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1.
Hamaker interaction energies and cutoff distances have been calculated for disordered carbon films, in contact with purely dispersive (diiodomethane) or polar (water) liquids, using their experimental dielectric functions ε (q, ω) obtained over a broad energy range. In contrast with previous works, a q-averaged <ε (q, ω) >  q is derived from photoelectron energy-loss spectroscopy (XPS-PEELS) where the energy loss function (ELF) < Im[?1/ε (q, ω)] >  q is a weighted average over allowed transferred wave vector values, q, given by the physics of bulk plasmon excitation. For microcrystalline diamond and amorphous carbon films with a wide range of (sp3/sp2 + sp3) hybridization, non-retarded Hamaker energies, A 132 (L < 1 nm), were calculated in several configurations, and distance and wavenumber cutoff values were then calculated based on A 132 and the dispersive work of adhesion obtained from contact angles. A geometric average approximation, H 0?CVL ?=?(H 0?CVC H 0?LVL )1/2, holds for the cutoff separation distances obtained for carbon-vacuum-liquid (CVL), carbon-vacuum-carbon (CVC) and liquid-vacuum-liquid (LVL) equilibrium configurations. The linear dependence found for A CVL, A CLC and A CLV values as a function of A CVC, for each liquid, allows predictive relationships for Hamaker energies (in any configuration) using experimental determination of the dispersive component of the surface tension, \( {\gamma}_{CV}^d \), and a guess value of the cutoff distance H 0?CVC of the solid.
Graphical Abstract
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2.
We study an inverse problem for the two-dimensional random Schrödinger equation (Δ + q + k 2)u = 0. The potential q(x) is assumed to be a Gaussian random function whose covariance operator is a classical pseudodifferential operator. We show that the backscattered field, obtained from a single realization of the random potential q, determines uniquely the principal symbol of the covariance operator of q. The analysis is carried out by combining harmonic and microlocal analysis with stochastic methods.  相似文献   

3.
We revisit and prove some convexity inequalities for trace functions conjectured in this paper’s antecedent. The main functional considered is
$ \Phi_{p,q} (A_1,\, A_2, \ldots, A_m) = \left({\rm Tr}\left[\left( \, {\sum\limits_{j=1}^m A_j^p } \, \right) ^{q/p} \right] \right)^{1/q} $
for m positive definite operators A j . In our earlier paper, we only considered the case q = 1 and proved the concavity of Φ p,1 for 0 < p ≤ 1 and the convexity for p = 2. We conjectured the convexity of Φ p,1 for 1 < p < 2. Here we not only settle the unresolved case of joint convexity for 1 ≤ p ≤ 2, we are also able to include the parameter q ≥ 1 and still retain the convexity. Among other things this leads to a definition of an L q (L p ) norm for operators when 1 ≤ p ≤ 2 and a Minkowski inequality for operators on a tensor product of three Hilbert spaces – which leads to another proof of strong subadditivity of entropy. We also prove convexity/concavity properties of some other, related functionals.
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4.
On a fixed Riemann surface (M 0, g 0) with N Euclidean ends and genus g, we show that, under a topological condition, the scattering matrix S V (λ) at frequency λ > 0 for the operator Δ+V determines the potential V if \({V\in C^{1,\alpha}(M_0)\cap e^{-\gamma d(\cdot,z_0)^j}L^\infty(M_0)}\) for all γ > 0 and for some \({j\in\{1,2\}}\) , where d(z, z 0) denotes the distance from z to a fixed point \({z_0\in M_0}\) . The topological condition is given by \({N\geq \max(2g+1,2)}\) for j = 1 and by N ≥ g + 1 if j = 2. In \({\mathbb {R}^2}\) this implies that the operator S V (λ) determines any C 1, α potential V such that \({V(z)=O(e^{-\gamma|z|^2})}\) for all γ > 0.  相似文献   

5.
We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A?amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m?function associated with the Schrödinger operator H = ?? x 2  + q(x) on L 2(0, ∞) with Dirichlet boundary condition at x = 0.  相似文献   

