Biomaterial Database

Exactly solvable approximating models for Rabi Hamiltonian dynamics. 2006

Andrey Pereverzev, and Eric R Bittner

Department of Chemistry and Center for Materials Chemistry, University of Houston, Houston, TX 77204, USA. aperever@mail.uh.edu

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonalizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By keeping only certain terms, we can achieve an excellent approximation to the exact dynamics within specified parameter ranges.

UI	MeSH Term	Description	Entries
D008433	Mathematics	The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)	Mathematic
D008962	Models, Theoretical	Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.	Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D011336	Probability	The study of chance processes or the relative frequency characterizing a chance process.	Probabilities
D011789	Quantum Theory	The theory that the radiation and absorption of energy take place in definite quantities called quanta (E) which vary in size and are defined by the equation E	Quantum Theories,Theories, Quantum,Theory, Quantum
D001703	Biophysics	The study of PHYSICAL PHENOMENA and PHYSICAL PROCESSES as applied to living things.	Mechanobiology
D012996	Solutions	The homogeneous mixtures formed by the mixing of a solid, liquid, or gaseous substance (solute) with a liquid (the solvent), from which the dissolved substances can be recovered by physical processes. (From Grant & Hackh's Chemical Dictionary, 5th ed)	Solution
D055095	Optics and Photonics	A specialized field of physics and engineering involved in studying the behavior and properties of light and the technology of analyzing, generating, transmitting, and manipulating ELECTROMAGNETIC RADIATION in the visible, infrared, and ultraviolet range.	Photonics,Photonics and Optics
D055592	Biophysical Phenomena	The physical characteristics and processes of biological systems.	Biophysical Concepts,Biophysical Processes,Biophysical Phenomenon,Biophysical Process,Biophysical Concept,Concept, Biophysical,Concepts, Biophysical,Phenomena, Biophysical,Phenomenon, Biophysical,Process, Biophysical,Processes, Biophysical