We present a complete theory for the full particle statistics of the positions of bulk and extremal particles in a one-dimensional Coulomb gas (CG) with an arbitrary potential, in the typical and large deviations regimes. Typical fluctuations are described by a universal function which depends solely on the general properties of the external potential. The rate function controlling large deviations is, rather unexpectedly, not strictly convex and has a discontinuous third derivative around its minimum for both extremal and bulk particles. This implies, in turn, that the rate function cannot predict the anomalous scaling of the typical fluctuations with the system size for bulk particles, and it may indicate the existence of an intermediate phase in this case. Moreover, its asymptotic behavior for extremal particles differs from the predictions of the Tracy-Widom distribution. Thus many of the paradigmatic properties of the full particle statistics of Dyson log gases do not carry over into their one-dimensional counterparts, hence proving that one-dimensional CG belongs to a different universality class. Our analytical expressions are thoroughly compared with Monte Carlo simulations, showing excellent agreement.

Universal behavior of the full particle statistics of one-dimensional Coulomb gases with an arbitrary external potential / DIAZ HERNANDEZ ROJAS, RAFAEL ALBERTO; Christopher Sebastian Hidalgo Calva, ; and Isaac Pérez Castillo,. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 98:2-1(2018), p. 020104. [10.1103/PhysRevE.98.020104]

Universal behavior of the full particle statistics of one-dimensional Coulomb gases with an arbitrary external potential

Rafael Díaz Hernández Rojas
Primo
;
2018

Abstract

We present a complete theory for the full particle statistics of the positions of bulk and extremal particles in a one-dimensional Coulomb gas (CG) with an arbitrary potential, in the typical and large deviations regimes. Typical fluctuations are described by a universal function which depends solely on the general properties of the external potential. The rate function controlling large deviations is, rather unexpectedly, not strictly convex and has a discontinuous third derivative around its minimum for both extremal and bulk particles. This implies, in turn, that the rate function cannot predict the anomalous scaling of the typical fluctuations with the system size for bulk particles, and it may indicate the existence of an intermediate phase in this case. Moreover, its asymptotic behavior for extremal particles differs from the predictions of the Tracy-Widom distribution. Thus many of the paradigmatic properties of the full particle statistics of Dyson log gases do not carry over into their one-dimensional counterparts, hence proving that one-dimensional CG belongs to a different universality class. Our analytical expressions are thoroughly compared with Monte Carlo simulations, showing excellent agreement.
2018
Coulomb gasses; extreme value statistics; random matrices; long range interactions
01 Pubblicazione su rivista::01a Articolo in rivista
Universal behavior of the full particle statistics of one-dimensional Coulomb gases with an arbitrary external potential / DIAZ HERNANDEZ ROJAS, RAFAEL ALBERTO; Christopher Sebastian Hidalgo Calva, ; and Isaac Pérez Castillo,. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 98:2-1(2018), p. 020104. [10.1103/PhysRevE.98.020104]
File allegati a questo prodotto
File Dimensione Formato  
Hernández Rojas_Universal behavior_2018.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 312.19 kB
Formato Adobe PDF
312.19 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1279588
Citazioni
  • ???jsp.display-item.citation.pmc??? 0
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 6
social impact