An Eigenvalue Estimate and Its Application to Non-Selfadjoint Jacobi and Schrödinger Operators

For bounded linear operators A, B on a Hilbert space \({\mathcal{H}}\) we show that \({ \sum_{\lambda}{\rm dist}(\lambda, {\rm Num}(A))^p}\) is bounded from above by the Schatten-p-norm of B ? A. Here, the sum is taken over all discrete eigenvalues of B and Num(A) denotes the numerical range of A. We apply this estimate to recover and improve some Lieb–Thirring type inequalities for non-selfadjoint Jacobi and Schrödinger operators.     

Level-crossing-Untersuchung der Hyperfeinstruktur des 3d 10 4p 2 P 3/2-Terms von Cu63 und Cu65

The level-crossing technic has been used to investigate the hyperfinestructur of the 3d ¹⁰ 4p ² P _3/2-term in Copper I by scattering the resonance line λ=3248 Å on an atomic beam of separated isotop Cu⁶³ respectively Cu⁶⁵ in an external magnetic field. From the level-crossing signals values for the magnetic dipol interaction constantsA and for the electric quadrupol interaction constantsB are deduced to beeA(Cu⁶³)=(194,72±0,15) Mc/secB(Cu⁶³)=?(28,8±0,6) Mc/secA(Cu⁶⁵)=(208,57±0,15) Mc/secB(Cu⁶⁵)=?(25,9±0,6) Mc/sec. With theA-value of the 3d ¹⁰ 4p²P_1/2-term from optical measurements the ratioA(² P _3/2)∶A(² P _1/2)≈0,4 is about twice greater than for an unperturbetalkali-like²P-term. From the width of the level-crossing signals a mean lifetime of the 3d¹⁰ 4p²P_3/2-term τ=(7,0±0,2) · 10^?9 sec is deduced.     

A consequence from the model description of a decomposing liquid mixture

In terms of representation [1] of a decomposing binary liquid mixture as a system of two coupled self-oscillators with partial frequencies ν _A and ν _B , the following conjecture is verified: given frequency ratios ν _A /ν _B and ν _A /ν _C for decomposing liquid mixtures A-B and A-C at the same temperature, it is possible to determine the ν _B /ν _C ratio, which is independent of the choice of the A component.     

Phase diagrams of bosonic AB<Subscript>n</Subscript> chains

The AB_{N ?1} chain is a system that consists of repeating a unit cell withN siteswhere between the A and B sites there is an energy difference ofλ. Weconsidered bosons in these special lattices and took into account the kinetic energy, thelocal two-body interaction, and the inhomogenous local energy in the Hamiltonian. We foundthe charge density wave (CDW) and superfluid and Mott insulator phases, and constructedthe phase diagram for N =2 and 3 atthe thermodynamic limit. The system exhibited insulator phases for densitiesρ =α/N, with α being an integer. Weobtained that superfluid regions separate the insulator phases for densities larger thanone. For any N value, we found that for integer densitiesρ, thesystem exhibits ρ +1 insulator phases, a Mott insulator phase, and ρ CDW phases. Fornon-integer densities larger than one, several CDW phases appear.     

Temperature Dependence of the Thermal Conductivity of a Trapped Dipolar Bose-Condensed Gas

The thermal conductivity of a trapped dipolar Bose condensed gas is calculated as a function of temperature in the framework of linear response theory. The contributions of the interactions between condensed and noncondensed atoms and between noncondensed atoms in the presence of both contact and dipole-dipole interactions are taken into account to the thermal relaxation time, by evaluating the self-energies of the system in the Beliaev approximation. We will show that above the Bose-Einstein condensation temperature (T?>?T _BEC ) in the absence of dipole-dipole interaction, the temperature dependence of the thermal conductivity reduces to that of an ideal Bose gas. In a trapped Bose-condensed gas for temperature interval k _B T?<<?n ₀ g _B , E _p ?<<?k _B T (n ₀ is the condensed density and g _B is the strength of the contact interaction), the relaxation rates due to dipolar and contact interactions between condensed and noncondensed atoms change as \( {\tau}_{dd12}^{-1}\propto {e}^{-E/{k}_BT} \) and τ _c12?∝?T ^?5, respectively, and the contact interaction plays the dominant role in the temperature dependence of the thermal conductivity, which leads to the T ^?3 behavior of the thermal conductivity. In the low-temperature limit, k _B T?<<?n ₀ g _B , E _p ?>>?k _B T, since the relaxation rate \( {\tau}_{c12}^{-1} \) is independent of temperature and the relaxation rate due to dipolar interaction goes to zero exponentially, the T ² temperature behavior for the thermal conductivity comes from the thermal mean velocity of the particles. We will also show that in the high-temperature limit (k _B T?>?n ₀ g _B ) and low momenta, the relaxation rates \( {\tau}_{c12}^{-1} \) and \( {\tau}_{dd12}^{-1} \) change linearly with temperature for both dipolar and contact interactions and the thermal conductivity scales linearly with temperature.     

