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We approximate the observable Universe by a collection of equal mass galaxies linked into a many body system by their mutual gravitational interaction. Under the assumptions of (i) nonrelativistic approximation and (ii) global quasi-equilibrium, the partition function of this system can be cast in terms of Ising model spin variables and maps exactly onto a three-dimensional scalar classical field theory. The full machinery of the renormalization group and critical phenomena is brought to bear on this field theory allowing one to calculate the galaxy-to-galaxy correlation function, whose critical exponent is predicted to be between 1.530 to 1.862, to be compared to the phenomenological/observational value of 1.6 to 1.8. 相似文献
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Noise and imperfection of realistic devices are major obstacles for implementing quantum cryptography. In particular, birefringence in optical fibers leads to decoherence of qubits encoded in photon polarization. We show how to overcome this problem by doing single qubit quantum communication without a shared spatial reference frame and precise timing. Quantum information will be encoded in pairs of photons using tag operations, which corresponds to the time delay of one of the polarization modes. This method is robust against the phase instability of the interferometers despite the use of time bins. Moreover synchronized clocks are not required in the ideal no photon loss case as they are necessary only to label the different encoded qubits. 相似文献
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We report the implementation of a 3-qubit quantum error-correction code on a quantum information processor realized by the magnetic resonance of carbon nuclei in a single crystal of malonic acid. The code corrects for phase errors induced on the qubits due to imperfect decoupling of the magnetic environment represented by nearby spins, as well as unwanted evolution under the internal Hamiltonian. We also experimentally demonstrate sufficiently high-fidelity control to implement two rounds of quantum error correction. This is a demonstration of state-of-the-art control in solid state nuclear magnetic resonance, a leading test bed for the implementation of quantum algorithms. 相似文献
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Claude Laflamme Maurice Pouzet Norbert Sauer 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2017,87(2):369-408
A tree is scattered if it does not contain a subdivision of the complete binary tree as a subtree. We show that every scattered tree contains a vertex, an edge, or a set of at most two ends preserved by every embedding of T. This extends results of Halin, Polat and Sabidussi. Calling two trees equimorphic if each embeds in the other, we then prove that either every tree that is equimorphic to a scattered tree T is isomorphic to T, or there are infinitely many pairwise non-isomorphic trees which are equimorphic to T. This proves the tree alternative conjecture of Bonato and Tardif for scattered trees, and a conjecture of Tyomkyn for locally finite scattered trees. 相似文献
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Let
be a universal binary countable homogeneous structure and n∈ω. We determine the equivalence relation
on [U]n with the smallest number of equivalence classes r so that each one of the classes is indivisible. As a consequence we obtain
and a characterization of the smallest number r so that the arrow relation above holds.
For the case of infinitely many colors we determine the canonical set of equivalence relations, extending the result of Erdős
and Rado for the integers to countable universal binary homogeneous structures.
* Supported by NSERC of Canada Grant # 690404.
† Supported by NSERC of Canada Grant # 691325. 相似文献
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Salvador Garcia-Ferreira Claude Laflamme 《Proceedings of the American Mathematical Society》1998,126(6):1791-1798
The property may be generalized by using filters on in a very natural way. We analyze the necessary requirements for a space to have property for a filter . We construct special filters for which has the property, in particular a P-point and a Q-point.
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