diode or rectification effect, in one--dimensional electronic conductors can have their origin from scattering off a single asymmetric impurity in the system. We investigate this effect in the framework of the Tomonaga--Luttinger model for electrons with spin. We show that electron interactions strongly enhance the diode effect and lead to a pronounced current rectification even if the impurity potential is weak. For strongly interacting electrons and not too small voltages, the rectification current, $I_r = [I(V)+I(-V)]/2$, measuring the asymmetry in the current--voltage curve, has a power--law dependence on the voltage with a negative exponent, $I_r \sim V^{-|z|}$, leading to a bump in the current--voltage curve.

cond-mat.mes-hall↗
arXiv2005

Transport anomalies in a simplified model for a heavy electron quantum critical point

We discuss the transport anomalies associated with the development of heavy electrons out of a neutral spin fluid using the large-N treatment of the Kondo-Heisenberg lattice model. At the phase transition in this model the spin excitations suddenly acquire charge. The Higgs process by which this takes place causes the constraint gauge field to loosely ``lock'' together with the external, electromagnetic gauge field. From this perspective, the heavy fermion phase is a Meissner phase in which the field representing the difference between the electromagnetic and constraint gauge field, is excluded from the material. We show that at the transition into the heavy fermion phase, both the linear and the Hall conductivity jump together. However, the Drude weight of the heavy electron fluid does not jump at the quantum critical point, but instead grows linearly with the distance from the quantum critical point, forming a kind of ``gossamer'' Fermi-liquid.

cond-mat.str-el↗
arXiv2005

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping delta away from half-filling, finite-size density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k_F and 4k_F for the currents and densities, where 2k_F = pi(1-delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities.

cond-mat.str-el↗
arXiv2003

Dynamical 1/N approach to time-dependent currents through quantum dots

A systematic truncation of the many-body Hilbert space is implemented to study how electrons in a quantum dot attached to conducting leads respond to time-dependent biases. The method, which we call the dynamical 1/N approach, is first tested in the most unfavorable case, the case of spinless fermions (N=1). We recover the expected behavior, including transient ringing of the current in response to an abrupt change of bias. We then apply the approach to the physical case of spinning electrons, N=2, in the Kondo regime for the case of infinite intradot Coulomb repulsion. In agreement with previous calculations based on the non-crossing approximation (NCA), we find current oscillations associated with transitions between Kondo resonances situated at the Fermi levels of each lead. We show that this behavior persists for a more realistic model of semiconducting quantum dots in which the Coulomb repulsion is finite.

cond-mat.str-el↗
arXiv2003

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.

cond-mat.str-el↗
arXiv2003

Weak-coupling functional renormalization-group analysis of the Hubbard model on the anisotropic triangular lattice

Motivated by experiments on the layered compounds $κ$-(BEDT-TTF)$_2$X, Cs$_2$CuCl$_4$, and very recently Na$_x$CoO$_2 \cdot y$H$_2$O, we present a weak-coupling functional renormalization-group analysis of the Hubbard model on the anisotropic triangular lattice. As the model interpolates between the nearest-neighbor square lattice and decoupled chains via the isotropic triangular lattice, it permits the study of competition between antiferromagnetic and BCS Cooper instabilities. We begin by reproducing known results for decoupled chains, and for the square lattice with only nearest-neighbor hopping amplitude $t_1$. We examine both repulsive and attractive Hubbard interactions. The role of formally irrelevant contributions to the one-loop renormalization-group flows is also studied, and these subleading contributions are shown to be important in some instances. We then observe that crossover to a BCS-dominated regime can occur even at half-filling when antiferromagnetism is frustrated through the introduction of a next-nearest-neighbor hopping amplitude $t_2$ along one of the two diagonal directions. Stripes are not expected to occur and time-reversal breaking $d_{x^2 - y^2} \pm i d_{xy}$ superconducting order does not arise spontaneously; instead pure $d_{x^2 - y^2}$ order is favored. At the isotropic triangular point ($t_1 = t_2$) we find the possibility of re-entrant antiferromagnetic long-range order.

cond-mat.supr-con↗