L-7: Difference between revisions
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== The Gaussian packet of free particles: the ballistic behaviour == | == The Gaussian packet of free particles: the ballistic behaviour == | ||
Consider the Hamiltonian of a free particle together with its separable solutions | |||
[[File:Localization1DB.png|thumb|left|x140px|BCE and 1D localization]] | [[File:Localization1DB.png|thumb|left|x140px|BCE and 1D localization]] |
Revision as of 11:31, 8 March 2024
Goal : This is the first lecture about the localization. Localization is a wave phenomenon induced by disorder.
The Gaussian packet of free particles: the ballistic behaviour
Consider the Hamiltonian of a free particle together with its separable solutions
The conductance and the diffusive behaviour
Ohm's laws characterize electric transport of (good or bad) conductors:
- First law:
Here is the resistence of the sample and is its conductance.\
- Second law
Here are the resistivity and the conductivity. These are material properties, independent of the geometry of the sample These phenomenological laws are a macroscpic manifestation of the diffusive motion of the electrons. From the Drude model we know that disorder is the crucial ingredient to justify the presence of diffusion. ]