On averaging of time evolution of quantum spin lattice systems

1980 ◽  
Vol 4 (5) ◽  
pp. 413-416
Author(s):  
K. Napi�rkowski ◽  
W. Pusz
Keyword(s):  
Time Evolution ◽  
Quantum Spin ◽  
Lattice Systems ◽  
Spin Lattice

scholarly journals On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system

2019 ◽  
Vol 6 (5) ◽  
Author(s):  
Maurizio Fagotti
Keyword(s):  
Time Evolution ◽  
Time Window ◽  
Error Function ◽  
Nonequilibrium State ◽  
Quantum Spin ◽  
Lattice System ◽  
Spin Lattice

We consider the time evolution of a state in an isolated quantum spin lattice system with energy cumulants proportional to the number of the sites L^dLd. We compute the distribution of the eigenvalues of the time averaged state over a time window [t_0,t_0+t][t0,t0+t] in the limit of large L. This allows us to infer the size of a subspace that captures time evolution in [t_0,t_0+t][t0,t0+t] with an accuracy 1-\epsilon1−ϵ. We estimate the size to be \frac{\sqrt{2{\mathfrak e}_2}}{\pi}erf^{-1}(1-\epsilon) L^{\frac{d}{2}}t2𝔢2πerf−1(1−ϵ)Ld2t, where {\mathfrak e}_2𝔢2 is the energy variance per site, and erf^{-1}erf−1 is the inverse error function.

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