Distant measurement

Distant correlations are investigated within the framework of quantum mechanics. They are inherent to any physical situation in which two separated quantal systems are described by one composite state vector. Owing to correlations of this kind one can perform a measurement on one of the systems, thereby measuring a certain observable on the other (distant) system without interacting with it. Necessary and sufficient conditions are given for such a distant measurement to take place. It is found which are the observables that can be measured distantly, and which are the states of the distant system obtainable in this way. Solution of these problems is achieved by replacing the composite state vector by two entities equivalent to it: the reduced statistical operator of the system which is directly measured and a correlation operator. The latter gives a connection between states, observables, and probabilities of the two systems. Experimental evidence for distant measurement is discussed.     

Quantum registers based on single NV + <Emphasis Type="Italic">n</Emphasis><Superscript>13</Superscript>C centers in diamond: II. Spin characteristics of registers and spectra of optically detected magnetic resonance

The spin Hamiltonian method in combination with ab initio calculations of the spin characteristics of quantum registers that include an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1/2 of several atoms ¹³C located at different lattice sites near the vacancy of the NV center is applied to find eigenvalues and eigenfunctions of spin systems NV + n ¹³C for cases where the lattice sites nearest to the vacancy of the NV center contain one, two, or three ¹³C nuclear spins, as well as for cases where ¹³C atoms are located at sites more distant from the vacancy. For these single spin NV + n ¹³C systems, the spectra of optically detected magnetic resonance (ODMR) are calculated, which agree well with available experimental data.     

Invariant Banach limits and applications

Let ?_∞ be the space of all bounded sequences x=(x₁,x₂,…) with the norm

     

Integrability of higher pentagram maps

We define higher pentagram maps on polygons in $\mathbb{P }^d$ for any dimension $d$ , which extend R. Schwartz’s definition of the 2D pentagram map. We prove their integrability by presenting Lax representations with a spectral parameter for scale invariant maps. The corresponding continuous limit of the pentagram map in dimension $d$ is shown to be the $(2,d+1)$ -equation of the KdV hierarchy, generalizing the Boussinesq equation in 2D. We also study in detail the 3D case, where we prove integrability for both closed and twisted polygons and describe the spectral curve, first integrals, the corresponding tori and the motion along them, as well as an invariant symplectic structure.     

Structure of precipitates and orientation relationships in Al,Ge, Mo-doped higher manganese silicide crystals

Abstract

The structure of Al, Ge, Mo-doped Higher Manganese Silicide (HMS) crystals with the general formulas Mn(Si_0.99Ge_0.01)_1.75, Mn(Si_0.995Ge_0.005)_1.75 and (Mn_0.98Mo_0.02)[(Si_0.98Ge_0.02)_1.75]_0.99Al_0.01 was investigated by scanning and transmission electron microscopy, electron diffraction and X-ray energy dispersive spectrometry in a wide scale range from a few mm to several Å. Several secondary phases were identified in the Mn₄Si₇ matrix: Ge_1?xSi_x (0.1 < x < 0.9) solid solution precipitates with Ge concentration ranging from 5 at. % up to 93 at.%, MoSi₂ platelets, MnSi and Mn₅Si₃ precipitates. Their morphology, structure and crystallographic relationships with the HMS matrix were determined. Mostly local strains in the matrix and precipitates due to lattice misfits at interfaces derived from crystallographic relationships were found two orders of magnitude higher than deformation induced by thermal expansion mismatch. Only a few exceptions of specific relationships were found when the lattice misfit and thermal mismatch have close values. The largest misfit of about 22% was observed between MnSi and Mn₄Si₇ what led to big and numerous cracks in crystals. Therefore, doping can improve the material performance (1) by preventing the formation of MnSi precipitates with metallic properties and (2) by reduction of cracking and crack propagation because of larger MnSi /Mn₄Si₇ lattice misfit compared to Ge_1?xSi_x /Mn₄Si₇ or MoSi₂/Mn₄Si₇ misfits.     

Biodegradable liposome–chitosan complexes: enzyme-mediated release of encapsulated substances

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Hyperfine Characteristics of Quantum Registers NV-13С in Diamond Nanocrystals Formed by Seeding Approach from Isotopic Aza-Adamantane and Methyl-Aza-Adamanthane

Semiconductors - We predict the characteristics of hyperfine interactions (hfi) for a number of electron-nuclear spin systems NV-13C in diamonds grown by seeding approach from the specific isotopic...