in bose systems - isaac newton institute€¦ · · 2014-05-31lecture notes: arxiv:1302.1448...
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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)
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Transient stationaritye.g. Turbulence
Time flies
Initial state:Far from equilibrium
Final state:Thermal equilibrium
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Transient stationaritye.g. Turbulence
Prethermalisation
Time flies
Initial state:Far from equilibrium
Final state:Thermal equilibrium
(partially) universal dynamicspre-thermalisation
[Berges, Borsanyi, Wetterich (2004), Moeckel, Kehrein (2008), and many more now ]
[Ske
tch
by C
. W
ette
rich
]
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Transient stationaritye.g. Turbulence
Prethermalisation
Universal dynamics
Initial state:Far from equilibrium
Final state:Thermal equilibrium
Non-thermal fixed point
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
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)
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Kolmogorov41 Turbulence CascadeTransport of kinetic energy E:
log E(k)
log k
pump
dump
Leonardo da Vinci (1452-1519)
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
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
Leonardo da Vinci (1452-1519)
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Semi-classical Simulations (c-field methods, TWA)
Done on GPUs& Multicore Cl.
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
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
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
2D Bose gas: Quench dynamicsB. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)
thermal
~T/k2
(Rayleigh-Jeans regime of BE distribution)
1e/T−1
≈ T
“Final” distribution
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
2D Bose gas: Quench dynamicsB. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)
⇒ bidirectional redistribution
1e/T−1
≈ T
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
2D Bose gas: Quench dynamicsB. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)
thermal
~T/k2
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Superfluid hydro of Bose-condensed Gas
The Gross-Pitaevskii Equation, (g = 4πa0/m)
using the defs.
can be written as
Continuity equation Euler equation
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
2D Bose gas: Quench dynamicsB. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)
( + zero-mode )
Phase angle
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
2D Bose gas: Quench dynamicsB. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
2D Bose gas: Quench dynamicsB. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
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)
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Wave Turbulence – e.g. on water [H. Xia et al., EPL 91 (10) 14002]
[Zakharov & Filonenko (67)]
(kinetic) WT Theory prediction:
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Non-Thermal Fixed Point
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.
B. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)
= 0
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Non-Thermal Fixed Point
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:
B. Nowak, D. Sexty, TG, PRB 84(R) (11); B. Nowak, J. Schole, D. Sexty, TG, PRA 85 (12)
= 0
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Transient stationaritye.g. Turbulence
Prethermalisation
Non-thermal fixed point
Initial state:Far from equilibrium
Final state:Thermal equilibrium
Non-thermal fixed point
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
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
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Approach of the NTFP
J. Schole, B. Nowak, TG, PRA 86 (12) 013624
mor
e ph
ase
cohe
renc
e
larger Vortex-Antivortex distances
logtime steps
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Approach of the NTFP
J. Schole, B. Nowak, TG, PRA 86 (12) 013624
mor
e ph
ase
cohe
renc
e
larger Vortex-Antivortex distances
dilu
tion
, un
bind
ing
pair binding
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
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
)
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
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
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
The End
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
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
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
2-component Bose gas
~ g
~ g12
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
M. Karl, B. Nowak, TG, Sci. Rep. 3, 2394 (2013); & new paper: arXiv:1307.7368 [cond-mat.quant-gas]
Build-up of IR scaling
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
Gauge Turbulence
TG, L. McLerran, J.M. Pawlowski, D. Sexty, 1307.5301 [hep-ph]
U(1) Higgs model:
Electricchargedistribution
Gauge invariantHiggs phase
Holography: From Gravity to Quantum Matter · Isaac Newton Institute · Cambridge · 18 Sep 2013 Thomas Gasenzer
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
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