Deriving the London's equation for superconductor

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Discussion Overview

The discussion revolves around deriving London's equation for superconductors, exploring theoretical foundations and interpretations. Participants reference various sources and concepts related to superconductivity, including canonical momentum, broken symmetry, and the response of superconductors to external fields.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant notes that the canonical momentum of the ground state of a superconductor is zero but questions the origin of this fact.
  • Another participant suggests starting with the Wikipedia page on London equations, mentioning the minimal coupling prescription and the transformation of momentum.
  • A different participant references broken symmetry arguments as a general explanation for the phenomenon, citing Weinberg's work.
  • One participant expresses appreciation for a source provided but admits to a lack of understanding, requesting a simpler explanation without field theory.
  • A later reply discusses Kittel's work on the response of superconductors to an applied transversal field, mentioning the concept of "rigidity of the wavefunction" and its implications for momentum expectation.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are multiple competing views and approaches to understanding the derivation of London's equation.

Contextual Notes

Some claims depend on specific interpretations of theoretical concepts, and there are unresolved aspects regarding the application of broken symmetry and the implications of Kittel's findings.

Trave11er
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The equation can be obtained from the fact that the "canonical momentum of the ground grstate of superconductor is zero", but where does this fact follow from.
P.S. Jackson gives a vague reference to Kittel, which I couldn't find in his Introduction_to_solid_state/Quantum_theory_of_Solids.
 
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There are plenty of explanations around. Maybe the most general is due to broken symmetry arguments as expounded by Weinberg:
http://ptp.ipap.jp/link?PTPS/86/43/
 
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Thank you for the gem, DrDu - it is beautiful.
 
Actually, it is beautiful, but I don't understand much. Can you provide an explanation without calling for field theory?
 
In Kittel Quantum theory of solids he discusses how a superconductor reacts to an applied transversal field of long wavelength. He finds that the wavefunction remains unchanged to lowest order. Hence the expectation of the momentum <p>=0 also does not change with A. This has already been called "rigidity of the wavefunction" by the Londons.
 

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