6.
We consider fluctuations of the solution W ε (t, x, k) of the Wigner equation which describes energy evolution of a solution of the Schrödinger equation with a random white noise in time potential. The expectation of W ε (t, x, k) converges as ε → 0 to \({\bar{W}(t,x,k)}\) which satisfies the radiative transport equation. We prove that when the initial data is singular in the x variable, that is, W ε (0, x, k) = δ(x)f(k) and \({f\in {\mathcal{S}}(\mathbb{R}^d)}\), then the laws of the rescaled fluctuation \({Z_\varepsilon(t):=\varepsilon^{-1/2}[W_\varepsilon(t,x,k)-\bar{W}(t,x,k)]}\) converge, as ε → 0+, to the solution of the same radiative transport equation but with a random initial data. This complements the result of [6], where the limit of the covariance function has been considered.  相似文献   

7.
We report on the effect of hexagonal warping on the dynamical conductivity of the surface states of a topological insulator in the presence of nonmagnetic impurities. It is found that the photon energy dependent conductivities are determined by a polarization-function-liked term,  Π2 (q,ω), which contains a velocity term corresponding to the difference of group velocities between the two states due to an electron-impurity scattering. This is different from the conductivity of 2-dimentional electron systems where the conductivity depends on the inverse imaginary part of the dielectric function Im [1/κ(q,ω)]. We present both the real part and imaginary part of the polarization function with different warping strength. It is found that the warping strength can both enhance single particle excitations (SPEs) and suppress the screening effect of electrons. As a result the inverse scattering time is enhanced by up to about two orders of magnitudes. The real part of the longitudinal conductivity of the intra-band process is analog to the case with a conductivity of σ ~ μδ(ω). The broadening of the spectrum in the low energy is not only determined by chemical potential, but also dependent on the warping strength. At higher frequency, the real part of conductivity shows a jump at the threshold photon energy of μ, where the inter-band contribution takes over.  相似文献   

8.
Differential cross sections have been measured for the small angle scattering ofγ-rays by iron, silver, tantalum, lead and uranium with 17 MeV photons from Li7 (p, γ) Be8 at mean four momentum transfersq of 0·5mc and 1·3mc and with 7 MeV photons from F19(p, αγ)O16 at mean four momentum transfer of 0·5mc. Under these experimental conditions only Compton, Rayleigh and possibly Delbrück scattering are of importance. Extrapolation of known theoretical results to higher energies shows, that Rayleigh and Compton scattering from bound electrons should depend only onq for small angles, smallq and fixedZ. Using this it follows, that at 17 MeV andq≈0·5mc an additional scattering process must be present, which increases with growingZ and which is negligible in the measurements at 17 MeV withq≈1·3mc and at 7 MeV withq≈0·5mc. These results are in qualitative agreement with the approximate theory for Delbrück scattering ofBethe andRohrlich, however experimental cross sections at 17 MeV andq≈0·5mc are about a factor of 1·6 lower than those predicted by this theory. This discrepancy is not unexpected, since exact calculations of Delbrück scattering amplitude fromKessler andZernik at 2·62 MeV and 6·14 MeV show even greater deviations in the same sense.  相似文献   

9.
The structure of unitary irreducible representations of the noncompact uq(2, 1) quantum algebra that are related to a negative discrete series is examined. With the aid of projection operators for the suq(2) subalgebra, a q analog of the Gelfand-Graev formulas is derived in the basis corresponding to the reduction uq(2, 1) → suq(2)×u(1). Projection operators for the suq(1, 1) subalgebra are employed to study the same representations for the reduction uq(2, 1) → u(1)×suq(1, 1). The matrix elements of the generators of the uq(2, 1) algebra are computed in this new basis. A general analytic expression for an element of the transformation brackets <U∣T>q between the bases associated with the above two reductions (the elements of this matrix are referred to as q Weyl coefficients) is obtained for a general case where the deformation parameter q is not equal to a root of unity. It is shown explicitly that, apart from a phase, the q Weyl coefficients coincide with the q Racah coefficients for the suq(2) quantum algebra.  相似文献   

