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1.
We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω0, where ω0 is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small. 相似文献
2.
Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX
W ⊂A
Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove
that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite
type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations,
we obtain all sofic systems.
The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716. 相似文献
3.
Chau O. Shillor M. Sofonea M. 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(1):32-47
A model for the dynamic, adhesive, frictionless contact
between a viscoelastic body and a deformable foundation is
described. The adhesion process is modeled by a bonding field on
the contact surface. The contact is described by a modified normal
compliance condition. The tangential shear due to the bonding
field is included. The problem is formulated as a coupled system
of a variational equality for the displacements and a differential
equation for the bonding field. The existence of a unique weak
solution for the problem is established, together with a partial
regularity result. The existence proof proceeds by construction of
an appropriate mapping which is shown to be a contraction on a
Hilbert space. 相似文献
4.
We obtain various results involving the centroid branches of randomly chosen trees from simply generated families. 相似文献
5.
6.
7.
8.
The outer-distance of a nodeu in a rooted treeT
n
is the height of the subtree determined byu and all nodesv such thatu is on the path joiningv and the root ofT. We show that the expected outer-distance of nodes of treesT
n
in certain families is asymptotic toB logn where the constantB depends on . 相似文献
9.
— , B
n
, B p1., , p=1 , - . , , , p. 相似文献
10.