scholarly journals Low-frequency vibrational spectrum of mean-field disordered systems

2021 ◽  
Vol 103 (17) ◽  
Author(s):  
Eran Bouchbinder ◽  
Edan Lerner ◽  
Corrado Rainone ◽  
Pierfrancesco Urbani ◽  
Francesco Zamponi
Keyword(s):  
Vibrational Spectrum ◽  
Disordered Systems ◽  
Mean Field ◽  
Low Frequency

Low-frequency vibrational spectrum of a KYb(MoO4)2 crystal

2010 ◽  
Vol 36 (4) ◽  
pp. 317-319 ◽  
Author(s):  
N. S. Bondar’ ◽  
S. N. Poperezhaĭ ◽  
V. I. Kut’ko
Keyword(s):  
Vibrational Spectrum ◽  
Low Frequency

Gaussian Processes for Classification: Mean-Field Algorithms

2000 ◽  
Vol 12 (11) ◽  
pp. 2655-2684 ◽  
Author(s):  
Manfred Opper ◽  
Ole Winther
Keyword(s):  
Support Vector Machines ◽  
Gaussian Processes ◽  
Disordered Systems ◽  
Binary Classification ◽  
Computational Cost ◽  
Mean Field ◽  
Strong Support ◽  
Support Vector ◽  
Vector Machines ◽  
Leave One Out

We derive a mean-field algorithm for binary classification with gaussian processes that is based on the TAP approach originally proposed in statistical physics of disordered systems. The theory also yields an approximate leave-one-out estimator for the generalization error, which is computed with no extra computational cost. We show that from the TAP approach, it is possible to derive both a simpler “naive” mean-field theory and support vector machines (SVMs) as limiting cases. For both mean-field algorithms and support vector machines, simulation results for three small benchmark data sets are presented. They show that one may get state-of-the-art performance by using the leave-one-out estimator for model selection and the built-in leave-one-out estimators are extremely precise when compared to the exact leave-one-out estimate. The second result is taken as strong support for the internal consistency of the mean-field approach.

Interpretation of temperature-dependent low frequency vibrational spectrum of solid-state benzoic acid dimer

2009 ◽  
Vol 479 (4-6) ◽  
pp. 211-217 ◽  
Author(s):  
Masae Takahashi ◽  
Yoshiyuki Kawazoe ◽  
Yoichi Ishikawa ◽  
Hiromasa Ito
Keyword(s):  
Solid State ◽  
Vibrational Spectrum ◽  
Benzoic Acid ◽  
Low Frequency ◽  
Temperature Dependent

Low-Frequency Vibrational Spectrum of Water around Cyclodextrin and Its Methyl-Substituted Derivatives

Langmuir ◽  
2010 ◽  
Vol 26 (17) ◽  
pp. 14097-14102 ◽  
Author(s):  
Madhurima Jana ◽  
Sanjoy Bandyopadhyay
Keyword(s):  
Vibrational Spectrum ◽  
Low Frequency

scholarly journals Continuum limit of the vibrational properties of amorphous solids

2017 ◽  
Vol 114 (46) ◽  
pp. E9767-E9774 ◽  
Author(s):  
Hideyuki Mizuno ◽  
Hayato Shiba ◽  
Atsushi Ikeda
Keyword(s):  
Large Scale ◽  
Continuum Limit ◽  
Scaling Law ◽  
Mean Field ◽  
Low Frequency ◽  
Amorphous Solids ◽  
Mode Analysis ◽  
Vibrational Modes ◽  
Phonon Modes ◽  
The Continuum

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

ChemInform Abstract: Microwave Spectrum, Conformation, and Low Frequency Vibrational Spectrum of Cyclopropylisothiocyanate.

1986 ◽  
Vol 17 (28) ◽  
Author(s):  
J. R. DURIG ◽  
A. B. NEASE ◽  
R. J. BERRY ◽  
J. F. SULLIVAN ◽  
Y. S. LI ◽  
...  
Keyword(s):  
Vibrational Spectrum ◽  
Low Frequency ◽  
Microwave Spectrum

HALL EFFECT IN THIN FILMS WITH ROUGH SURFACE AND IMPURITY SCATTERING

1992 ◽  
Vol 06 (22) ◽  
pp. 1361-1369
Author(s):  
SHI-YUE QIU
Keyword(s):  
Thin Films ◽  
Rough Surface ◽  
Disordered Systems ◽  
Logarithmic Singularity ◽  
Low Frequency ◽  
Weak Localization ◽  
Impurity Scattering ◽  
Quantum Calculations ◽  
Hall Constant ◽  
Electronic Conductivities

The result of microscopic, quantum calculations of one-electron conductivities, σxx (ω) and σxy (ω), in thin films with rough surface and impurity scattering, is reported. Although electronic conductivities have logarithmic singularity at low frequency within the weak localization regime, no such singularity is found for the Hall constant just like in the strictly two-dimensional disordered systems.

Mean field like renormalization group for disordered systems

1982 ◽  
Vol 92 (6) ◽  
pp. 287-292 ◽  
Author(s):  
M. Droz ◽  
A. Maritan ◽  
A.L. Stella
Keyword(s):  
Renormalization Group ◽  
Disordered Systems ◽  
Mean Field
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