in Bose systems - Isaac Newton Institute€¦ · · 2014-05-31Lecture Notes: arXiv:1302.1448...

Non-Thermal Fixed Points –Universality, topology & turbulence

in Bose systems

Thomas GasenzerThomas Gasenzer

Institut für Theoretische PhysikInstitut für Theoretische PhysikRuprecht-Karls Universität HeidelbergRuprecht-Karls Universität Heidelberg

Philosophenweg 16 • 69120 Heidelberg • GermanyPhilosophenweg 16 • 69120 Heidelberg • Germany

ExtreMe Matter Institute EMMIExtreMe Matter Institute EMMIGSI Helmholtzzentrum für Schwerionenforschung GmbHGSI Helmholtzzentrum für Schwerionenforschung GmbH

Lecture Notes:arXiv:1302.1448 [cond-mat.quant-gas]

Non-Thermal Fixed Points –Universality, topology & turbulence

in Bose systems

Thomas GasenzerThomas Gasenzer

Institut für Theoretische PhysikInstitut für Theoretische PhysikRuprecht-Karls Universität HeidelbergRuprecht-Karls Universität Heidelberg

Philosophenweg 16 • 69120 Heidelberg • GermanyPhilosophenweg 16 • 69120 Heidelberg • Germany

ExtreMe Matter Institute EMMIExtreMe Matter Institute EMMIGSI Helmholtzzentrum für Schwerionenforschung GmbHGSI Helmholtzzentrum für Schwerionenforschung GmbH

Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer

Thanks & credits

collaboration with:

… & my former students:Boris Nowak, Jan Schole ( Heidelberg), Maximilian Schmidt ( Jülich), Christian Scheppach ( Cambridge, UK) (all involved in work presented here),

as well as

Cédric Bodet, Alexander Branschädel ( KIT), Roman Hennig, Nikolai Philipp, Stefan Keßler ( Erlangen), Matthias Kronenwett, Philipp Struck ( Konstanz), Kristan Temme ( Vienna), Martin Trappe ( Singapore), Pascal Weckesser, Jan Zill ( Queensland)

LGFG BaWue

€€€...

Groups of Markus Oberthaler, Jörg Schmiedmayer,Jürgen Berges, Sebastian Diehl, Jan Pawlowski

Linda Martini Steven Mathey Sebastian Erne Sebastian Bock Markus Karl Thorge Müller Sebastian Heupts Bart Andrews Isara Chantesana Alexander Liluashvili

(not on picture: Martin Gärttner, Denes Sexty)


Transient stationaritye.g. Turbulence

Time flies

Initial state:Far from equilibrium

Final state:Thermal equilibrium



Prethermalisation

Time flies



(partially) universal dynamicspre-thermalisation

[Berges, Borsanyi, Wetterich (2004), Moeckel, Kehrein (2008), and many more now ]

[Ske

tch

by C

. W

ette

rich

]



Prethermalisation

Universal dynamics



Non-thermal fixed point


Classical Turbulence

“Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity.”

(Richardson, 1920)

Lewis F. Richardson(1881-1953)Richardson cascade

large scales (source) → small scales (sink)

Leonardo da Vinci (1452-1519)


Kolmogorov41 Turbulence CascadeTransport of kinetic energy E:

log E(k)

log k

pump

dump



Kolmogorov41 Turbulence CascadeStationary scaling E(k) within inertial region:

log E(k)

log k

Incompressible fluid:

E(k) ~ k—5/3

pump

dumpcascade

Uriel Frisch, Turbulence. The Legacy of A. N. Kolmogorov. (CUP, 1995)

Cascade



Semi-classical Simulations (c-field methods, TWA)

Done on GPUs& Multicore Cl.


