Nonlinear perturbation of Random Matrix Theory
by K.M.Frahm and D.L.Shepelyansky
arXiv:2212.11955[cond-mat.stat-mech] 















  Density plot of linear mode probability
    shown by color: (a) numerical data, (b) theory from energy equipartition anzats; 
    beta=1, size N=64; x-axis: initial mode number, y-axis: detected mode number











 
      
 		


     Article download  (22 Dec 2022, here) ,
    version v2 (17 May 2023, here)


     Article published  Phys. Rev. Lett. v.131. p.077201 (2023) (here) [no Refs. misprints in supmat]

    
   Additional figures  in zip file 
  (here) and  (README.txt)


   Updates 15 Feb 2023 (lines below)


  Matrix size N=256
   (N256a,
   N256b,
   N256c,
   N256d) 

   and (READMEupdate.txt see update point 2)


  Lyapunov exponents at large times
   (LyapunovA,
   LyapunovB,
   LyapunovC,
   LyapunovD) 

   and (READMEupdate.txt see update points respectively 6-9)


  All Additional figures  with updates 15 Feb 2023 in zip file 
  (here) and  (READMEupdate.txt)


    NOTE ADDED: after 22 Dec 2022 submission of our work there appeared
    PRL publication  "Observation of Light Thermalization to
    Negative-Temperature Rayleigh-Jeans Equilibrium States in Multimode Optical Fibers"
    by K. Baudi, J. Garnier, A. Fusaro, N. Berti, C. Michel, K. Krupa, G. Millot, A. Picozzi
    Phys. Rev. Lett. v.130, p.063601 (2023), dated by 8 Feb 2023:

    negative temperature energy equipartition distribution
    (EQ in Eq.(2) in our work or Rayleigh-Jeans in PRL) is experimentally observed
    with 45 modes in optical fiber, even if initial linear spectrum of modes is
    Em = (m1+m2+const) different from RMT, a dynamical thermalization is still present.
    


This webpage is created at December 22, 2022 and is maintained 

by K.M.Frahm and D.L.Shepelyansky