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Quantum swimming

Quantum swimming. Boris Gutkin, David Oaknin. Q. Q-Swimming. Swimmer in a quantum sea: Photon bath Fermi sea. C-swimming competition. Shape space=Control space. Swimming stroke=closed path in shape space. Euclidean motions. Shape space. swimming. Swimming: definition.

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Quantum swimming

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  1. Quantum swimming Boris Gutkin, David Oaknin

  2. Q Q-Swimming Swimmer in a quantum sea: Photon bath Fermi sea

  3. C-swimming competition Shape space=Control space Swimming stroke=closed path in shape space

  4. Euclidean motions Shape space swimming Swimming: definition Swimming: a map

  5. Untethered scatterers Balanced scatterer

  6. qswimming Euclidean motions Q-Swimming Qswimmer: a unthethered balanced periodic scatterer Scattering matrices Need: a principle to fix the location and orientation of balanced scatterer

  7. Swimmer=scaterer 1-d quantum medium Swimming in one dimension r t On-shell scattering matrix The swimmer controls the scatteringbut not its location

  8. Velocity of ball Force on ball Friction coeff C-Swimming: The role of friction mutual forces

  9. Control and response One unknown, the position X. Equation of motion: equilibrium

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

  11. The invisibility principle 1-d Fermi sea, T=0 The position adjusts so that the medium will think nothing has happened

  12. Quantized swimming 1-d Fermi sea, T=0 r-plane Control space Points of transparency

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

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

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

  16. Quantum friction Momentum transfer to medium

  17. Swimming equation Total force on swimmer vanishes

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

  19. (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

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

  21. Adiabatic as semi-classical limit E t T

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