Discrete phase-space approach to mutually orthogonal Latin squares

We show there is a natural connection between Latin squares and commutative sets of monomials defining geometric structures in finite phase-space of prime power dimensions. A complete set of such monomials defines a mutually unbiased basis (MUB) and may be associated with a complete set of mutually orthogonal Latin squares (MOLS). We translate some possible operations on the monomial sets into isomorphisms of Latin squares, and find a general form of permutations that map between Latin squares corresponding to unitarily equivalent mutually unbiased sets. We extend this result to a conjecture: MOLS associated to unitarily equivalent MUBs will always be isomorphic, and MOLS associated to unitarily inequivalent MUBs will be non-isomorphic

General properties of quantum optical systems in a strong field limit

We investigate the dynamics of an arbitrary atomic system (n-level atoms or many n-level atoms) interacting with a resonant quantized mode of an em field. If the initial field state is a coherent state with a large photon number then the system dynamics possesses some general features, independently of the particular structure of the atomic system. Namely, trapping states, factorization of the wave function, collapses and revivals of the atomic energy oscillations are discussed

Berry phase in Heisenberg representation

We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system

Immune System in the Brain: A Modulatory Role on Dendritic Spine Morphophysiology?

The central nervous system is closely linked to the immune system at several levels. The brain parenchyma is separated from the periphery by the blood brain barrier, which under normal conditions prevents the entry of mediators such as activated leukocytes, antibodies, complement factors, and cytokines. The myeloid cell lineage plays a crucial role in the development of immune responses at the central level, and it comprises two main subtypes: (1) resident microglia, distributed throughout the brain parenchyma; (2) perivascular macrophages located in the brain capillaries of the basal lamina and the choroid plexus. In addition, astrocytes, oligodendrocytes, endothelial cells, and, to a lesser extent, neurons are implicated in the immune response in the central nervous system. By modulating synaptogenesis, microglia are most specifically involved in restoring neuronal connectivity following injury. These cells release immune mediators, such as cytokines, that modulate synaptic transmission and that alter the morphology of dendritic spines during the inflammatory process following injury. Thus, the expression and release of immune mediators in the brain parenchyma are closely linked to plastic morphophysiological changes in neuronal dendritic spines. Based on these observations, it has been proposed that these immune mediators are also implicated in learning and memory processes

Geometrical approach to mutually unbiased bases

We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the Bloch-sphere principal axes. We suggest how to generalize the method to systems in dimensions that are powers of a prime.Comment: 10 pages. Some typos in the journal version have been correcte