notes/Machine Tips (Quantum)/Physics/Particle Terms.md

• 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.
  • Inferred 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 - !

• Fermions - elementary subatomic particle

  • follows Fermi-Dirac statistics [with half-odd integer spin ](!)

• 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 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 in certain conditions
  • this is why stars usually form in clusters (stellar nursery)

• Langmuir waves - plasma oscillations, 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. !

• 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 reported 3-photon form of light, involving polaritons, useful for development of quantum computers.
  • Many kinds 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 of such a particle are vast.