1 / 13

140 likes | 350 Vues

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”

Télécharger la présentation
## Brownian Entanglement: Entanglement in classical brownian motion

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Brownian Entanglement:Entanglement in classical brownian**motion Dr. Theo M. Nieuwenhuizen Institute for Theoretical PhysicsUniversity of Amsterdam Fluctuations, information flow and experimental measurements Paris, 27 Jan 2010**Outline**“Entanglement is a purely quantum phenomenon” Quantum entanglement Definition of classical entanglement Examples Conclusion**Entanglement**• Quantum case • Non-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**Quantum entanglement and uncertainty relations**• implies • Therefore if , then • This holds also for a mixture Thus entanglement is present when for at least one of the cases**Paul Langevin dynamics and coarse grained velocities**Forward Kolmogorov Average coarse grained velocities Departure velocity: overdamped Newtonian Arrival velocity: extra kick Ed Nelson: Osmotic velocity:**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 variable • Then also u(x,t) is a random variable • Joint distribution: • Of course:**Brownian uncertainty relations and entanglement for N=2**The relation implies Hence uncertainty relation: N=2: Absence of entanglement iff But entanglement occurs if for at least one of the cases**Explicit cases for entanglement**• Harmonic interaction with |g|<a • Same T; • Distribution remains • Gaussian, if initially • Osmotic velocities • I f , then sufficient condition for entanglement is:**Situations with entanglement**• In equilibrium, if |g|<a but , any T • Particles interact for t <0, but g=0 for t >0 • Brownianentanglement sudden death:No entanglement for large t • a=0: Entanglement, not present at t=0, can exist in interval**Summary**• Entanglement due to uncertainty relations on Brownian timescales • No 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 PRA’05**Conclusion**Entanglement can exist in classical physics. Examples also known in laser physics. Quantum entanglement is a purely quantum phenomenon

More Related