Von Neumann entropy-preserving quantum operations

For a given quantum state ρ and two quantum operations Φ and Ψ, the information encoded in the quantum state ρ is quantified by its von Neumann entropy S(ρ). By the famous Choi-Jamio?kowski isomorphism, the quantum operation Φ can be transformed into a bipartite state, the von Neumann entropy Smap(Φ) of the bipartite state describes the decoherence induced by Φ. In this Letter, we characterize not only the pairs (Φ,ρ) which satisfy S(Φ(ρ))=S(ρ), but also the pairs (Φ,Ψ) which satisfy Smap(Φ°Ψ)=Smap(Ψ).     

Functional properties of quantum logics

A quantum logic is defined as a setL of functions from the set of all statesS into [0, 1] satisfying the orthogonality postulate: for any sequencea ₁,a ₂, ... of members ofL satisfyinga _i+a _j≤1 fori≠j there isb∈L such thatb+a ₁+a ₂+...=1. Every logicL is in a natural way an orthomodular σ-orthocomplemented partially ordered set (L, ≤, ′) with members ofS inducing a full set of measures onL. It is shown that a logicL is quite full if and only if (L,≤,′) is isomorphic to an orthocomplemented set lattice of subsets ofS. Sufficient conditions are given in order that a quite full logic be representable in the set of projection quadratic formsf(u)=(Pu, u) on a complex Hilbert space, or in the set of trace functionsf(A)=Trace (AP) generated by projectionsP, where the domain off is the set of non-negative self-adjoint trace operators of trace 1 in a complex Hilbert space.     

Preparation and photoluminescent properties of europium complexes with methoxy derivatives of 2′-hydroxy-2-phenylacetophenones

The complexes Eu(L₁)₃·2H₂O (I) [where L₁=2′-hydroxy-4′-methoxy-2-phenylacetophenone], Eu(L₂)₃·2H₂O (II) [where L₂=2′-hydroxy-4′-methoxy-2-(p-methoxyphenyl) acetophenone], Eu(L₃)₃·2H₂O (III) [where L₃=2′-hydroxy-4′, 6′-dimethoxy-2-phenylacetophenone] and Eu(L₄)₃·2H₂O (IV) [where L₄=2′-hydroxy-4′, 6′-dimethoxy -2-(p-methoxyphenyl) acetophenone] were synthesized. Energy dispersive X-ray analysis (EDX) results showed the presence of europium in all the complexes. These complexes were further characterized by infra-red spectroscopy, thermal analysis, scanning electron microscopy (scanning electron microscope) and elemental analysis. The synthesized complexes emit red luminescent with main peak at 612 nm on exposure to UV light at 354 nm. The complexes emitting bright red color might be applicable for optical devices and solid-state lamps for general illumination purposes.     

Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ₁₂) − S(γ₁) is restricted to states of the form . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L ₁ → L _p for L _p spaces defined by the Schatten p-norm on matrices, and give another proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L ₁ → L _p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.     

SO2: High-resolution analysis of the (0 3 0), (1 0 1), (1 1 1), (0 0 2) and (2 0 1) vibrational states; determination of equilibrium rotational constants for sulfur dioxide and anharmonic vibrational constants

High resolution Fourier transform spectra of a sample of sulfur dioxide, enriched in ³⁴S (95.3%). were completely analyzed leading to a large set of assigned lines. The experimental levels derived from this set of transitions were fit to within their experimental uncertainties using Watson-type Hamiltonians. Precise band centers, rotational and centrifugal distortion constants were determined. The following band centers in cm⁻¹ were obtained: ν₀(3ν₂)=1538.720198(11), ν₀(ν₁ + ν₃)=2475.828004(29), ν₀(ν₁ + ν₂ + ν₃)=2982.118600(20), ν₀(2ν₃)=2679.800919(35), and ν₀(2ν₁ + ν₃)=3598.773915(38). The rotational constants obtained in this work have been fit together with the rotational constants of lower-lying vibrational states [W.J. Lafferty, J.-M. Flaud, R.L. Sams, EL Hadjiabib, J. Mol. Spectrosc. 252 (2008) 72-76] to obtain equilibrium constants as well as vibration-rotation constants. These equilibrium constants have been fit together with those of ³²S¹⁶O₂ [J.-M. Flaud, W.J. Lafferty, J. Mol. Spectrosc. 16 (1993) 396-402] leading to an improved equilibrium structure. Finally the observed band centers have been fit to obtain anharmonic rotational constants.     

