65 lines
5.7 KiB
Markdown
65 lines
5.7 KiB
Markdown
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- **Anyon** - a type of quasiparticle that occurs only in two-dimentional systems
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- Can be Abelian (discovered 2020) or Non-Abelian (generated with trapped ions) explained [here](https://phas.ubc.ca/~berciu/TEACHING/PHYS502/PROJECTS/20-Anyons-AD.pdf).
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- [Inferred](https://www.quantamagazine.org/milestone-evidence-for-anyons-a-third-kingdom-of-particles-20200512/) from quantum topology - novel properties of shapes made by quantum systems
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- Band structure - the range of energy levels that electrons may have within a solid-state object, as well as energies they may not have.
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- Bosons -
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![[Pasted image 20230517172518.png]]
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- Fermions - elementary subatomic particle
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- follows Fermi-Dirac statistics [with half-odd integer spin ](![[Pasted image 20230517172619.png]])
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- Fermi gas - a collection of non-interacting fermions (particles with half-integer spin) in a constant energy well.
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- behaves like an ideal gas at low particle number density& high temperature
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- concentrates a small number of particles per energy
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- prohibited from condensing into a Bose-Einstein condensate
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- may form a Cooper pair & condensate if weakly-interacting
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- pressure of Fermi-gas is non-zero even at zero-temperature unlike ideal gas
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- this pressure is what stabilizes a neutron star (is a fermi gas of neutrons )
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- pressure helps against inward pull of gravity for white dwarf star ( is a fermi gas of electrons ) which would otherwise collapse the star into a black hole
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- when a star is massive enough to overcome pressure, it can collapse into singularity.
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- Fermi temperature of a gas depends on mass of fermions and density of energy states
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- Free electron model - solid-state model for metals. Describes behavior of charge carriers in a metallic solid.
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- where metals are composed of a quantum electron gas where ions play almost no role
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- predictive when applied to alkali & noble metals
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- 4 main assumptions
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1. free electron approximation : ion & valence electrons ignored other than to keep charge neutrality for the metal
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2. independent electron approximation : interactions between electrons ignored because electrostatic fields in metals are weak due to screening effect, respective quadratic relation exists between energy and momentum.
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3. relaxation-time approximation: unknown scattering mechanism occurs s.t. electron probability of collision = inversely proportional to the relation time $\tau$ which represent the average time between collisions. Electronic configuration is not causing these collisions.
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4. pauli exclusion principle : each quantum state of the system can be occupied by a single electron. Restriction of electron states taken into account by Fermi-Dirac statistic which are derived by Sommerfield expansion of occupancy for energies around the Fermi level.
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- FQHE - Fractional Quantum Hall effect shows precisely quantized plateaus at fractional values
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- [measuring extremely directly](https://www.jstor.org/stable/3837560) is beyond reproach.
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- **Hadron** - when a subatomic particle is neither a Boson or Fermion
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- **Jeans instability** - causes collapse of interstellar gas clouds and subsequent star formation
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- when gas pressure is not strong enough to prevent gravitational collapse of a region fille with matter.
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- can give rise to [fragmentation](https://en.wikipedia.org/wiki/Jeans_instability) in certain conditions
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- this is why stars usually form in clusters ([stellar nursery](https://en.wikipedia.org/wiki/Molecular_cloud))
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- Langmuir waves - [plasma oscillations](https://en.wikipedia.org/wiki/Plasma_oscillation), instability occuring in electron density in conducting materials such as plasmas or metals in the UV region.
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- frequency depends only weakly on wavelength of oscillation
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- the instability in the dialectric function of a free electron gas
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- parallel in form to Jeans instability waves
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- may give rise to negative mass
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- **Phonons** - quantized quasiparticle sound waves, similar to photons as quantized light waves
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- is an excited state in the quantization of the modes of vibrations for elastic structures of interacting particles
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- long-wavelength phonons give rise to *sound*.
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![[Pasted image 20230517171306.png]]
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- Plasmons - a quasiparticle of plasma oscillations, just as photons are quasiparticles of optical oscillations
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- plasmon + photon = plasmon polariton (at optical frequencies)
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- **Polariton** - The result of a combination of a photon with a polar excitation of a material. These are Bosonic quasiparticles resulting from a coupling of electromagnetic waves with an electric/magnetic dipole-carrying excitation.
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- 2018, [scientists](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6467536/) reported 3-photon form of light, involving polaritons, useful for development of [quantum computers](https://www.newsweek.com/photons-light-physics-808862).
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- [Many kinds](https://en.wikipedia.org/wiki/Polariton) of polaritons exist:
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- phonon polaritons
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- exciton polaritons aka excitons
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- intersubband polaritons
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- surface plasmon polaritons
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- Bragg polaritons ("Braggoritons")
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- Plexcitons
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- Magon polaritons
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- Pi-tons
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- Cavity polaritons
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- **Quasiparticles** - or *collective excitations* are when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum.
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- ex. electron passing through semiconductor behaves differently (as if it has an effective mass traveling unperturbed in a vacuum) and so is refered to as an *electron quasiparticle*.
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- quasiparticles **only** exists inside of many-particle systems (primarily solids)
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- **Tachyon** - a hypothetical faster-than-light particle
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- The [implications](https://www.space.com/tachyons-facts-about-particles) of such a particle are vast.
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