On the error of the time–pulse method of measuring air consumption in mines

The derivation of a formula for the time during which a sound signal propagates between two given points A and B in a stationary gas flow is considered. It is shown that the gas flow changes the signal reception time by a quantity proportional to the consumption, regardless of the detailed velocity profile. The difference between the reception time of signals from point B to the point A and vice versa is proportional to air consumption with high accuracy. It is shown that the relative error of the obtained formula does not exceed the squared maximum Mach number in the gas flow. This allows measurement of the consumption of gas moving in a mine with an arbitrary stationary subsonic velocity field.     

A continuous time random walk (CTRW) integro-differential equation with chemical interaction

A nonlocal-in-time integro-differential equation is introduced that accounts for close coupling between transport and chemical reaction terms. The structure of the equation contains these terms in a single convolution with a memory function M?(t), which includes the source of non-Fickian (anomalous) behavior, within the framework of a continuous time random walk (CTRW). The interaction is non-linear and second-order, relevant for a bimolecular reaction A + B → C. The interaction term ΓP _A ?(s, t)?P _B ?(s, t) is symmetric in the concentrations of A and B (i.e. P _A and P _B ); thus the source terms in the equations for A, B and C are similar, but with a change in sign for that of C. Here, the chemical rate coefficient, Γ, is constant. The fully coupled equations are solved numerically using a finite element method (FEM) with a judicious representation of M?(t) that eschews the need for the entire time history, instead using only values at the former time step. To begin to validate the equations, the FEM solution is compared, in lieu of experimental data, to a particle tracking method (CTRW-PT); the results from the two approaches, particularly for the C profiles, are in agreement. The FEM solution, for a range of initial and boundary conditions, can provide a good model for reactive transport in disordered media.     

On the structure of the von Neumann algebras generated by local functions of the free bose field

It is shown that the von Neumann algebra\(R_\mathfrak{B} \)(B) generated by any scalar local functionB(x) of the free fieldA ₀(x) is equal either to\(R_\mathfrak{B} \)(A ₀) or to\(R_\mathfrak{B} \)(:A ₀ ² :). The latter statement holds if the state space space\(\mathfrak{H}_B \) obtained from the vacuum state by repeated application ofB(x) is orthogonal to the one particle subspace. In the proof of these statements, space-time limiting techniques are used.     

Change in the lattice properties and melting temperature of a face-centered cubic iron under compression

All four parameters of the Mie–Lennard-Jones pair interatomic potential have been determined, and the state equation (P) and baric dependences of the lattice properties of an fcc iron are calculated using a previously proposed method. The dependences have been studied for the following properties: Debye temperature; the first, second, and third Gruneisen parameters; isothermal bulk modulus B _T and B′(P); isochoric specific heat C _v and C _v ′(P); isobaric specific heat C _p ; coefficient of thermal expansion α _p and α _p ′(P); specific surface energy σ and σ′(P). Calculations performed along two isotherms (1500 and 3000 K) have shown good agreement with the experimental data. Analytical approximations of the baric dependences for B′(P), α _p (P), C _p (P), and σ′(P) have been obtained, and it is shown that at P → ∞ the functions B _T (P) and σ(P) change linearly, while the functions α _p′(P) and C _p ′(P) tend to zero. The calculated baric dependence of the melting temperature shows good agreement with the experimental data.     

