Arithmetic tools for quantum logic

This paper develops a general language of event configurations to discuss and compare various modes of proposition formation. It is shown that any finite orthogonality space can be numerically encoded. This encoding is applied to show that the quasimanual of all orthogonal subsets of any finite point-determining orthogonality space may be decomposed into a union of manuals and that the logic of these quasimanuals may be regarded as a composite of interlocking associative orthoalgebras.     

Frobenius transformation,mirror map and instanton numbers

We show that one can express Frobenius transformation on middle-dimensional p-adic cohomology of Calabi–Yau threefold in terms of mirror map and instanton numbers. We express the mirror map in terms of Frobenius transformation on p-adic cohomology. We discuss a p-adic interpretation of the conjecture about integrality of Gopakumar–Vafa invariants.     

Towards quantum superpositions of a mirror

We propose an experiment for creating quantum superposition states involving of the order of 10(14) atoms via the interaction of a single photon with a tiny mirror. This mirror, mounted on a high-quality mechanical oscillator, is part of a high-finesse optical cavity which forms one arm of a Michelson interferometer. By observing the interference of the photon only, one can study the creation and decoherence of superpositions involving the mirror. A detailed analysis of the requirements shows that the experiment is within reach using a combination of state-of-the-art technologies.     

The quantum poisson-Lie T-duality and mirror symmetry

Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also. Zh. éksp. Teor. Fiz. 116, 11–25 (July 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

The configurational quantum cat map

The first atomically resolved atomic force microscopy images of the LiF (001) surface are presented. A square lattice with a spacing of 2.8±0.1 Å is resolved, which can be attributed to the F^– ions. Li⁺ is not resolved due to its small size. The origin of the image contrast is discussed briefly and the results are compared with those from helium scattering.     

Convergence of the quantum Boltzmann map

We consider a non-linear map on the space of density matrices, which we call the Boltzmann map . It is the composition of a doubly stochastic mapT on the space ofn-body states, and the conditional expectation onto the one-body space. WhenT is ergodic, then the iterates of take any initial state to the uniform distribution. If the energy levels are equally spaced, andT conserves energy and is ergodic on each energy shell, then iterates of take any initial state of finite energy to a canonical distribution.     

Heating map in classical and quantum mechanics

Heating map of the classical probability-distribution function (in the phase space) and of density matrix (in the position representation) in quantum mechanics is introduced and its positivity is proved. The relation of the heating map to scaling transform and unitary squeezing transform of the momentum variable in the Wigner function is used to prove that noncanonical scaling transform of the position and momentum provides positive (but not completely positive!) map of density operator. The connection of momentum scaling transform with time scaling transform and Plancks constant scaling transform is discussed.     

Towards the map of quantum gravity

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Ho?ava–Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.     

Mirror symmetry,mirror map and applications to Calabi-Yau hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.On leave of absence from Dept. of Math., Toyama Univ., Toyama 930, Japan (address after Sept. 1, 1993)Address after Oct. 1, 1993: Dept. of Math., Harvard Univ., Cambridge, MA 02138, USA. after April 1, 1994: CERN, Theory Division, CH-1211 Geneva 23, Switzerland     

The linear optical properties in quantum dots under a single coupling field

Using the density matrix method, the linear optical properties of truncated pyramid quantum dots have been investigated when an additional coupling field is introduced. The absorption coefficients and refractive index changes are strongly affected by the amplitude of the coupling field and the phase difference between the probe and coupling fields. The numerical results indicate that negative absorption and transparency can be obtained when both of the probe and coupling fields are in resonance with the quantum dots.     

Influence of anomalous dispersion mirror properties on quantum efficiency of InGaAs/GaAs resonant cavity photodetector

We present a theoretical analysis of the quantum efficiency of a resonant cavity enhanced InGaAs/GaAs p-i-n photodetector (PD) for the ultrashort optical connections. The numerical method of calculation of quantum efficiency combining a transfer matrix method and an energy conservation law is offered. Using anomalous dispersion (AD) mirror, flat-topped QE spectrum has been obtained. Conditions for ideal flat-topped spectral response have been received. A design with a maximum QE of 93.5% and 3-nm bandwidth at 0.02 dB below the peak is presented.     

