Small time behaviour of an unstable quantum system

V Jayaram Menon

Zai-Qiao Bai, Wei‐Mou Zheng

We study the quantum evolution of an unstable system in su(1, 1) algebra: The evolution of any initial state \k, v> is recursively obtained. When t --> infinity, \\(2) decays as e(-4vt) or t(-4v) in the hyperbolic (H = 2K(1)) or parabolic (H = 2K(1) + 2K(3)) unstable cases, respectively. The quantum-classic correspondence independent of the Bargmann index v is established based on the long-time and large-scale behaviour of wavefunctions.

Aizar Enciso Domínguez, Piotr Kielanowski

S. Goldstein, Joel L. Lebowitz, Roderich Tumulka +1 more

Onkar Parrikar

The behaviour of a quantum rod, pivoted at its lower end on an impenetrable floor and restricted to moving in the vertical plane under the gravitational potential, is studied analytically under the approximation that the rod is initially localized to a 'small-enough' neighbourhood around the point of classical unstable equilibrium. It is shown that the rod evolves out of this neighbourhood. The time required for this to happen, i.e. the tipping time, is calculated using the semi-classical path integral. It is shown that equilibrium is recovered in the classical limit, and that our calculations are consistent with the uncertainty principle.

Jacob Levitan