CONDENSATION OF FLUCTUATIONS IN A TEMPERATURE QUENCH Marco Zannetti - U Salerno in collaboration with Federico Corberi - U Salerno Giuseppe Gonnella -

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Presentation transcript:

CONDENSATION OF FLUCTUATIONS IN A TEMPERATURE QUENCH Marco Zannetti - U Salerno in collaboration with Federico Corberi - U Salerno Giuseppe Gonnella - U Bari Antonio Piscitelli - U Napoli

temperature quench study of fluctuations during relaxation energy heat

temperature quench Brownian Oscillator Gaussian Model : collection of independent oscillators condensation of fluctuations

temperature quench Brownian Oscillator Gaussian Model Large – N Model: mean field of interacting system no equilibration!

Oscillator

effective temperature J.R.Gomez-Solano, A.Petrosyan, S.Ciliberto – PRL 106, (2011)

effective temperature

Energy fluctuations 0t

Heat fluctuations q < 0 heat released q > 0 heat absorbed

fluctuation relation

collection of brownian oscillators GAUSSIAN MODEL

Temperature Quench

spectrum of effective temperatures

Fluctuations of extensive quantities: Energy

partition function in the biased ensemble

Fluctuations of extensive quantities: Energy biased free energy

Fluctuations of extensive quantities: Energy large V saddle point ẑ

fluctuations in the gaussian model average properties in the biased ensemble condensation spherical model BEC

condensation

hottest mode

condensation

finite contribution from the zero mode

phase diagram condensed normal

phase diagram condensed normal

Fluctuations of extensive quantities: Heat

most releasing mode saddle point ẑ

phase diagram condensed normal

N-VECTOR MODEL

Large N limit self-average

Large N limit self-average

Large N limit self-average

Temperature Quench

unstable modes

effective temperatures

system permanently out of equilibrium «apparent» equilibrium

energy fluctuations

normal fluctuations

hottest mode coldest mode

condensation of negative energy fluctuations due to unstable modes

phase diagram normal condensed normal LARGE-N condensed normal GAUSSIAN

J. Phys. A: Math. Theor. 46, (2013) condensation

conclusions and outlook Fluctuations of energy and heat after a temperature quench non trivial even in trivial non interacting systems Condensation of fluctuations is related to the duality fluctuations in unbiased ensemble ↔ average properties in biased ensemble Effective temperature key quantity – relation with effective temperature from FDR Mean field qualitatively different from real system (energy unbounded below) - go beyond mean field