ALGEBRAIC STRUCTURE OF A MASTER EQUATION WITH GENERALIZED LINDBLAD FORM

Kazuyuki Fujii

Type: Article

Publication Date: 2008-11-01

Citations: 5

DOI: https://doi.org/10.1142/s0219887808003168

Abstract

The quantum damped harmonic oscillator is described by the master equation with usual Lindblad form. The equation has been solved completely by us in arXiv: 0710.2724 [quant-ph]. To construct the general solution a few facts of representation theory based on the Lie algebra su(1,1) were used. In this paper we treat a general model described by a master equation with generalized Lindblad form. Then we examine the algebraic structure related to some Lie algebras and construct the interesting approximate solution.

Locations

International Journal of Geometric Methods in Modern Physics - View
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	GENERAL SOLUTION OF THE QUANTUM DAMPED HARMONIC OSCILLATOR II: SOME EXAMPLES	2009	Kazuyuki Fujii Tatsuo Suzuki
+ PDF Chat	A short introduction to the Lindblad master equation	2020	Daniel Manzano
+	Master equation of the Lindblad form based on a microscopic Hamiltonian through stcchastic limit approximation〔邦文〕 (研究会報告第8回「非平衡系の統計物理」シンポジウム)	2001	一哉湯浅
+	Quantum model of an autonomous oscillator in hard excitation regime	2014	E. D. Vol M.A. Ialovega
+	Lindblad dynamics of the damped and forced quantum harmonic oscillator: General solution	2019	H. J. Korsch
+	Lindblad dynamics of the damped and forced quantum harmonic oscillator: General solution	2019	H. J. Korsch
+	A solution ansatz for Lindblad master equation with a dynamical system theory approach	2019	Gehad Sadiek E. I. Lashin
+	Quasithermodynamic Representation of the quantum master equations: its existence , advantages and applications	2014	E. D. Vol
+	Master equation of the Lindblad form based on a microscopic Hamiltonian through stochastic limit approximation(The 8th Symposium on Non-Equilibrium Statisitical Physics)	2001	一哉湯浅
+ PDF Chat	Dynamical symmetry and analytical solutions of the non-autonomous quantum master equation of the dissipative two-level system: decoherence of the quantum register	2003	Shun-Jin Wang Jun‐Hong An Hong‐Gang Luo Chenglong Jia
+ PDF Chat	Many Unstable Particles from an Open Quantum System's Perspective	2014	Kordian A. Smoliński
+ PDF Chat	Exact solution of a master equation applied to the two-level system of an atom	2014	Kazuyuki Fujii
+	Lie symmetry reductions and exact solutions of a coupled KdV–Burgers equation	2014	Shaojie Yang Hua Cun-cai
+	Liouvillian exceptional points in continuous variable system	2023	B. A. Tay
+	Master equation of the Lindblad form based on a microscopic Hamiltonian through stochastic limit approximation : For rapidly decaying systems (Analytical Study of Quantum Information and Related Fields)	2001	一哉湯浅元木村健太郎今福
+ PDF Chat	Solution of the Lindblad equation in the Kraus representation	2006	Hiromichi Nakazato Yuichiro Hida Kazuya Yuasa Benedetto Militello A. Napoli A. Messina
+	Structures of master-equation for the study of decoherence	2003	Bassano Vacchini
+	Master equation of the Lindblad form based on a microscopic Hamiltonian through stochastic limit approximation--For rapidly decaying systems〔和文〕 (量子情報とその周辺分野の解析的研究研究集会報告集)	2002	一哉湯浅元木村健太郎今福
+	Analog of Lie Algebra and Lie Group for Quantum Non-Hamiltonian Systems	1996	Vasily E. Tarasov
+	Lie algebraic solution of the Kratzer oscillator in diatomic molecules	2017	Boris Maulén José Mauricio González

Works That Cite This (5)

Action	Title	Year	Authors
+ PDF Chat	AN APPROXIMATE SOLUTION OF THE JAYNES–CUMMINGS MODEL WITH DISSIPATION II: ANOTHER APPROACH	2012	Kazuyuki Fujii Tatsuo Suzuki
+ PDF Chat	AN APPROXIMATE SOLUTION OF THE JAYNES–CUMMINGS MODEL WITH DISSIPATION	2011	Kazuyuki Fujii Tatsuo Suzuki
+ PDF Chat	A general formulation based on algebraic spinors for the quantum computation	2020	Marco A. S. Trindade Sérgio Floquet J. D. M. Vianna
+ PDF Chat	GENERAL SOLUTION OF THE QUANTUM DAMPED HARMONIC OSCILLATOR II: SOME EXAMPLES	2009	Kazuyuki Fujii Tatsuo Suzuki
+	An Approximate Solution of the Jaynes-Cummings Model with Dissipation II : Another Approach	2011	Kazuyuki Fujii Tatsuo Suzuki

Works Cited by This (12)

Action	Title	Year	Authors
+	An Approximate Solution of the Master Equation with the Dissipator being a Set of Projectors	2007	Kazuyuki Fujii
+	Dissipative Mechanics Using Complex-Valued Hamiltonians	2007	S. G. Rajeev
+	Introduction to Coherent States and Quantum Information Theory	2001	Kazuyuki Fujii
+	Matrix Elements of Generalized Coherent Operators	2002	Kazuyuki Fujii
+	Cavity QED and Quantum Computation in the Weak Coupling Regime II : Complete Construction of the Controlled-Controlled NOT Gate	2005	Kazuyuki Fujii Kyoko Higashida Ryosuke Kato Yukako Wada
+ PDF Chat	Cavity QED and quantum computation in the weak coupling regime	2004	Kazuyuki Fujii Kyoko Higashida Ryosuke Kato Yukako Wada
+ PDF Chat	GENERAL SOLUTION OF THE QUANTUM DAMPED HARMONIC OSCILLATOR	2008	Ryusuke Endo Kazuyuki Fujii Tatsuo Suzuki
+ PDF Chat	Population trapping due to cavity losses	2008	M. Scala Benedetto Militello A. Messina Sabrina Maniscalco Jyrki Piilo Kalle‐Antti Suominen
+ PDF Chat	Charge oscillations in superconducting nanodevices coupled to external environments	2007	Robert Alicki Fabio Benatti Roberto Floreanini
+	Quantum Mechanics with Complex Time : A Comment to the Paper by Rajeev	2007	Kazuyuki Fujii