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Generalised Gibbs Ensemble for spherically constrained harmonic models

by Damien Barbier, Leticia F. Cugliandolo, Gustavo S. Lozano, Nicolás Nessi

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Submission summary

Authors (as registered SciPost users): Nicolas Nessi
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-08-02
Date submitted: 2022-07-30 23:52
Submitted by: Nessi, Nicolas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model. This is the model of a classical particle which is constrained to move, on average over the initial conditions, on an $N$ dimensional sphere, and feels the effect of anisotropic harmonic potentials. We derive all relevant averaged static observables in the (thermodynamic) $N\rightarrow\infty$ limit. We compare them to their long-term dynamic averages finding excellent agreement in all phases of a non-trivial phase diagram determined by the characteristics of the initial conditions and the amount of energy injected or extracted in an instantaneous quench. We discuss the implications of our results for the proper Neumann model in which the spherical constraint is imposed strictly.

List of changes

* We have removed the green color text from some of the sentences of the manuscript.
* We added an explanatory statement around the issue of the secondary constrain raised by referre 2 after Eq. (9).
* We have explicitly stated that the brackets denote the Poisson bracket.
* In the caption of Fig. 4b We have added an explanatory sentence about the fact that in Fig. 4 we reproduce the phase diagram determined in a previous publication, in which we were not able to differentiate phase I from phase IV.

Published as SciPost Phys. 13, 048 (2022)

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