Certainty relations between local and nonlocal observables

We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or nonlocal) measurements. E.g., the more accurate we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite entangled state), the less accurate some other property, local to the three qubits, become. We also show that the corresponding complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.Comment: 4 pages, no figure

Two-photon imaging and quantum holography

It has been claimed that ``the use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever strength of the correlations between the two photons'' [A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett. 87, 123602 (2001)]. While we believe that the cited statement is true, we show that the method proposed in that paper, with ``bucket detection'' of one of the photons, will give identical results for entangled states as for appropriately prepared classically correlated states.Comment: 4 pages, 2 figures, REVTe

Charge Localization and Ordering in A2_2Mn8_8O16_{16} Hollandite Group Oxides: Impact of Density Functional Theory Approaches

The phases of A$_2$Mn$_8$O$_{16}$ hollandite group oxides emerge from the competition between ionic interactions, Jahn-Teller effects, charge ordering, and magnetic interactions. Their balanced treatment with feasible computational approaches can be challenging for commonly used approximations in Density Functional Theory. Three examples (A = Ag, Li and K) are studied with a sequence of different approximate exchange-correlation functionals. Starting from a generalized gradient approximation (GGA), an extension to include van der Waals interactions and a recently proposed meta-GGA are considered. Then local Coulomb interactions for the Mn $3d$ electrons are more explicitly considered with the DFT+$U$ approach. Finally selected results from a hybrid functional approach provide a reference. Results for the binding energy of the A species in the parent oxide highlight the role of van der Waals interactions. Relatively accurate results for insertion energies can be achieved with a low $U$ and a high $U$ approach. In the low $U$ case, the materials are described as band metals with a high symmetry, tetragonal crystal structure. In the high $U$ case, the electrons donated by A result in formation of local Mn$^{3+}$ centers and corresponding Jahn-Teller distortions characterized by a local order parameter. The resulting degree of monoclinic distortion depends on charge ordering and magnetic interactions in the phase formed. The reference hybrid functional results show charge localization and ordering. Comparison to low temperature experiments of related compounds suggests that charge localization is the physically correct result for the hollandite group oxides studied here. . . .Comment: 16 pages, 8 figure

Experimental study of the delayed threshold phenomenon in a semiconductor laser

An experimental study of the delayed threshold phenomenon in a Vertical Extended Cavity Semiconductor Emitting Laser is carried out. Under modulation of the pump power, the laser intensity exhibits a hysteresis behavior in the vicinity of the threshold. The temporal width of this hysteresis is measured as a function of the modulation frequency, and is proved to follow the predicted scaling law. A model based on the rate equations is derived and used to analyze the experimental observations. A frequency variation of the laser around the delayed threshold and induced by the phase-amplitude coupling is predicted and estimated

Entangled-State Lithography: Tailoring any Pattern with a Single State

We demonstrate a systematic approach to Heisenberg-limited lithographic image formation using four-mode reciprocal binominal states. By controlling the exposure pattern with a simple bank of birefringent plates, any pixel pattern on a $(N+1) \times (N+1)$ grid, occupying a square with the side half a wavelength long, can be generated from a $2 N$-photon state.Comment: 4 pages, 4 figure

Polariton Dispersion Law in Periodic Bragg and Near-Bragg Multiple Quantum Well Structures

The structure of polariton spectrum is analyzed for periodic multiple quantum well structures with periods at or close to Bragg resonance condition at the wavelength of the exciton resonance. The results obtained used to discuss recent reflection and luminescent experiments by M. H\"{u}bner et al [Phys. Rev. Lett. {\bf 83}, 2841 (1999)] carried out with long multiple quantum well structures. It is argued that the discussion of quantum well structures with large number of wells is more appropriate in terms of normal modes of infinite periodic structures rather then in terms of super- and sub- radiant modes.Comment: replaced with a new version, an error in one of the equations is correcte

Cystatins as calpain inhibitors: Engineered chicken cystatin- and stefin B-kininogen domain 2 hybrids support a cystatin-like mode of interaction with the catalytic subunit of μ-calpain

Within the cystatin superfamily, only kininogen domain 2 (KD2) is able to inhibit μ- and m-calpain. In an attempt to elucidate the structural requirements of cystatins for calpain inhibition, we constructed recombinant hybrids of human stefin B (an intracellular family 1 cystatin) with KD2 and Delta L110 deletion mutants of chicken cystatin-KD2 hybrids. Substitution of the N-terminal contact region of stefin B by the corresponding KD2 sequence resulted in a calpain inhibitor of K-i = 188 nM. Deletion of L110, which forms a beta -bulge in family 1 and 2 cystatins but is lacking in KD2, improved inhibition of mu -calpain 4- to 8-fold. All engineered cystatins were temporary inhibitors of calpain due to slow substrate-like cleavage of a single peptide bond corresponding to Gly9-Ala10 in chicken cystatin. Biomolecular interaction analysis revealed that, unlike calpastatin, the cystatin-type inhibitors do not bind to the calmodulin-like domain of the small subunit of calpain, and their interaction with the mu -calpain heterodimer is completely prevented by a synthetic peptide comprising subdomain B of calpastatin domain 1. Based on these results we propose that (i) cystatin-type calpain inhibitors interact with the active site of the catalytic domain of calpain in a similar cystatin-like mode as with papain and (ii) the potential for calpain inhibition is due to specific subsites within the papain-binding regions of the general cystatin fold

Many-Body Effects on Tunneling of Electrons in Magnetic-Field-Induced Quasi One-Dimensional Electron Systems in Semiconductor Nanowhiskers

Effects of the electron-electron interaction on tunneling in a semiconductor nanowhisker are studied in a magnetic quantum limit. We consider the system with which bulk and edge states coexist. In bulk states, the temperature dependence of the transmission probability is qualitatively similar to that of a one-dimensional electron system. We investigate contributions of edge states on transmission probability in bulk states. Those contributions can be neglected within our approximation which takes into account only most divergent terms at low temperatures.Comment: 9 pages, 6 figure

Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio

We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price options on non-traded assets for which there is a traded asset that is correlated to the non-traded asset. Our main contribution to this particular problem is to show that our seller/buyer prices are the upper/lower good deal bounds of Cochrane and Sa\'{a}-Requejo (2000) and of Bj\"{o}rk and Slinko (2006) and to determine the analytical properties of these prices. Second, we apply our method to price options in the presence of stochastic volatility. Our main contribution to this problem is to show that the instantaneous Sharpe ratio, an integral ingredient in our methodology, is the negative of the market price of volatility risk, as defined in Fouque, Papanicolaou, and Sircar (2000).Comment: Keywords: Pricing derivative securities, incomplete markets, Sharpe ratio, correlated assets, stochastic volatility, non-linear partial differential equations, good deal bound