Modified multicomponent band pass optical reflection filters at oblique incidence

Reflection and transmission characteristics of a modified long-wavelength cutoff filter using a three-component system with an angular dependence are studied. In this case, a layer of high refractive index is sandwiched between edge layers of equivalent refractive index with the base structure [G(0.5AB0.5A)]^N; then, an optimized structure of the form [(0.5AB0.5A)^N?X (0.5AB0.5A)^X (0.5AB0.5A)^N?X] is taken and its spectral properties are studied. In the case of a short-wavelength three-component cutoff filter, a layer of low refractive index is sandwiched between two edge layers of high equivalent refractive index with a base structure [G(0.5BA0.5D)]^N and its spectral characteristics are studied. Then, the structure is optimized [(0.5BA0.5B)^{N? X}(0.5BA0.5B)^X(0.5BA0.5B)^N?tX] and spectral characteristics of this structure are also studied. Spectral properties of band pass optical reflection filters of the type [G(XY)A] whose components are the proposed long-wavelength cutoff [(0.5AB0.5B)^{N? X}(0.5AB0.5A)^X(0.5BA0.5B)^N?X] and short-wavelength cutoff [(0.5BA0.5B)^N?X(0.5BA0.5B)^X(0.5BA0.5B)^N?X] filter structures are studied with angular dependences. No increase in the bandwidth with the least oscillatory components at the edges can be precisely formed by known classes of a two-component system at normal incidence. It is shown that the use of reflection and transmission filters with oblique bands yields an ideal polarizer. Angular dependences of the filter and the transmission and reflection band shapes on the parameters of a high-reflectance multilayer coating, such as the thickness, refractive indices, and the number of layers, are analyzed in detail.     

Noise-Induced Drift in Stochastic Differential Equations with Arbitrary Friction and Diffusion in the Smoluchowski-Kramers Limit

We consider the dynamics of systems with arbitrary friction and diffusion. These include, as a special case, systems for which friction and diffusion are connected by Einstein fluctuation-dissipation relation, e.g. Brownian motion. We study the limit where friction effects dominate the inertia, i.e. where the mass goes to zero (Smoluchowski-Kramers limit). Using the Itô stochastic integral convention, we show that the limiting effective Langevin equations has different drift fields depending on the relation between friction and diffusion. Alternatively, our results can be cast as different interpretations of stochastic integration in the limiting equation, which can be parametrized by α∈?. Interestingly, in addition to the classical Itô (α=0), Stratonovich (α=0.5) and anti-Itô (α=1) integrals, we show that position-dependent α=α(x), and even stochastic integrals with α?[0,1] arise. Our findings are supported by numerical simulations.     

Microscopics of mesonic degrees of freedom in nucleons and mesons in nuclei: Quasielastic meson knockout by high-energy electrons

The following questions are considered: (i) that of what quasielastic-knockout reactions are; (ii) that of what experience has been gained in measuring, in various channels, the momentum distributions and spectroscopic factors of nucleons and clusters in nuclei and of electrons in atoms, molecules, and solid-state bodies; (iii) that of how it is possible to introduce the concept of quasielastic knockout in the theory of meson-electroproduction processes p(e, e′m)B at beam energies of a few GeV and at moderate values of the square of the virtual-photon 4-momentum, Q ² = 2–4 (GeV/c)²; and (iv) that of how the momentum distributions of mesons in various channels of virtual proton decay, p → B + π, p → B + ρ, and p → Y + K, are predicted on the basis of the microscopic model of a fluctuation of the QCD vacuum in a nucleon. Proposals for relevant experiments are formulated. It is indicated that quasielastic-knockout processes like (e, e′π) provide the best way to study the problem of a scalar pion condensate in nuclei. In conclusion, it is emphasized that quasielastic processes ²H(e, e′p)B involving various spectator baryons B are of great value for determining the composition of multiquark configurations in nucleon-nucleon systems.     

Structure-correlated diffusion anisotropy in nanoporous channel networks by Monte Carlo simulations and percolation theory

Nanoporous silicon consisting of tubular pores imbedded in a silicon matrix has found many technological applications and provides a useful model system for studying phase transitions under confinement. Recently, a model for mass transfer in these materials has been elaborated [Kondrashova et al., Sci. Rep. 7, 40207 (2017)], which assumes that adjacent channels can be connected by “bridges” (with probability p _bridge) which allows diffusion perpendicular to the channels. Along the channels, diffusion can be slowed down by “necks” which occur with probability p _neck. In this paper we use Monte-Carlo simulations to study diffusion along the channels and perpendicular to them, as a function of p _bridge and p _neck, and find remarkable correlations between the diffusivities in longitudinal and radial directions. For clarifying the diffusivity in radial direction, which is governed by the concentration of bridges, we applied percolation theory. We determine analytically how the critical concentration of bridges depends on the size of the system and show that it approaches zero in the thermodynamic limit. Our analysis suggests that the critical properties of the model, including the diffusivity in radial direction, are in the universality class of two-dimensional lattice percolation, which is confirmed by our numerical study.     

