Universal Dynamics of Independent Critical Relaxation Modes

M. P. Nightingale; H. W. J. Bloete

doi:10.1103/physrevlett.80.1007

Home/Archive/arXiv

arXiv · cond-mat/9708063

Universal Dynamics of Independent Critical Relaxation Modes

M. P. Nightingale·H. W. J. Bloete

View original source ↗Read source document ↗Export metadata ↓

Abstract

Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme is developed to optimize variational approximants of progressively rapid, independent relaxation modes. These approximants are used to reduce the variance of results obtained by means of an adaptation of a quantum Monte Carlo method to compute eigenvalues subject to errors predominantly of statistical nature. The resulting spectra and correlation times are found to be universal up to a single, non-universal time scale for each model.

Explore related subjects

cond-mat

Keep this discovery

BibTeX RIS

M. P. Nightingale, H. W. J. Bloete. 1997-08-08. Universal Dynamics of Independent Critical Relaxation Modes. https://doi.org/10.1103/physrevlett.80.1007

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2014

Towards quantum well hot hole lasers

It should be possible to improve hot-hole laser performance by moving from bulk materials to a quantum well structure. The extra design parameters enable us to alter the band structure by changing the crystal orientation of the growth direction; to use the well width to shift the subband offsets, enabling the effect of the LO phonon scattering cut-off to be controlled; and to use modulation doping to ensure a high hole concentration to increase the gain without the dopants being present in the gain region. We present the first simulations of THz quantum well hot-hole lasers that can produce inversion and optical gain.

cond-mat↗

arXiv2014

The Hall Effect and ionized impurity scattering in Si$_{(1-x)}$Ge$_x$

Using Monte Carlo simulations, we demonstrate that including ionized impurity scattering in models of Si$_{(1-x)}$Ge$_x$ is vital in order to predict the correct Hall parameters. Our results show good agreement with the experimental data of Joelsson et.al. (JAP, 1997).

cond-mat↗

arXiv2014

Elastic response of [111]-tunneling impurities

We study the dynamic response of a [111] quantum impurity, such as lithium or cyanide in alkali halides, with respect to an external field coupling to the elastic quadrupole moment. Because of the particular level structure of a eight-state system on a cubic site, the elastic response function shows a biexponential relaxation feature and a van Vleck type contribution with a resonance frequency that is twice the tunnel frequency $Δ/\hbar$. This basically differs from the dielectric response that does not show relaxation. Moreover, we show that the elastic response of a [111] impurity cannot be reduced to that of a two-level system. In the experimental part, we report on recent sound velocity and internal friction measurements on KCl doped with cyanide at various concentrations. At low doping (45 ppm) we find the dynamics of a single [111] impurity, whereas at higher concentrations (4700 ppm) the elastic response rather indicates strongly correlated defects. Our theoretical model provides a good description of the temperature dependence of $δv/v$ and $Q^{-1}$ at low doping, in particular the relaxation peaks, the absolute values of the amplitude, and the resonant contributions. From our fits we obtain the value of the elastic deformation potential $γ_t=0.192$ eV.

cond-mat↗