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Quantum swimming

Quantum swimming. Boris Gutkin, David Oaknin . Swimmers and pumps. Shape space=Control space. Swimming stroke. Shape and control . Velocity of ball. Force on ball. Friction coeff. Swimming and linear response. mutual forces. Control and response.

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Quantum swimming

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  1. Quantum swimming Boris Gutkin, David Oaknin

  2. Swimmers and pumps

  3. Shape space=Control space Swimming stroke Shape and control

  4. Velocity of ball Force on ball Friction coeff Swimming and linear response mutual forces

  5. Control and response One unknown, the position X, one equation of motion

  6. Swimming in geometric Swimming: when dX does not Integrate to a function

  7. Landauer formula for friction Reflection

  8. Swimmer=scaterer 1-d quantum medium Scattering The swimmer controls the scattering: q, a, g

  9. Swimming at T=0 Principle: If the swimmer can control the scattering matrix, Its position will adjust so that the medium will think nothing has happened

  10. Quantized swimming r-plane Control space Points of transparency

  11. Toolbox Avron, Buttiker, Elgart, Gutkin, Graf, Oaknin, Pretre, Sadun, Thomas

  12. Energy shift Dual to Wigner time delay Ex: in 2 channel case: sink battery snowplough Avron, Elgart, Graf, Sadun

  13. H Key formula r Avron, Elgart, Graf, Sadun

  14. BPT Standard pumping formula

  15. Landauer formula for friction Momentum transfer to Electron gas

  16. Swimming equation

  17. Conceptual issues Avron, Buttiker, Elgart, Gutkin, Graf, Oaknin, Pretre, Sadun, Thomas

  18. (E,t) as a canonical pair A function of non-commuting variables A canonical transformation of half-line E p t x Avron, elgart, graf, sadun

  19. Phase space A function of non-commuting variables E t

  20. Weyl calculus symbol operator S(E,t) is the classical symbol of the scattering matrix Avron, elgart, graf, sadun

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