Tensor operators and Wigner-Eckart theorem for the quantum superalgebra U_{q}[osp(1\mid 2)]

Tensor operators in graded representations of Z_{2}-graded Hopf algebras are defined and their elementary properties are derived. Wigner-Eckart theorem for irreducible tensor operators for U_{q}[osp(1\mid 2)] is proven. Examples of tensor operators in the irreducible representation space of Hopf algebra U_{q}[osp(1\mid 2)] are considered. The reduced matrix elements for the irreducible tensor operators are calculated. A construction of some elements of the center of U_{q}[osp(1\mid 2)] is given.Comment: 16 pages, Late

Convergence to equilibrium under a random Hamiltonian

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.Comment: 11 pages, 1 figure, v1-v3: some minor errors and typos corrected and new references added; v4: results for the degenerated spectrum added; v5: reorganized and rewritten version; to appear in PR

Percolation in Models of Thin Film Depositions

We have studied the percolation behaviour of deposits for different (2+1)-dimensional models of surface layer formation. The mixed model of deposition was used, where particles were deposited selectively according to the random (RD) and ballistic (BD) deposition rules. In the mixed one-component models with deposition of only conducting particles, the mean height of the percolation layer (measured in monolayers) grows continuously from 0.89832 for the pure RD model to 2.605 for the pure RD model, but the percolation transition belong to the same universality class, as in the 2- dimensional random percolation problem. In two- component models with deposition of conducting and isolating particles, the percolation layer height approaches infinity as concentration of the isolating particles becomes higher than some critical value. The crossover from 2d to 3d percolation was observed with increase of the percolation layer height.Comment: 4 pages, 5 figure

Correlation studies of open and closed states fluctuations in an ion channel: Analysis of ion current through a large conductance locust potassium channel

Ion current fluctuations occurring within open and closed states of large conductance locust potassium channel (BK channel) were investigated for the existence of correlation. Both time series, extracted from the ion current signal, were studied by the autocorrelation function (AFA) and the detrended fluctuation analysis (DFA) methods. The persistent character of the short- and middle-range correlations of time series is shown by the slow decay of the autocorrelation function. The DFA exponent $\alpha$ is significantly larger than 0.5. The existence of strongly-persistent long-range correlations was detected only for closed-states fluctuations, with $\alpha=0.98\pm0.02$. The long-range correlation of the BK channel action is therefore determined by the character of closed states. The main outcome of this study is that the memory effect is present not only between successive conducting states of the channel but also independently within the open and closed states themselves. As the ion current fluctuations give information about the dynamics of the channel protein, our results point to the correlated character of the protein movement regardless whether the channel is in its open or closed state.Comment: 12 pages, 5 figures; to be published in Phys. Rev.

Subsystem dynamics under random Hamiltonian evolution

We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and fluctuations. We show that the reduced density matrix can be described in terms of a noncentral correlated Wishart ensemble for which we are able to perform analytical calculations of the eigenvalue density. Our description accounts for a transition from an arbitrary initial state towards a random state at large times, enabling us to determine the convergence time after which random states are reached. We identify and describe a number of other interesting features, like a series of collisions between the largest eigenvalue and the bulk, accompanied by a phase transition in its distribution function.Comment: 16 pages, 8 figures; v3: slightly re-structured and an additional appendi

Determining the neurotransmitter concentration profile at active synapses

Establishing the temporal and concentration profiles of neurotransmitters during synaptic release is an essential step towards understanding the basic properties of inter-neuronal communication in the central nervous system. A variety of ingenious attempts has been made to gain insights into this process, but the general inaccessibility of central synapses, intrinsic limitations of the techniques used, and natural variety of different synaptic environments have hindered a comprehensive description of this fundamental phenomenon. Here, we describe a number of experimental and theoretical findings that has been instrumental for advancing our knowledge of various features of neurotransmitter release, as well as newly developed tools that could overcome some limits of traditional pharmacological approaches and bring new impetus to the description of the complex mechanisms of synaptic transmission

Distillation of entanglement by projection on permutationally invariant subspaces

We consider distillation of entanglement from two qubit states which are mixtures of three mutually orthogonal states: two pure entangled states and one pure product state. We distill entanglement from such states by projecting n copies of the state on permutationally invariant subspace and then applying one-way hashing protocol. We find analytical expressions for the rate of the protocol. We also generalize this method to higher dimensional systems. To get analytical expression for two qubit case, we faced a mathematical problem of diagonalizing a family of matrices enjoying some symmetries w.r.t. to symmetric group. We have solved this problem in two ways: (i) directly, by use of Schur-Weyl decomposition and Young symmetrizers (ii) showing that the problem is equivalent to a problem of diagonalizing adjacency matrices in a particular instance of a so called algebraic association scheme.Comment: 22 pages, comments welcom

Distinct Modulation of Spontaneous and GABA-Evoked Gating by Flurazepam Shapes Cross-Talk Between Agonist-Free and Liganded GABAA Receptor Activity

GABAA receptors (GABAARs) play a crucial inhibitory role in the CNS. Benzodiazepines (BDZs) are positive modulators of specific subtypes of GABAARs, but the underlying mechanism remains obscure. Early studies demonstrated the major impact of BDZs on binding and more recent investigations indicated gating, but it is unclear which transitions are affected. Moreover, the upregulation of GABAAR spontaneous activity by BDZs indicates their impact on receptor gating but the underlying mechanisms remain unknown. Herein, we investigated the effect of a BDZ (flurazepam) on the spontaneous and GABA-induced activity for wild-type (WT, α1β2γ2) and mutated (at the orthosteric binding site α1F64) GABAARs. Surprisingly, in spite of the localization at the binding site, these mutations increased the spontaneous activity. Flurazepam (FLU) upregulated this activity for mutants and WT receptors to a similar extent by affecting opening/closing transitions. Spontaneous activity affected GABA-evoked currents and is manifested as an overshoot after agonist removal that depended on the modulation by BDZs. We explain the mechanism of this phenomenon as a cross-desensitization of ligand-activated and spontaneously active receptors. Moreover, due to spontaneous activity, FLU-pretreatment and co-application (agonist + FLU) protocols yielded distinct results. We provide also the first evidence that GABAAR may enter the desensitized state in the absence of GABA in a FLU-dependent manner. Based on our data and model simulations, we propose that FLU affects agonist-induced gating by modifying primarily preactivation and desensitization. We conclude that the mechanisms of modulation of spontaneous and ligand-activated GABAAR activity concerns gating but distinct transitions are affected in spontaneous and agonist-evoked activity