Quantum mechanical resistivity

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SUMMARY

The quantum mechanical expression for the resistivity of plasma is closely related to the Hall parameter β, defined as the ratio of the electron gyrofrequency (Ωe) to the electron-heavy particle collision frequency (ν). The formula for β is β = e * B / (m_e * ν), where e is the electron charge (1.6 × 10-19 coulomb), B is the magnetic field in teslas, and m_e is the electron mass (0.9 × 10-30 kg). To express resistivity in quantum terms, Planck's constant (h) must be incorporated, indicating a fundamental relationship between quantum mechanics and electrical properties in plasma.

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  • Understanding of quantum mechanics principles
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  • Knowledge of Ohm's law and electrical conductivity
  • Basic grasp of electromagnetic theory
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Physicists, electrical engineers, and researchers in plasma physics seeking to understand the quantum mechanical aspects of resistivity in plasma systems.

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Q: What is the quantum mechanical expression for resistivity of Plasma?
 
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Are you talking about the inverse of Hall conductivity?

I know that the Hall parameter β beta in a plasma is the ratio between the electron gyrofrequency Ωe and the electron-heavy particle collision frequency ν:

β beta = Omega_e / nu = e * B / (m_e nu)

where

e is the electron charge (1.6 × 10-19 coulomb)
B is the magnetic field (in teslas)
m_e is the electron mass (0.9 × 10-30 kg).

Does that help?
 
I want to know the expression of Ohm's law at the level of quantum mechanics, ie. in expression of resistivity of Plasma there must be a h (Plank constant).
What will be the expression of row ( resistivity) of Plasma in terms of h ( Plank constant)?
 

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