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991.
F.?A.?ReuseEmail author K.?Maschke V.?de?Coulon J.?van?der?Klink J.-Ph?Ansermet 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,36(4):573-592
We present a detailed discussion of the evolution of a statistical ensemble of quantum mechanical systems coupled weakly to a bath. The Hilbert space of the full system is given by the tensor product between the Hilbert spaces associated with the bath and the bathed system. The statistical states of the ensemble are described in terms of density matrices. Supposing the bath to be held at some - not necessarily thermal - statistical equilibrium and tracing over the bath degrees of freedom, we obtain reduced density matrices defining the statistical states of the bathed system. The master equations describing the evolution of these reduced density matrices are derived under the most general conditions. On time scales that are large with respect to the bath correlation time
and with respect to the reciprocal transition frequencies of the bathed system, the resulting evolution of the reduced density matrix of the bathed system is of Markovian type. The detailed balance relations valid for a thermal equilibrium of the bath are derived and the conditions for the validity of the fluctuation-dissipation theorem are given. Based on the general approach, we investigate the non-linear response of the bathed subsystem to a time-periodic perturbation. Summing the perturbation series we obtain the coherences and the populations for arbitrary strengths of the perturbation.Received: 26 November 2003, Published online: 30 January 2004PACS:
05.30.-d Quantum statistical mechanics - 33.35. + r Electron resonance and relaxation - 33.25. + k Nuclear resonance and relaxation 相似文献
992.
We study the expansion of derivatives along orbits of real and complex one-dimensional mapsf, whose Julia setJ
f attracts a finite setCrit of non-flat critical points. Assuming that for eachcεCrit, either |D f
n(f(c))|→∞ (iff is real) orb
n·|Df
n(f(c))|→∞ for some summable sequence {b
n} (iff is complex; this is equivalent to summability of |D f
n(f(c))|−1), we show that for everyxεJ
f\U
i
f
−i(Crit), there existℓ(x)≤max
c
ℓ(c) andK′(x)>0
for infinitely manyn. Here 0=n
s<…<n
1<n
0=n are so-called critical times,c
i is a point inCrit (or a repelling periodic point in the boundary of the immediate basin of a hyperbolic periodic attractor), which shadows
orb(x) forn
i−ni
+1 iterates, and
, for uniform constantsK>0 and λ>1. If allcεCrit have the same critical order, thenK′(x) is uniformly bounded away from 0. Several corollaries are derived. In the complex case, eitherJ
f=
orJ
f has zero Lebesgue measure. Also (assuming all critical points have the same order) there existk>0 such that ifn is the smallest integer such thatx enters a certain critical neighbourhood, then |Df
n(x)|≥k.
The original paper used an incorrect version of the Koebe Lemma cited from [21] as was pointed out by the referee and Genadi
Levin in the autumn of 2001. The corrected version of November 2001 only uses the classical Koebe Lemma. Apparently, all results
in Feliks Przytycki’s paper [21] go through using the classical Koebe Lemma instead of his Lemma 1.2.
Both authors gratefully acknowledge the support of the PRODYN program of the European Science Foundation. HB was partially
supported by a fellowship of The Royal Netherlands Academy of Arts and Sciences (KNAW). SvS was partially supported by GR/M82714/01. 相似文献
993.
In an earlier article, Willem H. Haemers has determined the minimum number of parallel classes in a resolvable 2‐(qk,k,1) covering for all k ≥ 2 and q = 2 or 3. Here, we complete the case q = 4, by construction of the desired coverings using the method of simulated annealing. Secondly, we look at equitable resolvable 2‐(qk,k,1) coverings. These are resolvable coverings which have the additional property that every pair of points is covered at most twice. We show that these coverings satisfy k < 2q ? , and we give several examples. In one of these examples, k > q. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 113–123, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10024 相似文献
994.
Rein van der Hout 《Journal of Differential Equations》2003,192(1):188-201
Let and be the unit disk and the unit sphere, and let be a radially symmetric harmonic map heat flow, whose singularities coincide with downward energy jumps. Then its finite time singularities are simple in the sense that precisely one harmonic sphere separates at a time. 相似文献
995.
