The extended metamorphosis of a complete bipartite design into a cycle system

A K-t,K-t-design of order n is an edge-disjoint decomposition of K-n into copies of K-t,K-t. When t is odd, an extended metamorphosis of a K-t,K-t-design of order n into a 2t-cycle system of order n is obtained by taking (t - 1)/2 edge-disjoint cycles of length 2t from each K-t,K-t block, and rearranging all the remaining 1-factors in each K-t,K-t block into further 2t-cycles. The 'extended' refers to the fact that as many subgraphs isomorphic to a 2t-cycle as possible are removed from each K-t,K-t block, rather than merely one subgraph. In this paper an extended metamorphosis of a K-t,K-t-design of order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is given for all odd t > 3. A metamorphosis of a 2-fold K-t,K-t-design of any order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is also given, for all odd t > 3. (The case t = 3 appeared in Ars Combin. 64 (2002) 65-80.) When t is even, the graph K-t,K-t is easily seen to contain t/2 edge-disjoint cycles of length 2t, and so the metamorphosis in that case is straightforward. (C) 2004 Elsevier B.V. All rights reserved.

Steiner trade spectra of complete partite graphs

The Steiner trade spectrum of a simple graph G is the set of all integers t for which there is a simple graph H whose edges can be partitioned into t copies of G in two entirely different ways. The Steiner trade spectra of complete partite graphs were determined in all but a few cases in a recent paper by Billington and Hoffman (Discrete Math. 250 (2002) 23). In this paper we resolve the remaining cases. (C) 2004 Elsevier B.V. All rights reserved.

Deterministic generation of tailored-optical-coherent-state superpositions

Pulsed coherent excitation of a two-level atom strongly coupled to a resonant cavity mode will create a superposition of two coherent states of opposite amplitudes in the field. By choosing proper parameters of interaction time and pulse shape the field after the pulse will be almost disentangled from the atom and can be efficiently outcoupled through cavity decay. The fidelity of the generation approaches unity if the atom-field coupling strength is much larger than the atomic and cavity decay rates. This implies a strong difference between even and odd output photon number counts. Alternatively, the coherence of the two generated field components can be proven by phase-dependent annihilation of the generated nonclassical superposition state by a second pulse.

Fungible dynamics: There are only two types of entangling multiple-qubit interactions

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? It has been shown that all two-body Hamiltonian evolutions can be simulated using any fixed two-body entangling n-qubit Hamiltonian and fast local unitaries. By entangling we mean that every qubit is coupled to every other qubit, if not directly, then indirectly via intermediate qubits. We extend this study to the case where interactions may involve more than two qubits at a time. We find necessary and sufficient conditions for an arbitrary n-qubit Hamiltonian to be dynamically universal, that is, able to simulate any other Hamiltonian acting on n qubits, possibly in an inefficient manner. We prove that an entangling Hamiltonian is dynamically universal if and only if it contains at least one coupling term involving an even number of interacting qubits. For odd entangling Hamiltonians, i.e., Hamiltonians with couplings that involve only an odd number of qubits, we prove that dynamic universality is possible on an encoded set of n-1 logical qubits. We further prove that an odd entangling Hamiltonian can simulate any other odd Hamiltonian and classify the algebras that such Hamiltonians generate. Thus, our results show that up to local unitary operations, there are only two fundamentally different types of entangling Hamiltonian on n qubits. We also demonstrate that, provided the number of qubits directly coupled by the Hamiltonian is bounded above by a constant, our techniques can be made efficient.

Molecular dynamics simulation of the structural and dynamic properties of dioctadecyldimethyl ammoniums in organoclays

The structural and dynamic properties of dioctadecyldimethylammoniums (DODDMA) intercalated into 2:1 layered clays are investigated using isothermal-isobaric (NPT) molecular dynamics (MD) simulation. The simulated results are in reasonably good agreement with the available experimental measurements, such as X-ray diffraction (XRD), atom force microscopy (AFM), Fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR) spectroscopies. The nitrogen atoms are found to be located mainly within two layers close to the clay surface whereas methylene groups form a pseudoquadrilayer structure. The results of tilt angle and order parameter show that interior two-bond segments of alkyl chains prefer an arrangement parallel to the clay surface, whereas the segments toward end groups adopt a random orientation. In addition, the alkyl chains within the layer structure lie almost parallel to the clay surface whereas those out of the layer structure are essentially perpendicular to the surface. The trans conformations are predominant in all cases although extensive gauche conformations are observed, which is in agreement with previous simulations on n-butane. Moreover, an odd-even effect in conformation distributions is observed mainly along the chains close to the head and tail groups. The diffusion constants of both nitrogen atoms and methylene groups in these nanoconfined alkyl chains increase with the temperature and methelene position toward the tail groups.

