Lévy flights in a box

• A quantum Lévy process in a box involves topological constraints in space.
• The eigenvalue problem is formulated for the Lévy process in the box.
• The path integral formalism with the Lévy measure is constructed.
• The evolution operator is obtained in the path integral presentation.

It is shown that a quantum Lévy process in a box leads to a problem involving topological constraints in space, and its treatment in the framework of the path integral formalism with the Lévy measure is suggested. The eigenvalue problem for the infinite potential well is properly defined and solved. An analytical expression for the evolution operator is obtained in the path integral presentation, and the path integral takes the correct limit of the local quantum mechanics with topological constraints. An example of the Lévy process in oscillating walls is also considered in the adiabatic approximation.