Fracton

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A fracton is a collective quantized vibration on a substrate with a fractal structure. [1] [2]

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Fractons are the fractal analog of phonons. Phonons are the result of applying translational symmetry to the potential in a Schrödinger equation. Fractal self-similarity can be thought of as a symmetry somewhat comparable to translational symmetry. Translational symmetry is symmetry under displacement or change of position, and fractal self-similarity is symmetry under change of scale. The quantum mechanical solutions to such a problem in general lead to a continuum of states with different frequencies. In other words, a fracton band is comparable to a phonon band. The vibrational modes are restricted to part of the substrate and are thus not fully delocalized, unlike phonon vibrational modes. Instead, there is a hierarchy of vibrational modes that encompass smaller and smaller parts of the substrate.[ citation needed ]

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<span class="mw-page-title-main">Spontaneous symmetry breaking</span> Symmetry breaking through the vacuum state

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<span class="mw-page-title-main">Raman scattering</span> Inelastic scattering of photons by matter

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<span class="mw-page-title-main">Effective field theory</span> Type of approximation to an underlying physical theory

In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale or energy scale, while ignoring substructure and degrees of freedom at shorter distances. Intuitively, one averages over the behavior of the underlying theory at shorter length scales to derive what is hoped to be a simplified model at longer length scales. Effective field theories typically work best when there is a large separation between length scale of interest and the length scale of the underlying dynamics. Effective field theories have found use in particle physics, statistical mechanics, condensed matter physics, general relativity, and hydrodynamics. They simplify calculations, and allow treatment of dissipation and radiation effects.

<span class="mw-page-title-main">Polaron</span> Quasiparticle in condensed matter physics

A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was proposed by Lev Landau in 1933 and Solomon Pekar in 1946 to describe an electron moving in a dielectric crystal where the atoms displace from their equilibrium positions to effectively screen the charge of an electron, known as a phonon cloud. This lowers the electron mobility and increases the electron's effective mass.

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<span class="mw-page-title-main">Franck–Condon principle</span> Quantum chemistry rule regarding vibronic transitions

The Franck–Condon principle is a rule in spectroscopy and quantum chemistry that explains the intensity of vibronic transitions. The principle states that during an electronic transition, a change from one vibrational energy level to another will be more likely to happen if the two vibrational wave functions overlap more significantly.

<span class="mw-page-title-main">Boron arsenide</span> Chemical compound

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<span class="mw-page-title-main">Sound amplification by stimulated emission of radiation</span>

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<span class="mw-page-title-main">Davydov soliton</span> Quasiparticle used to model vibrations within proteins

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In the field of physics concerning condensed matter, a Kohn anomaly is an anomaly in the dispersion relation of a phonon branch in a metal. It is named for Walter Kohn. For a specific wavevector, the frequency of the associated phonon is considerably lowered, and there is a discontinuity in its derivative. They have been first proposed by Walter Kohn in 1959. In extreme cases, the energy of this phonon is zero, meaning that a static distortion of the lattice appears. This is one explanation for charge density waves in solids. The wavevectors at which a Kohn anomaly is possible are the nesting vectors of the Fermi surface, that is vectors that connect a lot of points of the Fermi surface. The electron phonon interaction causes a rigid shift of the Fermi sphere and a failure of the Born-Oppenheimer approximation since the electrons do not follow any more the ionic motion adiabatically.

<span class="mw-page-title-main">Surface phonon</span>

In solid state physics, a surface phonon is the quantum of a lattice vibration mode associated with a solid surface. Similar to the ordinary lattice vibrations in a bulk solid, the nature of surface vibrations depends on details of periodicity and symmetry of a crystal structure. Surface vibrations are however distinct from the bulk vibrations, as they arise from the abrupt termination of a crystal structure at the surface of a solid. Knowledge of surface phonon dispersion gives important information related to the amount of surface relaxation, the existence and distance between an adsorbate and the surface, and information regarding presence, quantity, and type of defects existing on the surface.

The transport of heat in solids involves both electrons and vibrations of the atoms (phonons). When the solid is perfectly ordered over hundreds of thousands of atoms, this transport obeys established physics. However, when the size of the ordered regions decreases new physics can arise, thermal transport in nanostructures. In some cases heat transport is more effective, in others it is not.

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In condensed matter physics, the Lyddane–Sachs–Teller relation determines the ratio of the natural frequency of longitudinal optic lattice vibrations (phonons) of an ionic crystal to the natural frequency of the transverse optical lattice vibration for long wavelengths. The ratio is that of the static permittivity to the permittivity for frequencies in the visible range .

Heat transfer physics describes the kinetics of energy storage, transport, and energy transformation by principal energy carriers: phonons, electrons, fluid particles, and photons. Heat is thermal energy stored in temperature-dependent motion of particles including electrons, atomic nuclei, individual atoms, and molecules. Heat is transferred to and from matter by the principal energy carriers. The state of energy stored within matter, or transported by the carriers, is described by a combination of classical and quantum statistical mechanics. The energy is different made (converted) among various carriers. The heat transfer processes are governed by the rates at which various related physical phenomena occur, such as the rate of particle collisions in classical mechanics. These various states and kinetics determine the heat transfer, i.e., the net rate of energy storage or transport. Governing these process from the atomic level to macroscale are the laws of thermodynamics, including conservation of energy.

<span class="mw-page-title-main">Phonovoltaic</span>

A phonovoltaic (pV) cell converts vibrational (phonons) energy into a direct current much like the photovoltaic effect in a photovoltaic (PV) cell converts light (photon) into power. That is, it uses a p-n junction to separate the electrons and holes generated as valence electrons absorb optical phonons more energetic than the band gap, and then collects them in the metallic contacts for use in a circuit. The pV cell is an application of heat transfer physics and competes with other thermal energy harvesting devices like the thermoelectric generator.

A fracton is an emergent topological quasiparticle excitation which is immobile when in isolation. Many theoretical systems have been proposed in which fractons exist as elementary excitations. Such systems are known as fracton models. Fractons have been identified in various CSS codes as well as in symmetric tensor gauge theories.

Phase space crystal is the state of a physical system that displays discrete symmetry in phase space instead of real space. For a single-particle system, the phase space crystal state refers to the eigenstate of the Hamiltonian for a closed quantum system or the eigenoperator of the Liouvillian for an open quantum system. For a many-body system, phase space crystal is the solid-like crystalline state in phase space. The general framework of phase space crystals is to extend the study of solid state physics and condensed matter physics into phase space of dynamical systems. While real space has Euclidean geometry, phase space is embedded with classical symplectic geometry or quantum noncommutative geometry.

References

  1. Alexander, S; C. Laermans; R. Orbach; H.M. Rosenberg (15 October 1983). "Fracton interpretation of vibrational properties of cross-linked polymers, glasses, and irradiated quartz". Physical Review B. 28 (8): 4615–4619. Bibcode:1983PhRvB..28.4615A. doi:10.1103/physrevb.28.4615.
  2. Srivastava, G. P. (1990), The Physics of Phonons, CRC Press, pp. 328–329, ISBN   9780852741535 .

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