  A Tomonaga-Luttinger (TL) liquid is known as an integrable system, in which a
non-equilibrium many-body state survives without relaxing to a thermalized
state. This intriguing characteristic is tested experimentally in copropagating
quantum Hall edge channels at bulk filling factor nu = 2. The unidirectional
transport allows us to investigate the time evolution by measuring the spatial
evolution of the electronic states. The initial state is prepared with a biased
quantum point contact, and its spatial evolution is measured with a quantum-dot
energy spectrometer. We find strong evidences for a non-thermal metastable
state in agreement with the TL theory before the system relaxes to thermal
equilibrium with coupling to the environment.