Virasoro type Lie algebras and deformations

The first and second cohomologies of Cartan Type Lie algebras with coefficients in irreducible tensor modules are calculated. The spaceH ¹(L, U) is interpreted as a space of deformations of (L, U)-modules.H ²(L, L)≠0 ifL=S ₂,S ₂ ⁺ orL=H _n ,H _n ⁺ . Lie algebra of divergenceless vector fieldsS ₂ ⁺ has only one nontrivial local deformation. The two-sided simple hamiltonian algebraH _n has 2n ²+n new local deformations in addition to Moyal cocycle. The Lie algebrasL=W _n (n>3),S _n?1(n>2),H _n (n>1),K _n+1(n>1) have 3, 1, 1, 3 nonisomorphic tensor modules with irreducible bases and nonzero 1-cohomologies; respectively, the corresponding numbers for 2-cohomologies are 9, 6, 7 and 9.     

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures.The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A₁,…,A_r. For every ρ=1,…,r there is prescribed a strict contraction Γ_ρ:A_ρ→M. A random walk (X_m)_m∈N0 on M is then defined as follows. The starting position is X₀=x₀, where x₀∈M is fixed, and if the walk at the m’th step is at position X_m∈M, then one chooses a ρ among the ρ with X_m∈A_ρ (with equal probability, say) and defines X_m+1 as Γ_ρ(X_m). Associated with the walk is a gainφ(X_m) in every round, where φ:M→R is a continuous function.The aim of the present investigations is the study of the expectation G_m of φ(X_m) as a function of m. Our main result states that the sequence (G_m) is “eventually approximately periodic” provided that all A_ρ are not only closed but also open in M: for every ε there is an l₀∈N such that (G_m) is l₀-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain.In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A₁,A₂, the contractions Γ₁,Γ₂ are rather simple, but the expectations of the gains are not even Cesáro convergent.     

Boson peak of AsxS1−x glasses and theoretical calculations of low frequencies clusters vibrations

The results of comparison of spectral position of the LF bands of g-As₂S₃ and g-As₂₂S₇₈ with theoretical calculations of vibrational spectra of different clusters (As₂S₄, As₂S₅, As₂S₆, AsS₃-As₃) in the LF region (10-85 cm⁻¹) are given. The torsion type vibrations of the small chain-like clusters are located in the same spectral region as Boson peak of As-S glasses system. They can make several contributions to the LF spectrum. The cluster lengths by weight distribution functions f(L)*L are from 5.5 to 10.1 Å and from 4.5 to 7.5 Å for g-As₂S₃ and g-As₂₂S₇₈, respectively. The lognormal fittings of the f(L)*L functions give the most probably values about the 7.6 Å (for g-As₂S₃) and 6.2 Å (for g-As₂₂S₇₈).     

Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(S_α(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)^2H+σX(τ)dB_H(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.     

