𝔖 Bobbio Scriptorium
✦   LIBER   ✦

An algebraic condition for the approach to equilibrium of an openN-level system

✍ Scribed by Herbert Spohn

Publisher
Springer
Year
1977
Tongue
English
Weight
256 KB
Volume
2
Category
Article
ISSN
0377-9017

No coin nor oath required. For personal study only.

✦ Synopsis

We give an algebraic condition in order that a completely positive dynamical semigroup of an N-level system has a unique (invariant) equilibrium state and that every initial state approaches this equilibrium state as t ~ oo. We apply our result to a semigroup arising in the weak coupling limit.

πŸ“œ SIMILAR VOLUMES

The Hexagon Condition and Additive Repre
The Hexagon Condition and Additive Representation for Two Dimensions: An Algebraic Approach
✍ Edi Karni; Zvi Safra πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 267 KB

Within the algebraic approach the Thomsen condition may be replaced with the hexagon condition to imply the existence of additive representation for two dimensions. In some models the Thomsen condition does not have a natural interpretation whereas the hexagon condition does, which makes it better s

An algebraic condition for the separatio
An algebraic condition for the separation of two ellipsoids
✍ Wenping Wang; Jiaye Wang; Myung-Soo Kim πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 80 KB

Given two ellipsoids, we show that their characteristic equation has at least two negative roots and that the ellipsoids are separated by a plane if and only if their characteristic equation has two distinct positive roots. Furthermore, the ellipsoids touch each other externally if and only if the c

An algebraic approach to bound states of
An algebraic approach to bound states of simple one-electron systems
✍ J. Čížek; J. Paldus πŸ“‚ Article πŸ“… 1977 πŸ› John Wiley and Sons 🌐 English βš– 898 KB

## Abstract A very general realization of the so(2, 1) algebra, which easily follows from the basic commutation relations that are satisfied by any pair of mutually conjugate generalized coordinates and momenta, is constructed. Using special cases of this general realization, and closely following

An Algebraic Computational Approach to t
An Algebraic Computational Approach to the Identifiability of Fourier Models
✍ M. Caboara; E. Riccomagno πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 506 KB

Computer algebra and in particular GrΓΆbner bases are powerful tools in experimental design (Pistone and Wynn, 1996, Biometrika 83, 653-666). This paper applies this algebraic methodology to the identifiability of Fourier models. The choice of the class of trigonometric models forces one to deal with