- **Anyon** - a type of quasiparticle that occurs only in two-dimentional systems
	- 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). 
	- [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
- Band structure - the range of  energy levels that electrons may have within a solid-state object, as well as energies they may not have. 
- Bosons - 
![[Pasted image 20230517172518.png]]
- Fermions - elementary subatomic particle 
	- follows Fermi-Dirac statistics [with half-odd integer spin ](![[Pasted image 20230517172619.png]])
- Fermi gas - a collection of non-interacting fermions (particles with half-integer spin) in a constant energy well. 
	- behaves like an ideal gas at  low particle number density& high temperature
	- concentrates a small number of particles per energy 
	- prohibited  from condensing into a Bose-Einstein condensate 
	- may form a Cooper pair & condensate if weakly-interacting
	- pressure of Fermi-gas is non-zero even at zero-temperature unlike ideal gas
	- this pressure is what stabilizes a neutron star (is  a fermi gas of neutrons ) 
	- 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
		- when a star is massive enough to overcome pressure, it can collapse into singularity.
		- Fermi temperature of a gas depends on mass of fermions and density of energy states
- Free electron model - solid-state model for metals. Describes behavior of charge carriers in a metallic solid.
	- where metals are composed of a quantum electron gas  where ions play almost no role 
	- predictive when applied to alkali & noble metals
	- 4 main assumptions 
	1. free  electron approximation : ion & valence electrons ignored other than to keep charge neutrality for the metal 
	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. 
	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.
	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. 
- FQHE  - Fractional Quantum Hall effect shows precisely quantized plateaus at fractional values
	- [measuring extremely directly](https://www.jstor.org/stable/3837560) is beyond reproach.
- **Hadron** - when a subatomic particle is neither a Boson or Fermion
- **Jeans instability** - causes collapse of interstellar  gas clouds and subsequent star formation  
	- when gas pressure is not  strong enough to prevent gravitational collapse  of a region fille with matter.
	- can give rise to [fragmentation](https://en.wikipedia.org/wiki/Jeans_instability) in certain conditions
	- this is why stars usually form in clusters ([stellar nursery](https://en.wikipedia.org/wiki/Molecular_cloud))
- 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. 
	- frequency depends only weakly on wavelength of oscillation  
	- the instability in the dialectric function of a free  electron gas
	- parallel in form to Jeans instability waves  
	- may give rise to  negative mass
- **Phonons** - quantized quasiparticle sound waves,  similar to photons as quantized light waves
	- is an excited state in the quantization of the modes of vibrations for elastic structures of interacting particles
	- long-wavelength phonons give rise to *sound*.
![[Pasted image 20230517171306.png]]

- Plasmons - a quasiparticle of plasma oscillations, just as photons are quasiparticles of optical oscillations
	- plasmon + photon = plasmon polariton (at optical frequencies)
- **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. 
	- 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).
	- [Many kinds](https://en.wikipedia.org/wiki/Polariton) of polaritons exist: 
		- phonon polaritons 
		- exciton polaritons aka excitons
		- intersubband polaritons 
		- surface plasmon polaritons
		- Bragg polaritons ("Braggoritons")
		- Plexcitons
		- Magon polaritons 
		- Pi-tons
		- Cavity polaritons
- **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.
	- 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*. 
	- quasiparticles **only** exists inside of many-particle systems (primarily solids)
- **Tachyon** - a hypothetical faster-than-light particle 
	- The [implications](https://www.space.com/tachyons-facts-about-particles) of such a particle  are vast. 
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