Brownian Entanglement: Entanglement in classical brownian motion

Click here to load reader

  • date post

    01-Jan-2016
  • Category

    Documents

  • view

    60
  • download

    4

Embed Size (px)

description

Brownian Entanglement: Entanglement in classical brownian motion. Dr. Theo M. Nieuwenhuizen Institute for Theoretical Physics University of Amsterdam. Fluctuations, information flow and experimental measurements Paris, 27 Jan 2010. Outline. “Entanglement is a purely quantum phenomenon” - PowerPoint PPT Presentation

Transcript of Brownian Entanglement: Entanglement in classical brownian motion

  • Brownian Entanglement: Entanglement in classical brownian motionDr. Theo M. Nieuwenhuizen Institute for Theoretical Physics University of AmsterdamFluctuations, information flow and experimental measurementsParis, 27 Jan 2010

  • OutlineEntanglement is a purely quantum phenomenon

    Quantum entanglement

    Definition of classical entanglement

    Examples

    Conclusion

  • EntanglementQuantum caseNon-entangled pure state

    Non-entangled mixed state

    In terms of Wigner functions

    In classical physics one always has

    Only entanglement if is not allowed distribution.This happens if there are uncertainty relations between x and p

  • implies

    Therefore if , then

    This holds also for a mixture Thus entanglement is present when

    for at least one of the casesQuantum entanglement and uncertainty relations

  • Forward Kolmogorov

    Average coarse grained velocities

    Departure velocity: overdamped Newtonian

    Arrival velocity: extra kick

    Ed Nelson:Osmotic velocity:

    Paul Langevin dynamics and coarse grained velocities

  • Ensemble view for N particles : ensemble of all trajectories through N-dim point x at time t, embedded with prob. density P(x,t) in ensemble of all configs.

    In this sense, x is a random variableThen also u(x,t) is a random variable

    Joint distribution:

    Of course:

  • Brownian uncertainty relations and entanglement for N=2The relation

    implies

    Hence uncertainty relation:

    N=2: Absence of entanglement iff

    But entanglement occurs iffor at least one of the cases

  • Harmonic interaction with |g|
  • Situations with entanglementIn equilibrium, if |g|
  • Summary Entanglement due to uncertainty relations on Brownian timescalesNo entanglement in Newtonian regime (few collisions of water molecules with tea particle)

    Entanglement occurs for osmotic velocity u defined in terms of ensemble of all (N=2) particles: It does not exist when each u_j is defined in terms of ensemble of trajectories of particle j alone

    Paper: Brownian Entanglement: Allahverdyan, Khrennikov, Nh PRA05

  • Conclusion Quantum entanglement is a purely quantum phenomenon Entanglement can exist in classical physics. Examples also known in laser physics.