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11.
The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance. 相似文献
12.
Aspects of Generic Entanglement 总被引:4,自引:4,他引:0
Patrick Hayden Debbie W. Leung Andreas Winter 《Communications in Mathematical Physics》2006,265(1):95-117
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations
are quantified by parameters that are subject to the ``concentration of measure' phenomenon, meaning that on a large-probability
set these parameters are close to their expectation. For the entropy of entanglement, this has the counterintuitive consequence
that there exist large subspaces in which all pure states are close to maximally entangled. This, in turn, implies the existence
of mixed states with entanglement of formation near that of a maximally entangled state, but with negligible quantum mutual
information and, therefore, negligible distillable entanglement, secret key, and common randomness. It also implies a very
strong locking effect for the entanglement of formation: its value can jump from maximal to near zero by tracing over a number
of qubits negligible compared to the size of the total system. Furthermore, such properties are generic. Similar phenomena
are observed for random multiparty states, leading us to speculate on the possibility that the theory of entanglement is much
simplified when restricted to asymptotically generic states. Further consequences of our results include a complete derandomization
of the protocol for universal superdense coding of quantum states. 相似文献
13.
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process. 相似文献
14.
Andreas Speiser 《Monatshefte für Mathematik》1939,48(1):240-244
Ohne Zusammenfassung 相似文献
15.
16.
Thorsten Brand Kyle Ratinac Jeffrey V. Castro Robert G. Gilbert 《Journal of polymer science. Part A, Polymer chemistry》2004,42(22):5706-5713
A method was developed for free‐radical polymerization in the confines of a hollow latex particle. Hollow particles were prepared via the dynamic swelling method from polystyrene seed and divinylbenzene and had hollows of 500–1000 nm. So that these hollow poly(divinylbenzene) particles could function as submicrometer reactors, the particles were filled with a monomer (N‐isopropylacrylamide) via the dispersion of the dried particles in the molten monomer. The monomer that was not contained in the hollows was removed by washing and gentle abrasion. Free‐radical polymerization was then initiated by γ radiolysis in the solid state. Transmission electron microscopy showed that poly(N‐isopropylacrylamide) formed in the hollow interior of the particles, which functioned as submicrometer reactors. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5706–5713, 2004 相似文献
17.
Selecting, modifying or creating appropriate problems for mathematics class has become an activity of increaing importance in the professional development of German mathematics teachers. But rather than asking in general: “What is a good problem?” there should be a stronger emphasis on considering the specific goal of a problem, e.g.: “What are the ingredients that make a problem appropriate for initiating a learning process” or “What are the characteristics that make a problem appropriate for its use in a central test?” We propose a guiding scheme for teachers that turns out to be especially helpful, since the newly introduced orientation on outcome standards a) leads to a critical predominance of test items and b) expects teachers to design adequate problems for specific learning processes (e.g. problem solving, reasoning and modelling activities). 相似文献
18.
Arno Jüschke Johannes Jahn Andreas Kirsch 《Computational Optimization and Applications》1997,7(3):261-276
In this paper we consider a special optimization problem withtwo objectives which arises in antenna theory. It is shown that thisabstract bicriterial optimization problem has at least one solution.Discretized versions of this problem are also discussed, and therelationships between these finite dimensional problems and the infinitedimensional problem are investigated. Moreover, we presentnumerical results for special parameters using a multiobjectiveoptimization method. 相似文献
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