75 research outputs found
2 and 3-dimensional Hamiltonians with Shape Invariance Symmetry
Via a special dimensional reduction, that is, Fourier transforming over one
of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator
Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape
invariance symmetry. Using this symmetry we have obtained their eigenspectrum.
In the mean time we show equivalence of shape invariance symmetry and Lie
algebraic symmetry of these Hamiltonians.Comment: 24 Page
Hierarchy of random deterministic chaotic maps with an invariant measure
Hierarchy of one and many-parameter families of random trigonometric chaotic
maps and one-parameter random elliptic chaotic maps of type with an
invariant measure have been introduced. Using the invariant measure
(Sinai-Ruelle-Bowen measure), the Kolmogrov-Sinai entropy of the random chaotic
maps have been calculated analytically, where the numerical simulations support
the resultsComment: 11 pages, Late
Generating GHZ state in 2m-qubit spin network
We consider a pure 2m-qubit initial state to evolve under a particular
quantum me- chanical spin Hamiltonian, which can be written in terms of the
adjacency matrix of the Johnson network J(2m;m). Then, by using some techniques
such as spectral dis- tribution and stratification associated with the graphs,
employed in [1, 2], a maximally entangled GHZ state is generated between the
antipodes of the network. In fact, an explicit formula is given for the
suitable coupling strengths of the hamiltonian, so that a maximally entangled
state can be generated between antipodes of the network. By using some known
multipartite entanglement measures, the amount of the entanglement of the final
evolved state is calculated, and finally two examples of four qubit and six
qubit states are considered in details.Comment: 22 page
Evaluation of effective resistances in pseudo-distance-regular resistor networks
In Refs.[1] and [2], calculation of effective resistances on distance-regular
networks was investigated, where in the first paper, the calculation was based
on the stratification of the network and Stieltjes function associated with the
network, whereas in the latter one a recursive formula for effective
resistances was given based on the Christoffel-Darboux identity. In this paper,
evaluation of effective resistances on more general networks called
pseudo-distance-regular networks [21] or QD type networks \cite{obata} is
investigated, where we use the stratification of these networks and show that
the effective resistances between a given node such as and all of the
nodes belonging to the same stratum with respect to
(, belonging to the -th stratum with respect
to the ) are the same. Then, based on the spectral techniques, an
analytical formula for effective resistances such that
(those nodes , of
the network such that the network is symmetric with respect to them) is given
in terms of the first and second orthogonal polynomials associated with the
network, where is the pseudo-inverse of the Laplacian of the network.
From the fact that in distance-regular networks,
is satisfied for all nodes
of the network, the effective resistances
for ( is diameter of the network which
is the same as the number of strata) are calculated directly, by using the
given formula.Comment: 30 pages, 7 figure
Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory
The method of the quantum probability theory only requires simple structural
data of graph and allows us to avoid a heavy combinational argument often
necessary to obtain full description of spectrum of the adjacency matrix. In
the present paper, by using the idea of calculation of the probability
amplitudes for continuous-time quantum walk in terms of the quantum probability
theory, we investigate quantum central limit theorem for continuous-time
quantum walks on odd graphs.Comment: 19 page, 1 figure
Tunneling in Decaying Cosmologies and the Cosmological Constant Problem
The tunneling rate, with exact prefactor, is calculated to first order in
for an empty closed Friedmann-Robertson-Walker (FRW) universe with
decaying cosmological term ( is the scale factor and
is a parameter ). This model is equivalent to a cosmology
with the equation of state . The calculations are
performed by applying the dilute-instanton approximation on the corresponding
Duru-Kleinert path integral.
It is shown that the highest tunneling rate occurs for corresponding to
the cosmic string matter universe. The obtained most probable cosmological
term, like one obtained by Strominger, accounts for a possible solution to the
cosmological constant problem.Comment: 21 pages, REVTEX, The section 3 is considerably completed including
some physical mechanisms supporting the time variation of the cosmological
constant, added references for the section 3. Accepted to be published in
Phys. Rev.
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