Exploring Scale Invariance in Flatland Jean Dalibard Collge de - PowerPoint PPT Presentation

Exploring Scale Invariance in Flatland Jean Dalibard Collège de France and Laboratoire Kastler Brossel Solvay mee*ng, Brussels, Feb. 18-20 2019

Scale invariance A concept that was introduced in the 70’s in high energy physics Can there be physical systems with no intrinsic energy/length scale? Need to explain the behavior of e - - nucleon sca6ering cross-sec8ons This concept later found many applicaJons in physics, maths, biology, etc. Phase transiJons and renormalizaJon group Fractals 2

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Outline of this talk Explore the expected consequences + find some unexpected ones for the case of an interacJng 2D Bose gas 1. Scale/conformal invariance in a cold atomic gas 2. Exploring experimentally dynamical probes of scale invariance 3. Two-dimensional breathers 4

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<latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> <latexit sha1_base64="(nul )">(nul )</latexit> Classical field approach to the 2D Bose gas Describe the gas by a classical field obeying the Gross-Pitaevskii equaJon ψ ( r , t ) Energy of the gas: E ( ψ ) = E kin ( ψ ) + E int ( ψ ) 1 . 5 E kin ( ψ ) = ~ 2 Z | r ψ | 2 1 2 m 0 . 5 E int ( ψ ) = ~ 2 1 Z | ψ | 4 0 2 m ˜ g 0 interacJon strength − 1 y g : ˜ − 0 . 5 0 0 . 5 1 − 1 x No singularity at the classical field level In 2D, the interacJon strength is dimensionless: no length scale, nor energy scale ˜ g associated with the interacJons, as required for scale invariance 6