10.
For an infinitely renormalizable quadratic map \({f_c: z\mapsto z^2+c}\) with the sequence of renormalization periods {k m } and rotation numbers {t m  = p m /q m }, we prove that if \({\limsup k_m^{-1} \log |p_m| >0 }\), then the Mandelbrot set is locally connected at c. We prove also that if \({\limsup |t_{m+1}|^{1/q_m} <1 }\) and q m → ∞, then the Julia set of f c is not locally connected and the Mandelbrot set is locally connected at c provided that all the renormalizations are non-primitive (satellite). This quantifies a construction of A. Douady and J. Hubbard, and weakens a condition proposed by J. Milnor.  相似文献   

11.
We study the asymptotic behavior of a finite network of oscillators (harmonic or anharmonic) coupled to a number of deterministic Lagrangian thermostats of finite energy. In particular, we consider a chain of oscillators interacting with two thermostats situated at the boundary of the chain. Under appropriate assumptions, we prove that the vector (p, q) of moments and coordinates of the oscillators in the network satisfies (p, q)(t) → (0, q c ) as t → ∞, where q c is a critical point of some effective potential, so that the oscillators just stop. Moreover, we argue that the energy transport in the system stops as well without reaching thermal equilibrium. This result is in contrast to the situation when the energies of the thermostats are infinite, studied for a similar system in [14] and subsequent works, where the convergence to a nontrivial limiting regime was established.The proof is based on a method developed in [22], where it was observed that the thermostats produce some effective dissipation despite the Lagrangian nature of the system.  相似文献   

12.
This study investigates the localization properties of dual electric transmission lines with non-linear capacitances. The VC,n voltage across each capacitor is selected as a non-linear function of the electric charge qn, i.e., VC,n = qn(1/Cnn|qn|2)where Cn is the linear part of the capacitance and εn the amplitude of the non-linear term. We follow a binary distribution of values of εn, according to the Thue-Morse m-tupling sequence. The localization behavior of this non-linear case indicates that the case m = 2 does not belong to the m ≥ 3, family because when m changes from m = 2 to m = 3, the number of extended states diminishes dramatically. This proves the topological difference of the m = 2 and m = 3 families. However, by increasing m values, localization behavior of the m-tupling family resembles that of the m = 2, case because the system begins to regain its extended states. The exact same result was obtained recently in the study of linear direct transmission lines with m-tupling distribution of inductances. Consequently, we state that the localization behavior of the m-tupling family as a function of the m value is independent of both the linear and the non-linear system under study, but independent of the kind of transmission line (dual or direct). This is curious behavior of the m-tupling family and thus deserves more scholarly attention.  相似文献   

13.
In this paper, we first construct the Cauchy q-shift operator T(a, b;D xy ) and the Cauchy q-difference operator L(a, b; θ xy ). We then apply these operators in order to represent and investigate some new families of q-polynomials which are defined in this paper. We derive some q-identities such as generating functions, symmetry properties and Rogers-type formulas for these q-polynomials. We also give an application for the q-exponential operator R(bD q ).  相似文献   

14.
We consider two-loop sunset diagrams with two mass scales m and M at the threshold and pseudothreshold that cannot be treated by earlier published formulas. The complete reduction to master integrals is given. The master integrals are evaluated as a series in ratio m/M and in ε with the help of a differential-equation method. The rules of asymptotic expansion in the case when q2 is at the (pseudo) threshold are given.  相似文献   

15.
For a two-dimensional Schrödinger operator H α V  = ?Δ ?αV with the radial potential V(x) = F(|x|), F(r) ≥ 0, we study the behavior of the number N ?(H α V ) of its negative eigenvalues, as the coupling parameter α tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth N ?(H α V ) = O(α) and for the validity of the Weyl asymptotic law.  相似文献   

