Quantum systems with time-dependent boundaries

Abstract

We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or changing. In all cases, unitarity is preserved and the change of boundaries does not introduce any decoherence in the system.

24 pages, 8 figures

References in corpus (9)

• Manipulating the Quantum State of an Electrical Circuit
• Tuning the Gap of a Superconducting Flux Qubit
• Photon generation in an electromagnetic cavity with a time-dependent boundary
• Global Theory of Quantum Boundary Conditions and Topology Change
• Coherent oscillations in a superconducting tunable flux qubit manipulated without microwaves
• A quantum particle in a box with moving walls
• Models of Topology Change
• A dynamical composition law for boundary conditions
• Quantum Physics and Fluctuating Topologies: Survey

Cited by in corpus (9)

• Self-adjoint extensions and unitary operators on the boundary
• Moving Walls and Geometric Phases
• Controlling a Quantum System via its Boundary Conditions
• Schrödinger equation in moving domains
• Unruh-DeWitt detector in ${\text{AdS}}_2$
• Quantum cavities with alternating boundary conditions
• Non-negative Wigner-like distributions and Renyi-Wigner entropies of arbitrary non-Gaussian quantum states: The thermal state of the one-dimensional box problem
• Problems with variable Hilbert space in quantum mechanics
• Unitary time-evolution in stochastic time-dependent Hilbert spaces