Instantaneous resonant modes in high-temperature gallium liquids

Wu, Ten-Ming; Tsay, Shiow-Fon; Chang, S. L.; Jong, W. de

doi:10.1103/physrevb.64.064204

Cited by 10 publications

(11 citation statements)

References 20 publications

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“…We have carried out the numerical calculation for the distribution of the nearest-neighbour level spacing s, in the spectra of the matrices with conservation constraints obtained by collecting the instantaneous configurations in the molecular dynamic simulations. We consider the liquid systems [26,27] of the LennardJones, truncated Lennard-Jones, sodium and gallium atoms, respectively. In figure 1, we present the data for the Hessian matrices with each 3×3 block T( r) in equation (8) replaced by a scalar value, either its scalar transverse component or the longitudinal component (appendix A) for the four systems of liquid.…”

Section: Level-spacing Distribution In the Zero Separation Limitmentioning

confidence: 99%

Conservation constraints on random matrices

Jong

Hsieh

2003

J. Phys. A: Math. Gen.

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We study the random matrices constrained by the summation rules that are present in the Hessian of the potential energy surface in the instantaneous normal mode calculations, as a result of momentum conservation. In this paper, we analyse the properties related to such conservation constraints in two classes of real symmetric matrices: one with purely row-wise summation rules and the other with the constraints on the blocks of each matrix, which underscores partially the spatial dimension. We show explicitly that the constraints are removable by separating the degrees of freedom of the zero-eigenvalue modes. The non-spectral degrees of freedom under the constraints can be realized in terms of the ordinary constraint-free orthogonal symmetry but with the rank deducted by the block dimension. We propose that the ensemble of real symmetric matrices with full randomness, constrained by the summation rules, is equivalent to the Gaussian orthogonal ensemble (GOE) with lowered rank. Independent of the joint probability distribution, the Jacobian contributed by the transformation from the matrix coordinates to the spectral coordinates, possesses the same spectral-variable dependence in these two cases. We verify numerically that the small-separation asymptotic in the nearest-neighbour level spacing distribution is indeed governed by the same symmetry power factor, β = 1, as that of the GOE, under conservation constraints and other underlying spatial correlations.

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Section: Level-spacing Distribution In the Zero Separation Limitmentioning

confidence: 99%

Conservation constraints on random matrices

Jong

Hsieh

2003

J. Phys. A: Math. Gen.

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“…Generally, ͑r͒ has a ledge-shape repulsive core and a long-range oscillatory part with a behavior following the Friedel oscillations. 33 In the intermediate region between 0.9 and 0.7, the value of 0 ͑r͒ varies from 6 to 30 and the shape of 0 ͑r͒ becomes soft and has a ramplike behavior, with a reflection point around 0.8. The corresponding temperature of is about 47 K and = 4.04 Å.…”

Section: Model Of Liquid Ga and Simulationsmentioning

confidence: 97%

Hard-sphere perturbation theory for a model of liquid Ga

Tsai

2008

The Journal of Chemical Physics

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Investigating thermodynamic properties of a model for liquid Ga, we have extended the application of the hard-sphere (HS) perturbation theory to an interatomic pair potential that possesses a soft repulsive core and a long-range oscillatory part. The model is interesting for displaying a discontinuous jump on the main-peak position of the radial distribution function at some critical density. At densities less than this critical value, the effective HS diameter of the model, estimated by the variational HS perturbation theory, has a substantial reduction with increasing density. Thus, the density dependence of the packing fraction of the HS reference fluid has an anomalous behavior, with a negative slope, within a density region below the critical density. By adding a correction term originally proposed by Mon to remedy the inherent deficiency of the HS perturbation theory, the extended Mansoori-Canfield/Rasaiah-Stell theory [J. Chem. Phys. 120, 4844 (2004)] very accurately predicts the Helmholtz free energy and entropy of the model, including an excess entropy anomaly. Almost occurring in the same density region, the excess entropy anomaly is found to be associated with the anomalous packing faction of the HS fluid.

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“…For instance, in a study for the lifetimes of the high-frequency INMs, which are localized only on two particles, the projection of an INM on a particle, defined as P a,j = je a,j j 2 with e a,j being the component of the normalized INM eigenvector for this particle, has been used as the tracing variable [5]. According to the characteristics of quasilocalization, an IRM can be identified by the reduced participation ratio s a of the INM in less than half [7]. Thus, we use both s a and the largest P a,j of an INM to monitor the time evolution of the IRMs.…”

Section: The Simulationmentioning

confidence: 99%

“…Recently, in a model of Ga liquid, the low-frequency quasilocalized INMs, termed as instantaneous resonant modes (IRMs), have been numerically evidenced [7], and the local structures around the quasilocalization center of an IRM have been reported [8]. The occurrence of the IRMs in this model is attributed to two factors: (A) the well-known curvature dip in the repulsive core of a Ga atom, with the atoms in this shell region being weakly connected in vibration with the central one, and (B) the local volume expansion, which pushes more neighbors of a Ga atom into this shell region.…”

Section: Introductionmentioning

confidence: 99%