2D Bose gas: Quench dynamicsB. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)

“Initial” distribution



thermal

~T/k2

(Rayleigh-Jeans regime of BE distribution)

1e/T−1

≈ T

“Final” distribution



⇒ bidirectional redistribution

1e/T−1

≈ T



thermal

~T/k2


Superfluid hydro of Bose-condensed Gas

The Gross-Pitaevskii Equation, (g = 4πa0/m)

using the defs.

can be written as

Continuity equation Euler equation



( + zero-mode )

Phase angle


Non-Thermal Fixed Point

Particles

Energy

B. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)


Wave Turbulence – e.g. on water [H. Xia et al., EPL 91 (10) 14002]

[Zakharov & Filonenko (67)]

(kinetic) WT Theory prediction:



Particles

Energy J. Berges, A. Rothkopf, J. Schmidt, PRL 101 (08) 041603, J. Berges, G. Hoffmeister, NPB 813 (09) 383,C. Scheppach, J. Berges, TG PRA 81 (10) 033611

Wave turbulence: Power laws from kinetic eqs.


= 0



Particles

Energy J. Berges, A. Rothkopf, J. Schmidt, PRL 101 (08) 041603, J. Berges, G. Hoffmeister, NPB 813 (09) 383,C. Scheppach, J. Berges, TG PRA 81 (10) 033611

nIR ~ k −d −2

IR power laws from (2PI 1/N & fRG) field theory:


= 0



Prethermalisation






Approach of the NTFP

J. Schole, B. Nowak, TG, PRA 86 (12) 013624

mor

e ph

ase

cohe

renc

e

larger Vortex-Antivortex distances

lC

* = Phase coherence lengthlD*

= Vortex-Antivortex pair distance

time




mor

e ph

ase

cohe

renc

e


logtime steps




mor

e ph

ase

cohe

renc

e


dilu

tion

, un

bind

ing

pair binding


Non-Thermal Fixed Point in 3DB. Nowak, J. Schole, TG, arXiv:1206.3181v2 [cond-mat.quant-gas]

lD ~ vortex ring radius,

lC ~ phase coherence length

Dilution process: cf. also Kelvin-wave cascade Kozik & Svistunov (03-11)

k‒ 2.5

k‒ 10

initial spectrum

log k

log

n(k

)


Many other phenomena

Non-Thermal Fixed Points

Vortex Dynamics in 2&3D

1D Soliton Gas

Charge confinement in Higgs models

“Kibble-Zurek”, Exciton-Polaritons, Cosmology, QGP, ...

Pattern formation in Spinor gases


The End

Supplementary slides


Kolmogorov scaling of Qu. Turbulence(Simulations of Gross-Pitaevskii Equation)

Figure from:

M. Kobayashi & M. Tsubota,J. Phys. Soc. Jpn (2005).M. Tsubota, arXiv:1004.5458 [cond-mat].

Extensive work on Qu. Turbulence (mainly beyond sf. Helium):

Vinen 1950's-; & Donnelly, 2002, 07.Svistunov, Berloff, Kozik, … 1995-.Nore, Abid, Brachet, 1995-. Krstulovic,Gurarie 1995.Maurer & Tabeling, 1999Tsubota 2000-.Parker & Adams, 2005L'vov, Nazarenko, Budenko, 2007...Horng, Gou, et al., 2008-Bagnato et al., 2009-Anderson, Bradley, Davis, Neely, … 2010-…

not to mention ≈∞ work on classical Turbulence


2-component Bose gas

~ g

~ g12


M. Karl, B. Nowak, TG, Sci. Rep. 3, 2394 (2013); & new paper: arXiv:1307.7368 [cond-mat.quant-gas]

Build-up of IR scaling


Gauge Turbulence

TG, L. McLerran, J.M. Pawlowski, D. Sexty, 1307.5301 [hep-ph]

U(1) Higgs model:

Electricchargedistribution

Gauge invariantHiggs phase


Gauge Turbulence

TG, L. McLerran, J.M. Pawlowski, D. Sexty, 1307.5301 [hep-ph]

Suppression of Higgs condensationfor strong gauge coupling (type I superconductor)

Electricchargedistribution

Gauge invariantHiggs phase

cond

ensa

te

time

in Bose systems - Isaac Newton Institute€¦ · · 2014-05-31Lecture Notes: arXiv:1302.1448...

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