Room 117

Quantum Equilibriation in Finite Time

Prathik Cherian

IMSc

It has recently been shown that small quantum subsystems
generically equilibriate over infinite time, in the sense that they spend most of
the time close to a fixed equilibrium state. This relies on just two assumptions: that
the state is spread over many different energies, and that the Hamiltonian has
non- degenerate energy gaps. Given the same assumptions, it has also been shown
that closed systems equilibriate with respect to realistic measurements. We extend
these results in two important ways. Firstly, we prove equilibriation over a finite
(rather than infinite) time-interval, allowing us to bound the equilibriation time.
Secondly, we weaken the non-degenerate energy gaps condition, showing that
equilibriation occurs provided that no energy gap is hugely degenerate.