A quantum system exhibiting chaotic behavior and information mixing on spherical or toroidal geometries.A quantum pendulum is a theoretical model of a quantum particle moving in a pendulum-like potential, but on curved surfaces such as a sphere or a torus. Unlike a classical pendulum, its motion is governed by the Schrödinger equation, leading to wave-like behavior and quantum interference. On these geometries, the system can exhibit quantum chaos, where the wavefunction becomes highly sensitive to initial conditions, and information spreads through the system in a way that mimics classical chaos but with quantum correlations.
The study of quantum chaos on curved geometries emerged in the late 20th century, with contributions from physicists like Michael Berry and Martin Gutzwiller, who explored the correspondence between classical and quantum behavior in chaotic systems.
The pendulum's state is described by a wavefunction that evolves according to the Hamiltonian of the system, which includes kinetic energy on the curved surface and a potential energy that depends on the angle. On a sphere, the potential might be a function of latitude, creating a double-well structure. The quantum dynamics can be studied numerically, revealing phenomena like level repulsion, scarring, and the entanglement of different angular momentum modes. The information mixing is quantified by measures such as the out-of-time-order correlator, which shows how quickly perturbations spread.
This model is used in theoretical physics to understand the foundations of quantum chaos and its role in quantum information processing, such as in the design of quantum simulators and the study of black hole information loss.
On a torus, the quantum pendulum can exhibit a phenomenon called 'quantum revival,' where the wavefunction periodically returns to its initial shape, something that never happens in a classical chaotic system.
No articles yet