Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace

P. Reimann and M. Kastner, Equilibration of isolated macroscopic quantum systems

2012

Cited alongside, same era.

More precisely, we assume 1 ≤ d ≤ const ​ D ​ ( log ⁡ D ) − 4 1\leq d\leq\text{const}\,D\,(\log D)^{-4}

Cited in the paper.

Throughout the present paper, A ∼ B A\sim B means that A / B A/B is close to one. A ≈ B A\approx B means the weaker relation that A / B A/B is O ⁡ ( 1 ) O(1) . Likewise, A ≲ B A\lesssim B and A ≈ < B A\mathrel{\raisebox{-2.8pt}{\mbox{$\stackrel{{\scriptstyle\textstyle<}}{{\approx}}$}}}B mean A ≤ B ′ A\leq B^{\prime} with B ′ ∼ B B^{\prime}\sim B and B ′ ≈ B B^{\prime}\approx B , respectively

Cited in the paper.

If τ / τ B \tau/\tau_{\mathrm{B}} is much larger, the right-hand side of ( 3

Cited in the paper.

One may interpret our theorem as providing information about how quickly states vary in a macroscopic quantum system. We find that, with probability close to one, any state (including mixed states) in ℋ rnd {\cal H}_{\mathrm{rnd}} escapes from ℋ rnd {\cal H}_{\mathrm{rnd}} on the order of the Boltzmann time

Cited in the paper.

It is sufficient to prove Proposition 2 for large enough d d , since λ max \lambda_{\mathrm{max}} is easily found to be non-decreasing in d d [ 17 ]

Cited in the paper.

S. Goldstein, T. Hara, and H. Tasaki, Time Scales in the Approach to Equilibrium of Macroscopic Quantum Systems

Original

2013

Later among the works it cites.

S. Goldstein, T. Hara, and H. Tasaki, The approach to equilibrium in a macroscopic quantum system for a typical nonequilibrium subspace

2014

Closest in time.