A theoretical assignment on excited‐state intramolecular proton transfer mechanism for quercetin

In the present work, we investigate a new chromophore (ie, quercetin) (Simkovitch et al J Phys Chem B 119 [2015] 10244) about its complex excited‐state intramolecular proton transfer (ESIPT) process based on density functional theory and time‐dependent density functional theory methods. On the basis of the calculation of electron density ρ( r ) and Laplacian ?²ρ( r ) at the bond critical point using atoms‐in‐molecule theory, the intramolecular hydrogen bonds (O₁‐H₂?O₅ and O₃‐H₄?O₅) have been supported to be formed in the S₀ state. Comparing the prime structural variations of quercetin involved in its 2 intramolecular hydrogen bonds, we find that these 2 hydrogen bonds should be strengthened in the S₁ state, which is a fundamental precondition for facilitating the ESIPT process. Concomitantly, infrared vibrational spectra analysis further verifies this viewpoint. In good agreement with previous experimental spectra results, we find that quercetin reveals 2 kinds of excited‐state structures (quercetin* and quercetin‐PT1*) in the S₁ state. Frontier molecular orbitals depict the nature of electronically excited state and support the ESIPT reaction. Our scanned potential energy curves according to variational O₁‐H₂ and O₃‐H₄ coordinates demonstrate that the proton transfer process should be more likely to occur in the S₁ state via hydrogen bond wire O₁‐H₂?O₅ rather than O₃‐H₄?O₅ because of the lower potential energy barrier 2.3 kcal/mol. Our present work explains previous experimental result and makes up the deficiency of mechanism in previous experiment. In the end, we make a reasonable assignment for ESIPT process of quercetin.     

Study of some co-precipitated manganite perovskite samples-doped iron

Polycrystalline La_0.70Sr_0.30Mn_1−yFe_yO₃ (0.05?y?0.07) samples are prepared by the co-precipitation method and have been studied. The substitution of Mn³⁺ by Fe³⁺ reduces the number of available hopping sites for the Mn e_g(↑) electron and suppresses the double exchange (DE), resulting in the reduction of the metal–semiconductor transition temperature (T_P) and the flux density saturation (B_s). Low-temperature resistivity (ρ) data (below T_P) well fit with the relation ρ(T)=ρ₀+ρ₂T², indicating the importance of grain/domain boundary effects and electron–electron scattering processes in the conduction of these materials. On the other hand, at high temperature (T_P<T<θ_D/2) conductivity data satisfy the variable range hopping (VRH) model. For T>θ_D/2 the small polaron hopping model is more appropriate than the VRH model.     

Structural and photo-luminescence properties of nanocrystalline silicon films deposited at low temperature by plasma-enhanced chemical vapor deposition

Nanocrystalline silicon (nc-Si) films were prepared by a plasma-enhanced chemical vapor deposition method at a deposition temperature below 220 °C with different dynamic pressures (P_g), hydrogen flow rates ([H₂]), and RF powers, using SiH₄/H₂/SiF₄ mixtures. We examined the photo-luminescence (PL) spectra and the structural properties. We observed two stronger and weaker PL spectra with a peak energies around E_PL = 1.8 and 2.2-2.3 eV, respectively, suggesting that the first band was related to nanostructure in the films, and another band was associated with SiO-related bonds. The nc-Si films with rather large PL intensity was obtained for high [H₂] and/or low pressure values, However, effects of [H₂] are likely to be different from those of P_g. The average grain size (δ) and the crystalline volume fraction (ρ) at first rapidly increase, and then slowly increase, with increasing P_g. Other parameters exhibited opposite behaviors from those of δ or ρ. These results were discussed in connection with the changes in the PL properties with varying the deposition conditions.     

Single-particle approximation to the canonical density operator of a system of N interacting fermions

A necessary condition for the minimum of free energy Tr(ρH^N) + β^-1 Tr(ρlnρ) is investigated for a system of N interacting fermions on the set of all density matrices of the form ρ=Z^-1 exp(-βNΓ^N₁h¹), where Γ^N₁ is Kummer's (1,N)-expansion map, and h¹ is a finite- dimensional one-particle operator. It is shown that for values of β in an open circle $\text{C}\text{(0,β}{}_0\text{)}$ in the complex plane there exists a unique bounded analytic in β one-particle operator X¹(β) such that Z^-1exp(-βNΓ^N₁X¹(β)) satisfies this condition.     