Roberto van der Putten 《Analysis Mathematica》2003,29(1):75-85
We give a sufficient analytic condition in order that a mapping fW
1,
n
(;R
n) satisfies Lusin's condition (N). 相似文献
996.
In this paper we introduce two tree-width-like graph
invariants. The first graph invariant, which we denote by
=(G), is defined in terms of positive
semi-definite matrices and is similar to the graph invariant
(G), introduced by Colin de Verdière in
[J. Comb. Theory, Ser. B., 74:121–146, 1998]. The second graph
invariant, which we denote by (G), is defined in terms of a certain
connected subgraph property and is similar to (G), introduced by van der Holst,
Laurent, and Schrijver in [J. Comb. Theory, Ser. B., 65:291–304,
1995]. We give some theorems on the behaviour of these
invariants under certain transformations. We show that
=(G)=(G)
for any graph G with
=(G)4, and we give minimal forbidden
minor characterizations for the graphs satisfying
=(G)k
for k=1,2,3,4.This paper is extracted from two chapters of [7].
This work was done while the author was at the Centrum voor
Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The
Netherlands. 相似文献
997.
Our purpose in the paper is to find the most general linear congruence relation of the Hardy-Williams type for linear combinations of special values of Kubota-Leopoldt 2-adic L-functions L2(k,χω1−k) with k running over any finite subset of not necessarily consisting of consecutive integers (see Acta Arith. 47 (1986) 263; Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, 1995/1996; Publ. Math. Debrecen 56 (2000) 677 and cf. Mathematics and Its Applications, Vol. 511, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000). If k runs over finite subsets of consisting of consecutive integers see Compositio Math. 111 (1998) 289; Publ. Math. Debrecen 56 (2000) 677; Hardy and Williams, 1986; Compositio Math. 75 (1990) 271; Acta Arith. 71 (1995) 273; 52 (1989) 147; J. Number Theory 34 (1990) 362. In order to obtain the most general congruences of this type we make use of divisibility properties of the generalized Vandermonde determinants obtained in Spie? et al. (Divisibility properties of generalized Vandermonde and Cauchy determinants, Preprint 627, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 2002). This allows us to simplify our main Theorem 2 and obtain Theorem 3 where the most general form of the linear congruence relation is given. 相似文献
998.
The anisotropy of the spin-orbit interaction, , in vicinal Co films has been measured using x-ray magnetic linear dichroism (XMLD). A linear increase in with Co step density is found using a new sum rule and represents the first experimental confirmation that XMLD probes the magnetocrystalline anisotropy energy (MAE). X-ray magnetic circular dichroism is used to confirm that the XMLD arises from changes in the local step-edge electronic structure. The XMLD sum rule gives a larger MAE compared to macroscopic values and is discussed with respect to other local probes of the MAE. 相似文献
999.
It is shown that the residue expansion of an elliptic Selberg integral gives rise to an integral representation for a multiple modular hypergeometric series. A conjectural evaluation formula for the integral then implies a closed summation formula for the series, generalizing both the multiple basic hypergeometric 87 sum of Milne-Gustafson type and the (one-dimensional) modular hypergeometric 87 sum of Frenkel and Turaev. Independently, the modular invariance ensures the asymptotic correctness of our multiple modular hypergeometric summation formula for low orders in a modular parameter. 相似文献
1000.
A. Priem P. J. M. van Bentum W. R. Hagen E. J. Reijerse 《Applied magnetic resonance》2001,21(3-4):535-548
Fe(III) and Gd(III) ions in α-alumina (A12O3) exhibit spin states ofS = 5/2 andS = 7/2 respectively. The magnitude of the zero-field interaction (ZFI) (D = 0.10?0.15 cm?1) gives rise to an inter Kramers doublet splitting in the same order of magnitude as the X-band electron paramagnetic resonance (EPR) quantum (0.3 cm?1). It is demonstrated that through a careful step-by-step analysis and spectral simulation of EPR spectra taken at D-band (130 GHz), Q-band (35 GHz), and X-band (9 GHz) at room temperature, the (relative) sign and magnitude of the ZFI parameters, b 2 0 , b 4 0 , and b 4 3 , can be reliably estimated. 相似文献