✦ LIBER ✦

Operator differential equation approach to the dissipative two-state system

✍ Scribed by Minhaeng Cho

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 537 KB
Volume: 241
Category: Article
ISSN: 0378-4371
DOI: 10.1016/s0378-4371(97)00171-4

No coin nor oath required. For personal study only.

✦ Synopsis

We consider a two-state system linearly coupled to a collection of harmonic oscillators, the spin-boson Hamiltonian. Expanding the density matrix in terms of Pauli spin matrices, a set of coupled operator differential equations of motion is obtained by solving the Heisenberg equation. Using the cumulant expansion methods, the expectation values of the Pauli spin matrices are obtained and found to be valid for both coherent and incoherent regimes. The results are compared with other approaches.

📜 SIMILAR VOLUMES

A projection operator approach to a diss

A projection operator approach to a dissipative two-level system

✍ M. Morillo; R.I. Cukier; M. Tij 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 784 KB

A Positive Operator Approach to the Neum

A Positive Operator Approach to the Neumann Problem for a Second Order Ordinary Differential Equation

✍ Alberto Cabada; Luis Sanchez 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 171 KB

We suppose that there is a lower solution ␥ and an upper solution ␤ in the reversed order, and we obtain optimal conditions in f to assure the existence of a solution lying between ␤ and ␥.

Solution to system of partial fractional

Solution to system of partial fractional differential equations using the fractional exponential operators

✍ A. Ansari; A. Refahi Sheikhani; H. Saberi Najafi 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 104 KB

In this article, fractional exponential operator is considered as a general approach for solving partial fractional differential equations. An integral representation for this operator is derived from the Bromwich integral for the inverse Mellin transform. Also, effectiveness of this operator for ob

Stratified quantization approach to diss

Stratified quantization approach to dissipative quantum systems: Derivation of the Hamiltonian and kinetic equations for reduced density matrices

✍ W.H. Richardson 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 474 KB

Two reduced-form approaches to the deriv

Two reduced-form approaches to the derivation of the maximum-likelihood estimators for simultaneous-equation systems

✍ D.S.G. Pollock 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 909 KB

Extension of the notion of “saddle point

Extension of the notion of “saddle point” to systems of two differential equations in three variables

✍ Luigi Amerio 📂 Article 📅 1953 🏛 John Wiley and Sons 🌐 English ⚖ 718 KB

Let us consider the differential equation (1) g(z, Y) f b , Y) dY = 0 and suppose that Po(zo , yo) is a singular point ( f ( z o , yo) = g(ro , yo) = O), more precisely a saddle point, i.e., that It is well known that, in this case, there whic.h pass through the point Po and separate 0. exist two i