Spectral statistics of the quenched normal modes of a network-forming molecular liquid

Matharoo, Gurpreet S.; Razul, M. Shajahan G.; Poole, Peter H.

doi:10.1063/1.3099605

Cited by 6 publications

(10 citation statements)

References 57 publications

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“…We use the flexible version of the model and hence all degrees of freedom to calculate the Hessian (see Refs. [54,55,57] for a more detailed explanation of the formalism and method). (b) Spatial dependence of the amplitude of normal modes A max (r) in the Boson peak regime.…”

Section: Methodsmentioning

confidence: 99%

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The Boson peak in supercooled water

Kumar

Wikfeldt

Schlesinger

et al. 2013

Sci Rep

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We perform extensive molecular dynamics simulations of the TIP4P/2005 model of water to investigate the origin of the Boson peak reported in experiments on supercooled water in nanoconfined pores, and in hydration water around proteins. We find that the onset of the Boson peak in supercooled bulk water coincides with the crossover to a predominantly low-density-like liquid below the Widom line TW. The frequency and onset temperature of the Boson peak in our simulations of bulk water agree well with the results from experiments on nanoconfined water. Our results suggest that the Boson peak in water is not an exclusive effect of confinement. We further find that, similar to other glass-forming liquids, the vibrational modes corresponding to the Boson peak are spatially extended and are related to transverse phonons found in the parent crystal, here ice Ih.

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Section: Methodsmentioning

confidence: 99%

“…We use the flexible version of the model and hence all degrees of freedom to calculate the Hessian (see Refs. [54,55,57] for a more detailed explanation of the formalism and method).…”

Section: Methodsmentioning

confidence: 99%

The Boson peak in supercooled water

Kumar

Wikfeldt

Schlesinger

et al. 2013

Sci Rep

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show abstract

“…This ensures all the eigenvalues are on same footing. The analytical fitting function used for unfolding need not be unique and, is generally different for different systems [30][31][32][33][34]. For this study, the eigenvalue spectra of all the correlation matrices generated is approximated extremely well by a function of the form…”

Section: Unfolding Of Datamentioning

confidence: 99%

“…In such a scenario, one settles for a model that captures the statistical properties of the energy spectrum. RMT finds extensive applications in the statistical studies of various complex systems such as quantum chaotic systems, complex nuclei, atoms, molecules, disordered mesoscopic systems [16][17][18][19][20][21][22][23][24], atmosphere [25], financial applications [26], complex networks [27], societal networks [28], network forming systems [29,30], amorphous clusters [31][32][33][34], biological networks [35], protein networks [36,37], and cancer networks [38] etc. In recent years, RMT has also been applied towards brain network studies in studying universal behavior of brain functional connectivity and has been effective in detecting the differences in resting state and visual stimulation state [39,40].…”

Section: Introductionmentioning

confidence: 99%

Spontaneous back-pain alters randomness in functional connections in large scale brain networks: A random matrix perspective

Matharoo

Hashmi

2020

Physica A: Statistical Mechanics and its Applications

Self Cite

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We use randomness as a measure to assess the impact of evoked pain on brain networks. Randomness is defined here as the intrinsic correlations that exist between different brain regions when the brain is in a task-free state. We use fMRI data of three brain states in a set of back pain patients monitored over a period of 6 months. We find that randomness in the task-free state closely follows the predictions of Gaussian orthogonal ensemble of random matrices. However, the randomness decreases when the brain is engaged in attending to painful inputs in patients suffering with early stages of back pain. A persistence of this pattern is observed in the patients that develop chronic back pain, while the patients who recover from pain after six months, the randomness no longer varies with the pain task. The study demonstrates the effectiveness of random matrix theory in differentiating between resting state and two distinct task states within the same patient. Further, it demonstrates that random matrix theory is effective in measuring systematic changes occurring in functional connectivity and offers new insights on how acute and chronic pain are processed in the brain at a network level.

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“…Studies of the spectra of these systems, which are in general system dependent, have established that the statistical properties of the spectral fluctuations can be associated with one of the three universality classes identified in RMT [48,49,55,56]. Vibrational spectra, obtained from computer simulations, of several disordered solids and liquid systems have revealed that the spectral fluctuations follow the Gaussian orthogonal ensemble (GOE) of RMT [46,[54][55][56][57]. Particularly, these studies have shown that the delocalized modes conform to GOE statistics while the localized modes were found to obey Poissonian statistics [51,57].…”

Section: B Level Spacing Statisticsmentioning

confidence: 99%

Analysis of vibrational normal modes for Coulomb clusters

2018

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We study various properties of the vibrational normal modes for Coulomb-interacting particles in twodimensional irregular confinement using numerical simulations. By analyzing the participation ratio and spectral statistics, we characterize the vibrational modes for Coulomb clusters as localized, quasi-localized and delocalized. We also study a novel correlation function to understand the spatial structure of these different kinds of modes and subsequently extract the associated characteristic length scales. We further demonstrate that, at any given temperature, particles exhibiting larger displacement over a time interval comparable to the structural relaxation time, are strongly correlated with the low-frequency quasi-localized modes of the inherent structure corresponding to the initial configuration. Establishing this correlation for Coulomb clusters paves the path to identify the particular feature of the initial configuration that determines the previously observed heterogeneous dynamics of the particles at low temperatures in these systems.

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Spectral statistics of the quenched normal modes of a network-forming molecular liquid

Cited by 6 publications

References 57 publications

The Boson peak in supercooled water

The Boson peak in supercooled water

Spontaneous back-pain alters randomness in functional connections in large scale brain networks: A random matrix perspective

Analysis of vibrational normal modes for Coulomb clusters

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