On the spectrum of non-Denniston maximal arcs in PG(2,2h)

In 1969, Denniston gave a construction of maximal arcs of degree n in Desarguesian projective planes of even order q, for all n dividing q. Recently, Mathon gave a construction method that generalized that of Denniston. In this paper we use that method to give maximal arcs that are not of Dermiston type for all n dividing q, 4 < n < q/2, q even. It is then shown that there are a large number of isomorphism classes of such maximal arcs when n is approximately rootq. (C) 2003 Elsevier Ltd. All rights reserved.

Coherent-state linear optical quantum computing gates using simplified diagonal superposition resource states

In this paper we explore the possibility of fundamental tests for coherent-state optical quantum computing gates [ T. C. Ralph et al. Phys. Rev. A 68 042319 (2003)] using sophisticated but not unrealistic quantum states. The major resource required in these gates is a state diagonal to the basis states. We use the recent observation that a squeezed single-photon state [S(r)∣1⟩] approximates well an odd superposition of coherent states (∣α⟩−∣−α⟩) to address the diagonal resource problem. The approximation only holds for relatively small α, and hence these gates cannot be used in a scalable scheme. We explore the effects on fidelities and probabilities in teleportation and a rotated Hadamard gate.

Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that are not universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner [Phys. Rev. A 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation.

A new class of critical sets in Latin squares

Previously the process of finding critical sets in Latin squares has been inside cumbersome by the complexity and number of Latin trades that, must be constructed. In this paper we develop a theory of Latin trades that yields more transparent constructions. We use these Latin trades to find a new class of critical sets for Latin squares which are a product of the Latin square of order 2 with a. back circulant Latin square of odd order.

Central elements of the elliptic Zn monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the Z(n) R-matrix are studied. When the crossing parameter w takes a special rational value w = n/N, where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the quantum determinant provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo. (c) 2004 Elsevier B.V. All rights reserved.

Primary Fields and Screening Currents of gl (2/2) non-unitary conformal field theory

The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields. (C) 2004 Elsevier B.V All rights reserved.

Decomposition of complete graphs into 5-cubes

Necessary conditions for the complete graph on n vertices to have a decomposition into 5-cubes are that 5 divides it - 1 and 80 divides it (it - 1)/2. These are known to be sufficient when n is odd. We prove them also sufficient for it even, thus completing the spectrum problem for the 5-cube and lending further weight to a long-standing conjecture of Kotzig. (c) 2005 Wiley Periodicals, Inc.

Irreducible 2-fold cycle systems

In this paper, it is shown that for any pair of integers (m, n) with 4 ≤ m ≤ n, if there exists an m-cycle system of order n, then there exists an irreducible 2-fold m-cycle system of order n, except when (m, n) = (5,5). A similar result has already been established for the case of 3-cycles. © 2005 Wiley Periodicals, Inc.

Naturalism and the paradox of revisability

This paper examines the paradox of revisability. This paradox was proposed by Jerrold Katz as a problem for Quinean naturalised epistemology Katz employs diagonalisation to demonstrate what he takes to be an inconsistency in the constitutive principles of Quine's epistemology. Specifically, the problem seems to rest with the principle of universal revisability which states that no statement is immune to revision. In this paper it is argued that although there is something odd about employing universal revisability to revise itself, there is nothing paradoxical about this. At least, there is no paradox along the lines suggested by Katz.

Steiner triple systems with two disjoint subsystems

It is shown that there exists a triangle decomposition of the graph obtained from the complete graph of order v by removing the edges of two vertex disjoint complete subgraphs of orders u and w if and only if u, w, and v are odd, ((v)(2)) - ((u)(2)) - ((w)(2)) equivalent to 0 (mod 3), and v >= w + u + max {u, w}. Such decompositions are equivalent to group divisible designs with block size 3, one group of size u, one group of size w, and v - u - w groups of size 1. This result settles the existence problem for Steiner triple systems having two disjoint specified subsystems, thereby generalizing the well-known theorem of Doyen and Wilson on the existence of Steiner triple systems with a single specified subsystem. (c) 2005 Wiley Periodicals, Inc.