Beethoven and Handel
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- exposé - matière potentielle : the ritornello scheme
- exposé - matière potentielle : the ritornello
- dissertation
- fiche de synthèse - matière potentielle : critical commentaries
- exposé
- nuanced account of czerny
- thematic areas
- part ritornello scheme to the sentence
- tonic bass pedal
- handel
- beethoven
- borrowings
- bars
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- sentence
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Lecture 4: London’s Equations
Outline
1. Drude Model of Conductivity
2. Superelectron model of perfect conductivity
• First London Equation
• Perfect Conductor vs “Perfect Conducting Regime
3. Superconductor: more than a perfect conductor
4. Second London Equation
5. Classical Model of a Superconductor
September 15, 2003
Massachusetts Institute of Technology
6.763 2003 Lecture 4Drude Model of Conductivity
First microscopic explanation of Ohm’s Law (1900)
1. The conduction electrons are modeled as a gas of
particles with no coulomb repulsion (screening)
2. Independent Electron Approximation
• The response to applied fields is calculated for
each electron separately.
• The total response is the sum of the individual
responses.
3. Electrons undergo collisions which randomize
their velocities.
4. Electrons are in thermal equilibrium with the
lattice.
Massachusetts Institute of Technology
6.763 2003 Lecture 4Response of individual electrons
Consider an electron of mass m and velocity v in an applied
electric E and magnetic B.
Ohm’s Law Hall Effect
Transport scattering time
Massachusetts Institute of Technology
6.763 2003 Lecture 4Response of a single electron
Consider a sinusoidal drive and response of a single electron
Then,
and
Massachusetts Institute of Technology
6.763 2003 Lecture 4Total Response of conduction electrons
The density of conduction electrons, the number per unit
volume, is n. The current density is
ω
Massachusetts Institute of Technology
6.763 2003 Lecture 4Scattering time
To estimate the scattering time
Hence for frequencies even as large at 1 THz,
Massachusetts Institute of Technology
6.763 2003 Lecture 4Equivalent Circuit for a Metal
v
Massachusetts Institute of Technology
6.763 2003 Lecture 4Perfect Conductor vs. Perfectly Conducting Regime
Perfect conductor:
A perfect inductor
Purely reactive
Lossless
Perfectly conducting regime:
A perfect resistor
Purely resistive
Lossy
Massachusetts Institute of Technology
6.763 2003 Lecture 4Ordering of time constants
Cannot be quasistatic and losses
Lossless & dispersive
Nondispersive σ = σ
0
quasistatic
1/ τ 1/ τ
em tr
Can be Quasistatic and losses
Lossless & dispersiv
nondispersive
quasistatic
1/ τ
tr 1/ τ
em
Can be Quasistatic and losses for all frequencies: Perfect conductor
quasistatic Lossless & dispersive
1/ τ
em
Massachusetts Institute of Technology
6.763 2003 Lecture 4First London Equation
Superelectron
Or Cooper Pair:
S
and
Therefore,
And we have the First London Equation
Massachusetts Institute of Technology
6.763 2003 Lecture 4
