title: ÐÐ¾Ð·Ð¾Ð½Ð½ÑÐ¹ Ð¿Ð¸Ðº Ð² Ð´Ð²ÑÐ¼ÐµÑÐ½ÑÑ Ð¸ ÑÑÐµÑ Ð¼ÐµÑÐ½ÑÑ Ð½ÐµÑÐ¿Ð¾ÑÑÐ´Ð¾ÑÐµÐ½Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼Ð°Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Boson peak in two-dimensional and third-dimensional disordered systems
Creators: name: ÐÐ¾Ð½ÑÑ, ÐÐ¼Ð¸ÑÑÐ¸Ð¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2019
Subjects: Ð°Ð¼Ð¾ÑÑÐ½ÑÐµ ÑÐµÐ»Ð°
Ð±Ð¾Ð·Ð¾Ð½Ð½ÑÐ¹ Ð¿Ð¸Ðº
Ð´Ð¸ÑÑÑÐ·Ð¾Ð½Ñ
ÑÐ°ÑÑÐ¾ÑÐ° ÐÐ¾ÑÑÐµ-Ð ÐµÐ³ÐµÐ»Ñ
ÑÐµÐ¾ÑÐ¸Ñ ÑÐ»ÑÑÐ°Ð¹Ð½ÑÑ Ð¼Ð°ÑÑÐ¸ÑÑ
Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ñ ÐÐ¸ÑÐµÑÑÐ°
Ð·Ð°ÐºÐ¾Ð½ ÐÐµÐ±Ð°Ñ
amorphous solids
boson peak
diffusons
Ioffe-Regel frequency
random matrix theory
Wishart ensemble
Debyeâs law

description: Ð Ð°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±Ð¾Ð·Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¿Ð¸ÐºÐ°, Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÐ¼Ð¾Ð³Ð¾ Ð²Ð¾ Ð²ÑÐµÑ
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ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ð¹, ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð½ÑÐµ Ð±Ð¾Ð·Ð¾Ð½Ð½ÑÐ¼ Ð¿Ð¸ÐºÐ¾Ð¼. ÐÐ¾Ð»ÑÑÐµÐ½Ð¾ ÑÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¾Ð±Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ðµ
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ÑÐ°Ð±Ð¾ÑÐ°Ñ.
description: This work is dedicated to the study of the boson peak, which observed in all
disordered (amorphous) systems, by the random matrix theory. Used to a calculation
of the distribution of the eigenvalues of the random dynamical matrix it was
obtained, that in two-dimensional systems, as well as in third-dimensional, exists
the excessive on the Debye density of states, so-called the boson peak. It allows
us to talk about the boson peak as a universal property of the random matrices
ensemble. In this framework in the present work, it was found of the analytical
equations, describing the boson peak form in the third-dimensional case. Analyze
of these equations shows, that exist two different on type vibrational area, separated
by boson peak. It was obtained the theoretical justification of the linear correlation
between the boson peak frequency, the Ioffe-Regel frequency and elasticity modules
of amorphous systems, early observed in many works.