Related papers: A Bundle-Theoretic Formulation of Phonons in Cryst…
Phonons are ubiquitous quasiparticles in solid state systems describing the quantized vibrations of a crystal lattice. Phonons play a central role in a wide range of physical phenomena, from transport to symmetry-breaking orders, such as…
Sorting and assigning phonon branches (e.g., longitudinal acoustic) of phonon modes is important for characterizing the phonon bands of a crystal and the determination of phonon properties such as the Gr\"uneisan parameter and group…
We formulate a generalized continuum theory of phonon angular momentum in crystals by introducing a local SO(3) material frame in addition to the macroscopic displacement field. The local frame represents rotational optical degrees of…
Positional polymorphism in solids refers to locally disordered unit cells that, on average, reproduce the high-symmetry structures observed in diffraction experiments. Standard theories of electron-phonon interactions fail to describe the…
We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses and liquids based on non-affine displacements and the consequent Goldstones phase relaxation. We relate the…
How to include spacetime translations in fibre bundle gauge theories has been a subject of controversy, because spacetime symmetries are not internal symmetries of the bundle structure group. The standard method for including affine…
Local positional disorder in soft, anharmonic materials has emerged as a central factor in shaping their electronic, vibrational, optical, and transport properties. Viewed mainly as a source of performance degradation, recent theoretical…
Phonon localization is a phenomenon that influences numerous material properties in condensed matter physics. Anderson localization brings rise to localized atomic-scale phonon interferences in disordered lattices with an influence limited…
Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk-edge correspondence where the interior of a material dictates the existence of stable surface or boundary modes. In the mechanical setup, such…
A dislocation, just like a phonon, is a type of atomic lattice displacement but subject to an extra topological constraint. However, unlike the phonon which has been quantized for decades, the dislocation has long remained classical. This…
A systematic study of small, time-dependent, perturbations to geometric wave-equation domains is hardly existent. Acoustic enclosures are typical examples featuring locally reacting surfaces that respond to a pressure gradient or a pressure…
We review the theory of second--order (ferro--)elastic phase transitions, where the order parameter consists of a certain linear combination of strain tensor components, and the accompanying soft mode is an acoustic phonon. In…
We show that the holonomy of a connection defined on a principal composite bundle is related by a non-abelian Stokes theorem to the composition of the holonomies associated with the connections of the component bundles of the composite. We…
We derive from an eigendielectric displacement vector summation approach the frequency order of the polar phonon modes and the polarization-dependent structure of the reststrahlen bands within the monoclinic plane of materials with…
We develop a geometric framework that characterizes the synchronization problem --- the problem of consistently registering or aligning a collection of objects. The theory we formulate characterizes the cohomological nature of…
Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation…
In the paper, the inhomogeneous states with local translational symmetry are under investigation in the framework of the Landau theory. The phonon potential is defined as a compensating field of local representation of the subgroup of…
This is the second in a series of papers that aim to develop rigorous and most encompassing foundations for field theory, where in the first installment, we laid out the natural formulation of bosonic variational field theory via the…
We provide a comprehensive theoretical framework to study how crystal dislocations influence the functional properties of materials, based on the idea of quantized dislocation, namely a "dislon". In contrast to previous work on dislons…
Disorder in crystals is rarely random, and instead involves local correlations whose presence and nature are hidden from conventional crystallographic probes. This hidden order can sometimes be controlled, but its importance for physical…