A new perturbative expansion of the time evolution operator associated with a quantum system

2005/08/02 by Paolo Aniello
Computer Science · Physics and Astronomy · #Laser-Matter Interactions and Applications #Quantum Information and Cryptography #Spectroscopy and Quantum Chemical Studies #quant-ph

paper · pdf · doi:10.1088/1464-4266/7/12/011

published as J.Opt.B Quant.Semiclass.Opt. 7 (2005) S507-S522 · 32 pages; modified version with examples of my previous paper quant-ph/0404056; to appear on the J. of Optics B: Quantum and Semiclassical Optics, Special Issue on 'Optics and Squeeze Transformations after Einstein'

arxiv created 2005/08/02 · openalex publication_date 2005/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

A novel expansion of the evolution operator associated with an—in general, time-dependent—perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to computational convenience or to satisfy specific requirements. As a remarkable example, the quantum Hamiltonian describing a laser-driven trapped ion is studied in detail.

Citations

• One-parameter semigroups for linear evolution equations
• Information and computation: Classical and quantum aspects
• Completely positive dynamical semigroups of N-level systems
• On the exponential solution of differential equations for a linear operator
• Coarse grained and fine dynamics in trapped ion Raman schemes