Probing Out of Equilibrium
Physics
Nick Evans
University of Southampton
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D3/D7 and time dependent solutions
Thermalization
Finite T phase transitions
Quenches
Inflation
Can also
apply to
D3/D5
defect
theory…
Orthonormal, complete set of
wave functions
Add Confinement & Chiral Symmetry Breaking
Dilaton Flow Geometry: Gubser, Sfetsos
BEEGK, Ghoroku..
B field enters the DBI action as a
dilaton profile – causes chiral
symmetry breaking but not
confinement.
Thermalizing N=2 Meson Clouds
Time dependent problems for the probe are simple and the ODEs
solvable in eg Mathematica
Das, Nishioka ,
Takayanagi
In linearized approx.. We can fill space with a cloud of non-interacting mesons…
UV
IR
For small amplitude interacting
solution.. at early times we see
classic perturbation theory mixing
between states
Leave for long enough and presumably,
time averaged, the energy per mode
will look Boltzman exp(-m/kT)….
Mesons thermalize but do they dissolve into quark
plasma?
Is the formation of a world-sheet zero in g_tt an
horizon and hence thermalization?
A full solution at large amplitude:
Horizons come, horizons
go…
Could the initial condition
have contained overlap
with a thermal state at line
one?
To form a static or growing
horizon we must have
back-reaction….
Phase Transitions in Gapped Systems
Eg B+T D3/D7 system
Johnson, Filev
Horizon grows and eats D7 - first
order phase transition…
To watch this transition in
real time we use Janik’s time
dependent solution for a
cooling/warming fireball…
Expectations of First Order Transition
NE, Kalaydzhyan, Kim,
Kirsch 10.11.2519
Transition proceeds by
bubble nucleation….
Quenches in Gapped Systems
We can also change B at
fixed T…
NE, French, Kim 1009.5678
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Rolls and over shoots
At finite T the additional physics emerges when the D7 hits the horizon… the
mesonic spectrum becomes quasi-normal and there is energy loss
Cf Bhaseen, Gauntlett , Simons, Julian
Sonner, Wiseman
We have identified five behaviours
No change after quench…
Oscillation away from black hole
Oscillation onto black hole either on
a) first pass onto black hole
b) After multiple passes over black hole
Oscillation onto black hole, loosing
energy and ending in oscillatory
phase just above horizon…
Currently mapping out phase diagram
(with Jon Shock, Keun-Young Kim)
Composite Inflatons
NE, French, Kim 1009.5678 ,1208.3060
The simple quench from
B=0 to B none zero is an
inflation roll…
How can we extend this
roll?
This would replace the unnatural scalar in inflation models with a
strongly coupled gauge theory… ie a composite inflaton…
We need…
Walking Dynamics
Such theories probably exist …
Cf Banks Zak
Seiberg N=1 SUSY duality
Such theories have enhanced UV quark condensate
Constructing gravity duals of such theories is hard work.. (cf Kiritsis,
Jarvinen.. Nunez, Piai… )…
What does a probe D7 see in a deformed AdS background?
Effective Probe Dynamics
Alvares, NE, Kim 1204.2474
The mass is just a statement of the
running of the dimension of qq
The instability is due to a violation of the BF bound
l
The roll from false
vacuum to true…
The meson masses of the
unstable vacuum.. There is a
single inflaton… whose mass
falls to zero as one
approaches the transition…
You can also time the roll in an explicit time dependent
computation and show it increases in time as one
approaches the CW transition…
If you’re willing to fine tune to the transition you can get an
arbitrarily flat potential/ long roll time…
Summary
• Probe branes provide a computational simple way to study nonequilibrium problems
• Meson thermalization is present but not breakdown into a quark
plasma
• Real time computations through gap-no gap phase transitions are
possible
• Expected features of a quench are present - oscillations damped
by energy loss to quasi-normal modes
• Can compute when strongly coupled physics contributes to
cosmology now - walking dynamics seems linked to inflation…