Geometric Phases and Mielnik's Evolution Loops

Abstract

The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called {\it evolution loops}). We make a detailed treatment of systems having equally-spaced energy levels. Special emphasis is made on the potentials which have the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and on their recently found coherent states.

11 pages, harvmac, 2 figures available upon request; CINVESTAV-FIS GFMR 11/94

References in corpus (2)

• New hydrogen-like potentials
• Is there a prescribed parameter's space for the adiabatic geometric phase?

Cited by in corpus (13)

• Distorted Heisenberg Algebra and Coherent States for Isospectral Oscillator Hamiltonians
• Magnetic operations: a little fuzzy physics?
• Algebraic and group structure for bipartite three dimensional anisotropic Ising model on a non-local basis
• Quantum control on entangled bipartite qubits
• Polynomial Heisenberg algebras, multiphoton coherent states and geometric phases
• Geometric Phases, Symmetries of Dynamical Invariants, and Exact Solution of the Schrödinger Equation
• Quantum Operations: technical or fundamental challenge?
• Quantum Fuzzy Orbits
• Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
• Harmonic Oscillator SUSY Partners and Evolution Loops
• Multiphoton supercoherent states
• Measurement in control and discrimination of entangled pairs under self-distortion
• Generation of non-local evolution loops and exchange operations for quantum control in three dimensional anisotropic Ising model