A Boltzmann map for quantum oscillators

We define a map on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points ofx. The map is the composition of a doubly stochastic map T^* and the quasifree reductionQ. Under mixing conditions onT, iterates of take any initial state to the Gibbs state, provided that the oscillator frequencies are mutually rational. We give an example of a system with three degrees of freedom with energies ₁, ₂, and ₃ mutually irrational, but obeying a relation n₁₁+n₂₂=n₃₃,n _i . The iterated Boltzmann map converges from an initial statep to independent Gibbs states of the three oscillators at betas (inverse temperatures) ₁,₂, ₃ obeying the equation n₁₁₁+n₂₂₂=n₃₃₃. The equilibrium state can be rewritten as a grand canonical state. We show that for two, three, or four fermions we can get the usual rate equations as a special case.     

Translation map in quantum principal bundles

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle E((B, V, A) associated to a quantum principal bundle P (B, A) are in bijective correspondence with equivariant maps V → P, and that a quantum principal bundle is trivial if it admits a cross section which is an algebra map. The vertical automorphisms and gauge transformations of a quantum principal bundle are discussed. In particular it is shown that vertical automorphisms are in bijective correspondence with Ad_R-covariant maps A → P.     

Gaussian beam coupling on a MEMS mirror array

A general formula for evaluating Gaussian beam coupling characteristics on a MEMS mirror array was developed, with consideration of parameters such as beam size, mirror width and mirror gap. Based on the formula, the influence of each parameter on the spectral response was simulated for MEMS mirror array employed in a wavelength selective switch and a tunable optical filter. The simulation results are helpful for the design of MEMS mirror array in optical devices.     

Spectral statistics of a quantum interval-exchange map

Curious spectral properties of an ensemble of random unitary matrices appearing naturally in the quantization of a simple interval-exchange map are investigated. It is demonstrated that, under certain conditions on map parameters, local spectral statistics of this ensemble tends to the semi-Poisson distribution with arbitrary integer or half-integer level repulsion at small distances depending on time-reversal symmetry of the map.     

Experimental implementation of the quantum baker's map

This Letter reports on the experimental implementation of the quantum baker's map via a three bit nuclear magnetic resonance quantum information processor. The experiments tested the sensitivity of the quantum chaotic map to perturbations. In the first experiment, the map was iterated forward and then backward to provide benchmarks for intrinsic errors and decoherence. In the second set of experiments, the least significant qubit was perturbed in between the iterations to test the sensitivity of the quantum chaotic map to controlled perturbations. These experiments can be used to investigate existing theoretical predictions for quantum chaotic dynamics.     

Shape and composition map of a prepyramid quantum dot

We present a theory for the shape, size, and nonuniform composition profile of a small prepyramid island in an alloy epitaxial film when surface diffusion is much faster than deposition and bulk diffusion. The predicted composition profile has segregation of the larger misfit component to the island peak, with segregation enhanced by misfit strain and solute strain but retarded by alloy solution thermodynamics. Vertical composition gradients through the center of the island due to this mechanism are on the order of 2%/nm for Ge(X)Si(1-X)/Si and 10-15%/nm for In(X)Ga(1-X)As/GaAs.     

Transport polygonal properties in a multi-terminal regular quantum ring with Rashba spin-orbit coupling

<正>Transport properties in a multi-terminal regular polygonal quantum ring with Rashba spin-orbit coupling(SOC) are investigated analytically using quantum networks and the transport matrix method.The results show that conductances remain at exactly the same values when the output leads are located at axisymmetric positions.However,for the nonaxisymmetrical case,there is a phase difference between the upper and lower arm,which leads to zero conductances appearing periodically.An isotropy of the conductance is destroyed by the Rashba SOC effect in the axisymmetric case. In addition,the position of zero conductance is regulated with the strength of the Rashba SOC.