Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field

1973/06/01 by H. Sambe · 1 voice · 10 citations
Physics and Astronomy · #Quantum optics and atomic interactions #Cold Atom Physics and Bose-Einstein Condensates #Quantum chaos and dynamical systems

paper · doi:10.1103/physreva.7.2203

openalex publication_date 1973/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A general formalism is presented for a system whose Hamiltonian is periodic in time. The formalism is intended to deal with the interactions between bond electrons and an external electromagnetic field, which can be treated semiclassically, such as electric and magnetic polarizations, optical rotation, and transitions among discrete levels. A particular bound-state solution of the Schr"odinger equation which belongs to an irreducible representation of the time-translation symmetry group is defined as a steady state, and the characteristic number of the irreducible representation as a quasienergy. It is shown that the defined steady states and quasienergies behave in a newly constructed Hilbert space like stationary states and energies of a conservative system in many respects. It is also shown that for a resonant case the unperturbed quasienergy becomes degenerate and the transitions among discrete levels can be accounted for by the familiar degenerate perturbation procedure. Using a suitable Hilbert space, the steady states are established as firmly as the stationary states stand in the theory of a conservative system.

Cited by

• Solving the Schrodinger equation directly for a particle in one-dimensional periodic potentials
• Theory of Multi-photon Processes for Applications in Quantum Control
• Directed chaotic transport in Hamiltonian ratchets
• Quantum neural ordinary and partial differential equations
• The quantum Ising chain for beginners
• Fast entangling gates on fluxoniums via parametric modulation of plasmon interaction
• Phase Structure of Driven Quantum Systems
• Non-invertible symmetries out of equilibrium: Eigenstate order and Floquet physics
• Geometric Floquet Theory
• Interband Heating Processes in a Periodically Driven Optical Lattice

Discussions

• The extended Hilbert space is defined as $\mathcal{R}+\mathcal{T}$ such that it consists of normalizable periodic functions $u(r, t+T)=u(r,t)$ . The inner product in this space is defined as: $$ ((u,v [stackexchange, 1 points]

Related

• Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time
• Bridging the Gap Between the Transient and the Steady State of a Nonequilibrium Quantum System
• Geometrical phase,generalized quasienergy and Floquet operator as invariants
• Quasi-calssical approach to two-level systems with dissipation
• Controlling the dynamics of open quantum systems with periodic driving field