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Phonons in disordered harmonic lattices
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Pinski, Sebastian (2013) Phonons in disordered harmonic lattices. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2688129~S1
Abstract
This work explores the nature of the normal modes of vibration for harmonic
lattices with the inclusion of disorder in one-dimension (1D) and three-dimensions
(3D). The model systems can be visualised as a `ball' and `spring' model in simple
cubic configuration, and the disorder is applied to the magnitudes of the masses, or
the force constants of the interatomic `springs' in the system.
With the analogous nature between the electronic tight binding Hamiltonian
for potential disordered electronic systems and the isotropic Born model for
phonons in mass disordered lattices we analyse in detail a transformation between
the normal modes of vibration throughout a mass disordered harmonic lattice and
the electron wave function of the tight-binding Hamiltonian. The transformation
is applied to density of states (DOS) calculations and is also particularly useful for
determining the phase diagrams for the phonon localisation-delocalisation transition
(LDT). The LDT phase boundary for the spring constant disordered system is
obtained with good resolution and the mass disordered phase boundary is verified
with high precision transfer-matrix method (TMM) results. High accuracy critical
parameters are obtained for three transitions for each type of disorder by finite size
scaling (FSS), and consequently the critical exponent that characterises the transition
is found as = 1:550+0:020
-0:017 which indicates that the transition is of the same
orthogonal universality class as the electronic Anderson transition.
With multifractal analysis of the generalised inverse participation ratio (gIPR)
for the critical transition frequency states at spring constant disorder width k = 10
and mass disorder width m = 1:2 we confirm that the singularity spectrum is the
same within error as the electronic singularity spectrum at criticality and can be considered to be universal.
We further investigate the nature of the modes throughout the spectrum of
the disordered systems with vibrational eigenstate statistics. We find deviations of
the vibrational displacement
uctuations away from the Porter-Thomas distribution
(PTD) and show that the deviations are within the vicinity of the so called `bosonpeak'
(BP) indicating the possible significance of the BP.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Library of Congress Subject Headings (LCSH): | Phonons, Lattice theory, Hamiltonian systems | ||||
Official Date: | May 2013 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Physics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Römer, Rudolf A. | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC); University of Warwick. Department of Physics | ||||
Extent: | xv, 138 leaves : illustrations. | ||||
Language: | eng |
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