Potential effects on instantaneous normal modes of liquids

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

doi:10.1016/s0378-4371(98)00029-6

Cited by 12 publications

(5 citation statements)

References 25 publications

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“…This explains why they do not participate the transformation between the matrix coordinates and the spectral coordinates. To establish the one-to-one correspondence (25), the additional condition (26) for the matrix K C 0 is, however, required.…”

Section: (C)mentioning

confidence: 99%

“…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%

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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: (C)mentioning

confidence: 99%

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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“…In this work, we performed MD simulation annealing of a LJ system, where particles interact via the LJ pair potential with a cutoff at r 0 , which is given as …”

Section: Simulation Annealingmentioning

confidence: 99%

Bond Orientational Order Parameters for Classifying Solid-like Clusters in a Lennard-Jones System near Liquid−Solid Transition and at Solid States

Zeng

Hsu

2022

J. Phys. Chem. A

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In this paper, we introduced an order parameter, named the local structure similarity (LSS), to measure the resemblance of a cluster structure in a liquid with respect to a perfect crystal. The LSS is based on a dot product of two bond orientational order complex vectors, with one vector associated with a particle in a liquid and the other vector with a particle in a crystal. The calculation of the LSS should scan the entire space of the Euler angles determined by the two coordinate frames describing individually the liquid and the crystal. The effectiveness of the LSS was examined by solid-like clusters in a Lennard-Jones (LJ) system near its liquid−solid phase transition and at solid states below its melting point, where the thermodynamic states of the LJ system were obtained by simulation annealing. The LSS measure was utilized to scrutinize the fcc-like, hcp-like, and bcc-like clusters classified by criteria based on W 4 and W 6 order parameters. As indicated by our results, the two ways of classification are consistent for fcc-like and hcp-like clusters, which are in a close resemblance to their crystalline counterparts. However, the classification with positive W 6 for bcc-like clusters is inconsistent with the results of the LSS measure, which was confirmed by clusters in a LJ system confined between two parallel slabs of particles in the bcc structure arrangement.

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“…The thermodynamic state of the TLJ fluid is chosen at reduced density ρ * = 0.972 and reduced temperature T * = 0.836 [12].…”

Section: Level-spacing Statisticsmentioning

confidence: 99%

Potential effects on instantaneous normal modes of liquids

Cited by 12 publications

References 25 publications

Conservation constraints on random matrices

Conservation constraints on random matrices

Bond Orientational Order Parameters for Classifying Solid-like Clusters in a Lennard-Jones System near Liquid−Solid Transition and at Solid States

Numerical studies for localization–delocalization transition in vibrational spectra

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