A compact 341 model at TeV scale

We build a gauge model based on the SU(3)_c⊗SU(4)_L⊗U(1)_X$SU{\left(3\right)}_c\otimes SU{\left(4\right)}_L\otimes U{\left(1\right)}_X$ symmetry where the scalar spectrum needed to generate gauge boson and fermion masses has a smaller scalar content than usually assumed in literature. We compute the running of its abelian gauge coupling and show that a Landau pole shows up at the TeV scale, a fact that we use to consistently implement those fermion masses that are not generated by Yukawa interactions, including neutrino masses. This is appropriately achieved by non renormalizable effective operators, suppressed by the Landau pole scale. Also, SU(3)_c⊗SU(3)_L⊗U(1)_N$SU{\left(3\right)}_c\otimes SU{\left(3\right)}_L\otimes U{\left(1\right)}_N$ models embedded in this gauge structure are bound to be strongly coupled at this same energy scale, contrary to what is generally believed, and neutrino mass generation is rather explained through the same effective operators used in the larger gauge group. Besides, their nice features, as the existence of cold dark matter candidates and the ability to reproduce the observed standard model Higgs-like phenomenology, are automatically inherited by our model. Finally, our results imply that this model is constrained to be observed or discarded soon, since it must be realized at the currently probed energy scale in LHC.     

Das K-Auger-Spektrum von Neon

TheKLL-Auger spectrum of neon was investigated with an electrostatic spectrometer with an energy resolution of 0.12%. The ionization in theK-shell was caused by electron impact. The use of a gaseous target made it possible to measure the Auger electrons without any energy loss. The relative intensities of the KLL-lines were determined to be:KL ₁ L ₁(¹ S ₀)=1.0;KL ₁ L _2,3(¹ P ₁)=3.06±0.07;KL ₁ L _2,3(³ P _0,1,2)=0.98±0.05;KL _2,3 L _2,3(¹ S ₀)=1.67±0.08;KL _2,3 L _2,3(¹ D ₂)=13.1±0.6;KL _2,3 L _2,3(² P _0,2)=0. This is in agreement with an earlier measurement byKörber andMehlhorn but disagrees with all theoretical values calculated nonrelativistically for low Z. It is shown that agreement may be achieved by applying quantitatively the configuration interaction, introduced very recently byAsaad, and using improved wave functions for the calculation of the transition amplitudes. As a consequence of the ionization by electron impact also theKL-LLL Auger spectrum was caused. 10 lines of this spectrum were measured and identified. Moreover, from the Auger energies measured, the binding energyE(K) of neon was calculated to be E(K)=(870.0±0.4) eV.     

Superconductivity and thermal properties of sulphur doped FeTe with effect of oxygen post annealing

Here, we report the synthesis and characterization of sulphur-substituted iron telluride i.e. FeTe_1?xS_x; (x = 0–30 %) system and study the impact of low temperature oxygen (O₂) annealing as well. Rietveld analysis of room temperature X-ray diffraction (XRD) patterns shows that all the compounds are crystallized in a tetragonal structure (space group P4/nmm) and no secondary phases are observed. Lattice constants are decreased with increasing S concentration. The parent compound of the system i.e. FeTe does not exhibit superconductivity but shows an anomaly in the resistivity measurement at around 78 K, which corresponds to a structural phase transition. Heat capacity C_p(T) measurement also confirms the structural phase transition of FeTe compound. Superconductivity appears by S substitution; the onset of superconducting transition temperature is about 8 K for FeTe_0.75S_0.25 sample. Thermoelectric power measurements S(T) also shows the superconducting transition at around 7 K for FeTe_0.75S_0.25 sample. The upper critical fields H_c2(10%), H_c2(50%) and H_c2(90%) are estimated to be 400, 650 and 900 kOe respectively at 0 K by applying Ginzburg Landau (GL) equation. Interestingly, superconducting volume fraction is increased with low temperature (200 °C) O₂ annealing at normal pressure. Detailed investigations related to structural (XRD), transport [S(T), R(T)H], magnetization (AC and DC susceptibility) and thermal [C_p(T)] measurements for FeTe_1?xS:O₂ system are presented and discussed.     

