arXiv subjects

R. A. Hyman

Publications and source records attributed to R. A. Hyman.

8 recordsLinked to original sources

arXiv2004

Bohmian Mechanics with Discrete Operators

A deterministic Bohmian mechanics for operators with continuous and discrete spectra is presented. Randomness enters only through initial conditions. Operators with discrete spectra are incorporated into Bohmian mechanics by associating with each operator a continuous variable in which a finite range of the continuous variable correspond to the same discrete eigenvalue. In this way Bohmian mechanics can handle the creation and annihilation of particles. Examples are given and generalizations are discussed.

quant-ph↗

arXiv2003

Been Down So Long it Looks Like Up to Me: A Unified Derivation of Conjugate Gradient and Variable Metric Minimization

Simple derivations, at a level appropriate for an undergraduate computational physics course, of the most popular methods for finding the minimum of a function of many variables are presented in a unified manner in the context of a general optimization scheme that emphasizes their essential similarities. The derivations in this paper encompass the conjugate gradient methods with and without conditioning, and the variable metric methods. The common variants of these methods including Fletcher-Reeves, Polak-Ribiere, Davidon-Fletcher-Powell, and Broyden-Fletcher-Goldfarb-Shanno are described and motivated.

physics.comp-ph↗

arXiv1999

Comment on ``Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets"

In a recent Letter (PRL 83, 3297 (1999)), Hida presented numerical results indicating that the Haldane phase of the Heisenberg antiferromagnetic spin-1 chain is stable against bond randomness, for box distributions of the bond strength, even when the box distribution stretches to zero bond strength. The author thus concluded that the Haldane phase is stable against bond randomness for any distribution of the bond strength, no matter how broad. In this Comment, we (i) point out that the randomness distributions studied in this Letter do not represent the broadest possible distributions, and therefore these numerical results do not lead to the conclusion that the Haldane phase is stable against any randomness; and (ii) provide a semiquantitative estimate of the critical randomness beyond which the Haldane phase yields to the Random Singlet phase, in a specific class of random distribution functions for the bond strength.

cond-mat.str-el↗

arXiv1998

Thickness evolution of coercivity in ultrathin magnetic films

The thickness evolution of in-plane magnetization reversal in ultrathin films is studied with a theoretical model that takes account of surface roughness typical of epitaxial growth. Guided by Néel's model, step edge sites of monolayer-height islands are assigned a two-fold anisotropy in addition to a four-fold anisotropy at all sites. Coercivity is found to depend essentially on both the film thickness and the partial coverage of the topmost layer. Its qualitative features are determined primarily by sample geometry and the size of the step anisotropy compared to the domain wall energy. Magnetostatic interactions change the results quantitatively, but not qualitatively. Their effect is understood by comparing calculations with and without their inclusion.

cond-mat.mtrl-sci↗

arXiv1998

Magnetic Reversal on Vicinal Surfaces

We present a theoretical study of in-plane magnetization reversal for vicinal ultrathin films using a one-dimensional micromagnetic model with nearest-neighbor exchange, four-fold anisotropy at all sites, and two-fold anisotropy at step edges. A detailed "phase diagram" is presented that catalogs the possible shapes of hysteresis loops and reversal mechanisms as a function of step anisotropy strength and vicinal terrace length. The steps generically nucleate magnetization reversal and pin the motion of domain walls. No sharp transition separates the cases of reversal by coherent rotation and reversal by depinning of a ninety degree domain wall from the steps. Comparison to experiment is made when appropriate.

cond-mat.mtrl-sci↗

arXiv1996

An Impurity Driven Phase Transition in the Antiferromagnetic Spin-1 Chain

Using an asymptotically exact real space renormalization procedure, we find that the Heisenberg antiferromagnetic spin-1 chain undergoes an impurity driven second order phase transition from the Haldane phase to the random singlet phase, as the bond distribution is broadened. In the Haldane phase and near the critical point, there is a Griffiths region in which the gap is filled and the susceptibility diverges in a non-universal manner. The correlation length critical exponent is approximately 2.3.

cond-mat↗

arXiv1995

Random Bonds and Topological Stability in Gapped Quantum Spin Chains

We study the effects of random bonds on spin chains that have an excitation gap in the absence of randomness. The dimerized spin-1/2 chain is our principal example. Using an asymptotically exact real space decimation renormalization group procedure, we find that dimerization is a relevant perturbation at the random singlet fixed point. For weak dimerization, the dimerized chain is in a Griffiths phase with short range spin-spin correlations and a divergent susceptibility. The string topological order, however, is not destroyed by bond randomness and dimerization is stabilized by the confinement of topological defects. We conjecture that random integer spin chains in the Haldane phase exhibit similar thermodynamic and topological properties.

cond-mat↗

arXiv1994

Current--Voltage Characteristics of Two--Dimensional Vortex Glass Models

We have performed Monte Carlo simulations to determine current--voltage characteristics of two different vortex glass models in two dimensions. The results confirm the conclusions of earlier studies that there is a transition at $T=0$. In addition we find that, as $T\to 0$, the linear resistance vanishes exponentially, and the current scale, $J_{nl}$, where non-linearities appear in the $I$--$V$ characteristics varies roughly as $T^3$, quite different from the predictions of conventional flux creep theory, $J_{nl} \sim T$. The results for the two models agree quite well with each other, and also agree fairly well with recent experiments on very thin films of YBCO.

cond-mat↗