Application of Fermat’s Principle to Calculation of the Errors of Acoustic Flow-Rate Measurements for a Three-Dimensional Fluid Flow or Gas

Fermat’s variational principle is used for derivation of the formula for the time of propagation of a sonic signal between two set points A and B in a steady three-dimensional flow of a fluid or gas. It is shown that the fluid flow changes the time of signal reception by a value proportional to the flow rate independently of the velocity profile. The time difference in the reception of the signals from point B to point A and vice versa is proportional with a high accuracy to the flow rate. It is shown that the relative error of the formula does not exceed the square of the largest Mach number. This makes it possible to measure the flow rate of a fluid or gas with an arbitrary steady subsonic velocity field.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

A Note on Quantum Coherence

In this paper, we discuss the coherence of the reduced state in system H _A ?H _B under taking different quantum operations acting on subsystem H _B . Firstly, we show that for a pure bipartite state, the coherence of the final subsystem H _A under the sum of two orthonormal rank 1 projections acting on H _B is less than or equal to the sum of the coherence of the state after two orthonormal projections acting on H _B , respectively. Secondly, we obtain that the coherence of reduced state in subsystem H _A under random unitary channel \({\Phi }(\rho )={\sum }_{s}\lambda _{s}U_{s}\rho U_{s}^{\ast }\) acting on H _B , is equal to the coherence of the state after each operation \({\Phi }_{s}(\rho )=\lambda _{s}U_{s}\rho U_{s}^{\ast }\) acting on H _B for every s. In addition, for general quantum operation \({\Phi }(\rho )={\sum }_{s}F_{s}\rho F_{s}^{\ast }\) on H _B , we get the relation

$$ C\left (\left ((I\otimes {\Phi })\rho ^{AB}\right )^{A}\right )\leq \sum \limits _{s}C\left (\left ((I\otimes {\Phi }_{s})\rho ^{AB}\right )^{A}\right ). $$

     

Die Winkelverteilung der Protonen der Reaktion B11 (d,p 0,1 B12 im Energiebereich von 0,7 ... 1,7 MeV

Angular distributions of the protons in this low-energy region have been measured by only few groups for obvious reasons: the energy of the emitted protons is very low. It will be shown that by using non-supported targets of B¹¹ with very little oxygen contamination the angular distributions can be obtained between approximately 5 and 165 degrees (cm.,p ₀-group) and between 20 and 165 degrees (cm.,p ₁) with high accuracy. The Butler-fits givel=1,r _B =5.2 fm forp ₀ andl=1,r _B =4.7 fm forp ₁. All angular distributions seem to exhibit strong participation of non-stripping mechanism.     

Asymptotic Normalization Coefficients (Nuclear Vertex Constants), Three-Body Asymptotic Normalization Functions (On-Shell Vertex Functions) and Nuclear Astrophysics

In the present review work, the main methods of the determination of asymptotic normalization coefficients (or respective nuclear vertex constants) for the A + x → B channel and of threebody asymptotic normalization functions (or respective on-shell vertex functions) for the A + b + c → B channel are briefly discussed. The main attention is paid both to the use of the specific asymptotic normalization coefficients and three-body asymptotic normalization functions as a source of getting the valuable information about the pair (nucleon–nucleon, nucleon–cluster and cluster–cluster) nuclear interactions and to their application for the specific direct nuclear-astrophysical radiative capture and peripheral transfer reactions at low energies.     

Microwave photoresistance of a two-dimensional electron gas in a ballistic microbar

The effect of millimeter microwave radiation on the electron transport of two-dimensional (2D) ballistic microbars formed on the basis of individual GaAs quantum wells at a temperature of T = 4.2 K in magnetic fields B < 0.6 T has been investigated. Differences have been revealed in the magnetic field dependences of the microwave photoresistance of a 2D electron gas in Hall bars with a length L and a width W for the cases L, W > l _p and L, W < l _p , where l _p is the electron mean free path for momentum. The microwave photoresistance in macroscopic bars (L, W > l _p ) is a periodic alternating function of the inverse magnetic field; in microbars (L, W < l _p ), it is a periodic positive function of 1/B. The experimental results indicate that the mechanisms of the microwave photoresistance of a 2D electron gas are different for macroscopic and microscopic bars.