Lewis number effects on laminar and turbulent expanding flames of NH3/H2/air mixtures at elevated pressures

This study clarifies the effects of Lewis number (Le) on laminar and turbulent expanding flames of NH₃/H₂/air mixtures. The laminar burning velocity (S_L) and turbulent burning velocity (S_T) were measured using a medium-scale, fan-stirred combustion chamber with ammonia/hydrogen molar ratio (NH₃/H₂) of 50/50 and 80/20 under the maximum pressures of 5 atm. The lean laminar flame with NH₃/H₂ = 50/50 is significantly accelerated by the diffusional–thermal instability, which dominated the trend of S_T,c=0.1 with the equivalence ratio (ϕ). The lean normalized turbulent burning velocity (S_T/S_L) increases with the decrease of hydrogen content due to the weakening effects of S_L. However, the S_T/S_L reaches peak with hydrogen volumetric content less than 20% due to effects made by diffusional–thermal instability than S_L did. The turbulent flame of NH₃/H₂/air mixtures is characterized by self-similar acceleration propagation, and propagation with Le < 1 is faster. A modified correlation considering the effects of Le was proposed, as (d<r>/dt)/σS_L = 0.118(Re_T,flameLe⁻²)^0.57, which was able to predict not only the self-similar propagation of NH₃/H₂/air but also the previous syngas/air flames. The Kobayashi correlations modified by three kinds of Le power exponents were used to clarify the effects of Le by comparing their fitting parameters and predictive powers on experimental data and literature data. Similar pre-factors, power exponents and the goodness of fit (R²) were obtained with Le ranging from 0.58 to 1.62, which suggested that the determination of Le power exponent had no significant effect on the prediction accuracy of the S_T/S_L trend with data of Le near unity. This might be attributed to the fact that the variation ranges of the dimensionless number that characterizes the experimental conditions is much larger than that of the Le.     

Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.     

L10 FePt thin films with [0 0 1] crystalline growth fabricated by SiO2 addition—rapid thermal annealing and dot patterning of the films

FePt films that have a high degree of order S in their L1₀ structure (S>0.90) and well-defined [0 0 1] crystalline growth perpendicular to the film plane were fabricated on thermally oxidized Si substrates by the addition of an oxide and successive rapid thermal annealing (RTA). The mechanism of L1₀ ordering and [0 0 1] crystalline growth perpendicular to the film plane arising through the oxide addition and RTA process is also discussed. The L1₀ ordering (S>0.90) and the [0 0 1] crystalline growth were achieved by (1) lowering the activation energy due to in-plane tensile stress and the initiation of L1₀ ordering at a low temperature, (2) [0 0 1] crystalline growth through in-plane tensile stress, and (3) enhancement of atomic diffusion via the addition of an oxide and the resultant lowering of the ordering temperature. Effect (1) was observed in the case of SiO₂ addition, effect (2) was generally observed in the case of oxide addition and the RTA process, and effect (3) was prominent in the case of ZnO addition. With the addition of ZnO, the L1₀ ordering started at below 400 °C and was completed at 500 °C. Finally, dot patterns were successfully fabricated down to a diameter of 15 nm using electron beam lithography, and the magnetic state of the dot pattern was observed by magnetic force microscopy.     

On States on Orthogonally Closed Subspaces of an Inner Product Space

We show that every finitely additive state on the system F(S) of all orthogonally closed subspaces of an infinite-dimensional inner product space S attains all values from the real interval [0,1]. In particular, we show that there is no finitely additive countably-valued state on F(S) whenever dim S=. The main technique we use is an embedding of L(H _n ) into F(S).