16.
The aim of the work was to determine the phenomena of internal friction (mechanical losses) occurring in ferroelectric-ferromagnetic composites created based on PZT-type ferroelectric powder and ferrite. The composites were obtained using ceramic powders – multi-component PZT-type solid solutions with ferroelectric properties. Their magnetic component included zinc-nickel powder Ni0.64Zn0.36Fe2O4. 30 × 10 × 1 mm3 test specimens were obtained using free sintering. Temperature Q-1(T) and amplitude Q-1(ε) internal friction dependencies were determined. Wide high temperature maxima were observed with regard to the internal friction temperature dependencies obtained for the tested specimens. The conducted measurements of amplitude (isothermal) dependencies of internal friction Q-1(ε) for the tested composites have allowed for interpreting the previously observed maximum on the temperature dependencies of internal friction.  相似文献   

17.
Based on the Heisenberg model including single-site uniaxial anisotropy and using aGreen’s function technique we studied the influence of size and composition effects on theCurie temperature T C , saturationmagnetization M S and coercivityH C of spherical nanoparticles with astructural formulaM e 1?x Zn x Fe2O4,Me = Ni, Cu, Co, Mn. It is shown that for x = 0.4–0.5and d = 10–20 nm these nanoparticles have aT C  = 315 K and are suitable for aself-controlled magnetic hyperthermia.  相似文献   

18.
The structure factor and correlation energy of a quantum wire of thickness b ? a B are studied in random phase approximation (RPA) and for the less investigated region r s < 1. Using the single-loop approximation, analytical expressions of the structure factor are obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy in RPA is found to be represented by ? c (br s ) = α(r s )/b + β(r s ) ln(b) + η(r s ), for small b and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data.  相似文献   

19.
We investigate two competing contact processes on a set of Watts–Strogatz networks withthe clustering coefficient tuned by rewiring. The base for network construction isone-dimensional chain of N sites, where each site i is directly linked tonodes labelled as i ±1 and i ±2. So initially, each node has the same degree ki =4. The periodic boundary conditions are assumed as well. For each nodei the linksto sites i +1 and i +2 are rewired to two randomly selected nodes so far not-connected tonode i. Anincrease of the rewiring probability q influences the nodes degree distribution and thenetwork clusterization coefficient ??. For given values of rewiring probabilityq the set ??(q)={??1,??2,...,??M} of M networks is generated. The network’s nodes aredecorated with spin-like variables si ∈ { S,D}. During simulation each S node having a D-site in its neighbourhoodconverts this neighbour from D to S state. Conversely, a node in D state having at least oneneighbour also in state D-state converts all nearest-neighbours of this pairinto D-state. The latter is realized with probabilityp. We plotthe dependence of the nodes S final density nST on initial nodes S fraction nS0. Then, we construct the surface of the unstable fixedpoints in (??, p, nS0) space. The system evolves more often toward nST for (??, p, nS0) points situated above this surface while startingsimulation with (??, p, nS0) parameters situated below this surface leads system to nST=0. The points on this surface correspond to such value ofinitial fraction nS* of S nodes (for fixed values ?? and p) for which their final density is nST=1/2.  相似文献   

20.
An optogalvanic method is used to measure photoemission coefficient γph in a gas discharge exposed to the resonant radiation of helium atoms. The range of working current j/P He 2 (j is the current density, and P He is the gas pressure) extends from 2 to 1000 μA/(cm2 Torr), and field strength E/N at the cathode varies from 0.45 to 13 kTd. Up to j/P He 2 = 10 μA/(cm2Torr2), photoemission coefficient γph grows and then tends toward saturation at a level of γph = 0.30 ± 0.01. Under the no-discharge conditions, γph = 0.35 ± 0.05. It is concluded that the emissivity of cold cathodes in a gas discharge is governed by adsorption of the working gas on the cathode surface and its implantation into the cathode. With allowance for this factor, the contribution of photoemission to the discharge current is reconsidered. It is shown that, for cathodes with diameter d c ? l c (l c is the length of the cathode layer), a normal or weakly abnormal glow discharge in noble gases is largely of a photoelectron character. In light noble gases, the photoelectron character of the discharge persists even for a strongly abnormal discharge. The energy dependences of coefficients γ of kinetic and potential emission in helium are calculated with allowance for implantation of helium atoms into the cathode and compared with published data. The influence of particle implantation on γ in a vacuum is estimated.  相似文献   

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