Quantum walk on the line: entanglement and non-local initial conditions

The conditional shift in the evolution operator of a quantum walk generates entanglement between the coin and position degrees of freedom. This entanglement can be quantified by the von Neumann entropy of the reduced density operator (entropy of entanglement). In the long time limit, it converges to a well defined value which depends on the initial state. Exact expressions for the asymptotic (long-time) entanglement are obtained for (i) localized initial conditions and (ii) initial conditions in the position subspace spanned by the +1 and -1 position eigenstates.Comment: A few mistakes where corrected. One of them leads to a factor of 2 in eq. (49), the other results remain unchanged. In this version, several figures where replaced by color version

Effects of non-local initial conditions in the Quantum Walk on the line

We report an enhancement of the decay rate of the survival probability when non-local initial conditions in position space are considered in the Quantum Walk on the line. It is shown how this interference effect can be understood analytically by using previously derived results. Within a restricted position subspace, the enhanced decay is correlated with a maximum asymptotic entanglement level while the normal decay rate corresponds to initial relative phases associated to a minimum entanglement level.Comment: 5 pages, 1 figure, Elsevier style, to appear in Physica

Studies concerning partially reduced nitrogen heterocycles

Carbanion rearrangement studies on selected N-acyl-isoquinoline and -quinoline Reissert compounds have shown that alternative intramolecular rearrangements can compete successfully with the normal 1,2-acyl-migration. The observations have been rationalised mechanistically and their potential value in synthesis demonstrated. In particular the formation of a 1-benzoyl-8-hydroxyisoquinoline derivative has been effected from carbanion rearrangement of the corresponding 8-benzoyloxy Reissert compound. N-Crotonoylisoquinoline Reissert compound carbanion and analogous structures have been shown to undergo a complex reaction in which Michael type attack competes with the normal migration. [Continues.

Sub-ballistic behavior in quantum systems with L\'evy noise

We investigate the quantum walk and the quantum kicked rotor in resonance subjected to noise with a L\'evy waiting time distribution. We find that both systems have a sub-ballistic wave function spreading as shown by a power-law tail of the standard deviation.Comment: 4 pages, 4 figure

Fellespotten i Regionale forskningsfond – status og utviklingsmuligheter

I denne rapporten presenteres en analyse av den såkalte fellespotten i Regionale forsk-ningsfond. Fellespotten utgjør 15 prosent av de midlene som årlig bevilges til Regionale Forskningsfond, og skal brukes til felles utlysninger i samarbeid mellom regionene for å stimulere til felles satsinger. Formålet med analysen er å gjennomføre en evaluering av ordningen og fremme forslag om videre utvikling av den

The Crossover beteween Aslamazov-Larkin and Short Wavelength Fluctuations Regimes in HTS Conductivity Experiments

We present paraconductivity (AL) measurements in three different high temperature superconductors: a melt textured $YBa_2Cu_3O_7$ sample, a $Bi_2Sr_2CaCu_2O_8$ epitaxial thin film and a highly textured $Bi_2Sr_2Ca_2Cu_3O_{10}$ tape. The crossovers between different temperature regimes in excess conductivity have been analysed. The Lawrence-Doniach (LD) crossover, which separates the 2D and 3D regimes, shifts from lower to higher temperatures as the compound anisotropy decreases. Once the LD crossover is overcome, the fluctuation conductivity of the three compounds shows the same universal behaviour: for $\epsilon =\ln T/T_c > 0.23$ all the curves bend down according to the $1/\epsilon^3$ law. This asymptotic behaviour was theoretically predicted previously for the high temperature region where the short wavelength fluctuations (SWF) become important.Comment: 4 pages, Revtex, 1 PostScript figure available upon request ([email protected]); submitted to Physical Review B rapid communication