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