Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion From Laminar Flow to Wave Turbulence in Holographic Superfluid University of Chinese Academy of Sciences (mainly based on the work in finalizing with Shan-Quan Lan, Wen-Biao Liu, Hong Liu and Hongbao Zhang) March 2, 2018 Gravity and Cosmology 2018 Yukawa Institute for Theoretical Physics, Kyoto University From Laminar Flow to Wave Turbulence in Holographic Superfluid Yu Tian ( 田雨 ) 中国科学院大学 Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion 1 Motivation and introduction 2 Laminar-turbulent transition in holographic superfluids 3 Wave turbulence in holographic superfluids 4 Conclusion and discussion From Laminar Flow to Wave Turbulence in Holographic Superfluid Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion 1 Motivation and introduction 2 Laminar-turbulent transition in holographic superfluids 3 Wave turbulence in holographic superfluids 4 Conclusion and discussion From Laminar Flow to Wave Turbulence in Holographic Superfluid Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion Turbulence: one of the most important scientific problems Figure: Turbulence in classical fluids From Laminar Flow to Wave Turbulence in Holographic Superfluid Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion Turbulence: characteristics temporal frequency sensitive to initial conditions (unpredictable) From Laminar Flow to Wave Turbulence in Holographic Superfluid • no consensus definition of turbulence • spatially complex • aperiodic in time • spanning several orders of magnitude in spatial extent and • chaotic Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion Quantum turbulence Bose-Einstein condensates, superconductors, etc) size of local defects (basically vortices) of the order parameter From Laminar Flow to Wave Turbulence in Holographic Superfluid • turbulence in quantum fluids (superfluid Heliums, • expected to be similar to classical turbulence at large scales • expected to be distinct from classical turbulence at small scales set by the healing length, which is the characteristic Yu Tian ( 田雨 )
Motivation and introduction eddy (or vortex) as the fundamental characteristic of the (compressible) Laminar-turbulent transition in holographic superfluids traditional turbulence (vortex turbulence) From Laminar Flow to Wave Turbulence in Holographic Superfluid turbulence Vortex turbulence vs wave turbulence Conclusion and discussion Wave turbulence in holographic superfluids • eddies in classical turbulence and vortices in quantum • wave turbulence: a type of turbulence different from the traditional one, where eddies (or vortices) exist but do not dominate the physics • decomposition: vortex (incompressible) and wave v = v i + v c ∇ · v i = 0 , ∇ × v c = 0 • vortex dominant vs wave dominant Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids state with excellent agreement with experimental measurements From Laminar Flow to Wave Turbulence in Holographic Superfluid [Navon et al, Nature 539, 72 (2016)] Quantum wave turbulence: experiments and numerics Conclusion and discussion Wave turbulence in holographic superfluids • onset of 3D turbulence in BEC by shaking • numerical modeling using Gross-Pitaevskii equation − ∇ 2 � � 2 m + V ( t , x ) + g | ϕ | 2 − µ i � ∂ t ϕ = ϕ • wave dominant (from numerics) isotropic steady turbulent Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion Turbulence: open problems number in classical turbulence) Kolmogorov-Zakharov scaling law, energy cascade, etc) From Laminar Flow to Wave Turbulence in Holographic Superfluid • onset mechanism of (classical and quantum) turbulence • control parameter of quantum turbulence (like the Reynolds • (non-)universal properties (Kolmogorov scaling law, Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion Why applied holography (AdS/CFT)? gravitational theories. transport processes can be easily realized. putting a black hole in the bulk. From Laminar Flow to Wave Turbulence in Holographic Superfluid • Quantum systems can be dually described by classical • Far-from-equilibrium dynamics as well as near-equilibrium • Dissipation at finite temperature is naturally included by Yu Tian ( 田雨 )
Motivation and introduction Conserved charge [YT, X.-N, Wu and H. Zhang, arXiv:1407.8273] Energy accretion Energy dissipation Electric potential Chemical potential Charge Laminar-turbulent transition in holographic superfluids From Laminar Flow to Wave Turbulence in Holographic Superfluid Hawking temperature Temperature is dual to a charged black hole in the bulk AdS: Facts about (applied) AdS/CFT Conclusion and discussion Wave turbulence in holographic superfluids • Finite temperature field theory with finite chemical potential ← → ← → ← → ← → Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion 1 Motivation and introduction 2 Laminar-turbulent transition in holographic superfluids 3 Wave turbulence in holographic superfluids 4 Conclusion and discussion From Laminar Flow to Wave Turbulence in Holographic Superfluid Yu Tian ( 田雨 )
Motivation and introduction [Hartnoll, Herzog and Horowitz, arXiv:0803.3295] h Laminar-turbulent transition in holographic superfluids From Laminar Flow to Wave Turbulence in Holographic Superfluid Wave turbulence in holographic superfluids Conclusion and discussion • Action of the simplest holographic superfluid model d 4 x √− g ( − 1 � 4 F AB F AB − | D Ψ | 2 − m 2 | Ψ | 2 ) . I = M • Background metric ds 2 = L 2 f ( z ) = 1 − z 3 z 2 [ − f ( z ) dt 2 − 2 dtdz + dx 2 + dy 2 ] , . z 3 • Heat bath temperature 3 T = . 4 π z h Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion phase transition of the boundary system. From Laminar Flow to Wave Turbulence in Holographic Superfluid • The hairless-hairy phase transition of the black hole occurs at the critical electric potential (chemical potential) µ c = 4 . 06 . • The above transition is interpreted as the normal-superfluid Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion The laminar-turbulent transition by shaking (periodic driving) From Laminar Flow to Wave Turbulence in Holographic Superfluid • Shaking a holographic superfluid in a periodic box of length L with an appropriate frequency ω u x = A sin ω t • Random initial perturbations • The laminar-turbulent transition observed at the shaking amplitude A = A c Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion at around the twentieth shaking cycles which changes direction and at the twentieth shaking cycles it is zero. From Laminar Flow to Wave Turbulence in Holographic Superfluid • The case of laminar flow Figure: Superfluid velocity fields for the shaking amplitude A < A c Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion before, at and after the twentieth shaking cycles where the total net velocity changes its direction. For the middle panel, the total net velocity is approximately zero. From Laminar Flow to Wave Turbulence in Holographic Superfluid • The case of turbulent flow Figure: Superfluid velocity fields for the shaking amplitude A > A c Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion From Laminar Flow to Wave Turbulence in Holographic Superfluid Figure: The configurations of | ψ | after 1, 2, 3, 4, 5 and 25 shaking cycles for A > A c . Yu Tian ( 田雨 )
Motivation and introduction Laminar-turbulent transition in holographic superfluids Wave turbulence in holographic superfluids Conclusion and discussion total kinetic energy at integral shaking cycles formation From Laminar Flow to Wave Turbulence in Holographic Superfluid • Characterization of the laminar-turbulent transition by the � 1 2 u 2 | ψ | 2 d 2 x E kin ( t ) = • Characterization of the laminar-turbulent transition by vortex Yu Tian ( 田雨 )
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