On the origin of the boson peak

Parisi, Giorgio

doi:10.1088/0953-8984/15/11/302

Cited by 34 publications

(23 citation statements)

References 29 publications

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“…Having in mind that g D ͑ ͒ ϰ 2 , it is clear from the shape of these plots that the frequency distribution of g͑ ͒ exc corresponds approximately to convexlike tails. This form is consistent with recent predictions of the Euclidean random matrix theory, 65,66 as already noticed by Yannopoulos et al 16 The change in the maximum frequency of the Boson peak when Rb + are replaced by K + ions in the studied glasses can be attributed to at least two contributions. Firstly, the g͑ ͒ exc may shift towards higher frequency in the KMWPO glass due to "strengthening" of the involved vibrational modes.…”

Section: -7supporting

confidence: 92%

Heat capacity, Raman, and Brillouin scattering studies of M2O–MgO–WO3–P2O5 glasses (M=K,Rb)

Mączka

Hanuza

Baran

et al. 2006

The Journal of Chemical Physics

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The authors report the results of temperature-dependent Brillouin scattering from both transverse and longitudinal acoustic waves, heat capacity studies as well as room temperature Raman scattering studies on M 2 O-MgO-WO 3 -P 2 O 5 glasses ͑M=K,Rb͒. These results were used to obtain information about structure and various properties of the studied glasses such as fragility, elastic moduli, ratio of photoelastic constants, and elastic anharmonicity. They have found that both glasses have similar properties but replacement of K + ions by Rb + ions in the glass network leads to decrease of elastic parameters and P 44 photoelastic constant due to increase of fragility. Based on Brillouin spectroscopy they show that a linear correlation between longitudinal and shear elastic moduli holds over a large temperature range. This result supports the literature data that the Cauchy-type relation represents a general rule for amorphous solids. An analysis of the Boson peak revealed that the form of the frequency distribution of the excess density of states is in agreement with the Euclidean random matrix theory. The reason of the observed shift of the maximum frequency of the Boson peak when K + ions are substituted for Rb + ions is also briefly discussed.

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Section: -7supporting

confidence: 92%

Heat capacity, Raman, and Brillouin scattering studies of M2O–MgO–WO3–P2O5 glasses (M=K,Rb)

Mączka

Hanuza

Baran

et al. 2006

The Journal of Chemical Physics

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“…3 This approach has much in common with the instantaneous normal mode theory developed by Keyes and coworkers, 45,46,47 where the focus of attention is the spectrum of Hessian eigenvalues for instantaneous configurations. Theoretical contributions based upon the premise of dividing configuration space into saddles have appeared, 48,49,50,51 following the observation that the Hessian index of the stationary points sampled in simulations approaches zero around the critical temperature of modecoupling theory. 1,2,52,53,54,55,56,57,58,59,60 However, in contrast with the partitioning scheme based upon local minima, a well-defined procedure for using other stationary points in this way has yet to be fully developed.…”

Section: Introductionmentioning

confidence: 99%

Stationary points and dynamics in high-dimensional systems

Wales¹,

Doye²

2003

The Journal of Chemical Physics

156

167

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We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using a combination of Newton-Raphson and eigenvector-following techniques. Numerical results are presented for a 256-atom supercell representation of a binary Lennard-Jones system. We then derive analytical formulae for the number of stationary points as a function of both system size and the Hessian index, using a framework based upon weakly interacting subsystems. This analysis reveals a simple relation between the total number of stationary points, the number of local minima, and the number of transition states connected on average to each minimum. Finally we calculate two measures of localisation for the displacements corresponding to Hessian eigenvectors in samples of stationary points obtained from the Newton-Raphson-based geometry optimisation scheme. Systematic differences are found between the properties of eigenvectors corresponding to positive and negative Hessian eigenvalues, and localised character is most pronounced for stationary points with low values of the Hessian index.

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“…[11] Here, this corresponds to increase the degree of nonlocality. In figure 1, some realizations of the SSs trajectories, obtained by the numerical solution of Eqs.…”

Section: Numerical Simulations Of the Brownian Dynamics Modelmentioning

confidence: 99%

“…Given some configuration of the filaments (x 1 , x 2 , ..., x N ), which can be either the instantaneous distribution at t max , or the IS, [11] the vibrational spectra can be found as the eigenvalues of the Hessian matrix H pq (p, q = 1...N ):…”

Section: Vibrational Spectra and The Random Matricesmentioning

confidence: 99%

“…Since phonons are the elementary excitations around minima of the PEL, this process is also denoted "phonon-saddle" transition, and can be realized while keeping fixed the temperature and acting on some parameter, like the particle density or the interaction range. [11] It is not difficult to recognize the fundamental character of these ideas, and the fact that they are not limited to the specific contexts where they originally developed. In this article I will show that a light beam propagating in disordered medium (i.e.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Complex light: Dynamic phase transitions of a light beam in a nonlinear nonlocal disordered medium

Conti

2005

Phys. Rev. E

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The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and non-local random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a dynamic phase transition. A connection with the random matrices approach for explaining the vibrational spectra of an ensemble of solitons is pointed out. General arguments based on a Brownian dynamics model are validated by the numerical simulation of a stochastic partial differential equation system. The results are also relevant for Bose condensed gases and plasma physics.

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On the origin of the boson peak

Cited by 34 publications

References 29 publications

Heat capacity, Raman, and Brillouin scattering studies of M2O–MgO–WO3–P2O5 glasses (M=K,Rb)

Heat capacity, Raman, and Brillouin scattering studies of M2O–MgO–WO3–P2O5 glasses (M=K,Rb)

Stationary points and dynamics in high-dimensional systems

Complex light: Dynamic phase transitions of a light beam in a nonlinear nonlocal disordered medium

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