Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Epidemic spreading on uncorrelated heterogenous networks with non-uniform transmission

We investigate the combinational effects of non-uniform transmission of edges and the network structure in susceptible-infected-removed models of the epidemic spreading. Here the degree-degree correlation is neglected and the transmission of individual edge depends on the degree of infected node. With the additional assumption that we can compartment a independent factor λ₀ from the transmission, we analyzed the effects of degree distribution P(k) and transmission distribution λ(k) on the threshold of λ₀.     

求近似波函数的一种方法

设H为量子体系的哈密顿算符,以算符(λ-H)和(H-λ)^-1作用于近似波函数ψ_k⁽⁰⁾。我们证明了,如果作用得到的函数中φ_k在H的变量的整个区间是连续、有限和平方可积的,则它们是比ψ_k⁽⁰⁾更接近于本征态ψ_k的近似波函数。由φ_k计算H的平均值接近于以{ψ_k⁽⁰⁾}为无微扰态的二级微扰的计算值。用此法计算类氢离子的极化率,得到很好的结果。     

On the temperature behavior of second sound and Poiseuille flow

The linearized Peierls equation for the phonon densityN (k λ,r t) is solved by replacing the collision operator in the subspace orthogonal to the collision invariants byk-dependent relaxation rates. For the normal process relaxation time the behaviorτ _N (k λ)∝|k|^?p for smallk is assumed. Taking into account thisk-dependence ofτ _N explicitly and avoiding an expansion with respect toΩτ _N (kλ) before performing the necessary integration overk yields new, non-analytic, terms in the hydrodynamic equations describing second sound and Poiseuille flow. It is shown that this may lead to a temperature dependence of second sound damping and thermal conductivity in the Poiseuille flow region differing from the usual theoretical predictions and in better agreement with experiments.     

Optical and electrical properties of thin NiO films deposited by reactive magnetron sputtering and spray pyrolysis

Thin NiO films are deposited by reactive magnetron sputtering and spray pyrolysis. The main optical constants, i.e., refractive index n(λ), absorption coefficient α(λ), extinction coefficient k(λ), and thickness d, are determined. The temperature dependence of the resistance of thin films is found, and the activation energy of films deposited by different methods is determined.     

Das Fluktuationsspektrum von Elektronen in einem stationären Nichtgleichgewichtszustand

The Boltzmann equation is used to calculate the time correlation function and the fluctuation spectrum for electrons obeying classical statistics. The stationary joint distribution for one electron to be initially ink ₀=k(0) and finally ink=k(t) is given by the product of the conditional probability and the stationary distribution. These quantities can be found from the Boltzmann equation if there exists, for any initial distribution, a unique solution which satisfies the Markov equation and tends to a stationary solution for large times under stationary conditions. It is proved that these conditions hold for linear collision operators and in the relaxation approximation. General operator expressions for the fluctuation spectrum and the differential conductivity in a stationary electric field are given, which can be evaluated within the usual approximation schemes known for the stationary, nonequilibrium solutions of the Boltzmann equation. In equilibrium they reproduce the classical fluctuation dissipation theorem. In a nonequilibrium state they define a noise temperature depending on the field. In the relaxation approximation and for polynomial band structure the exact solution can be found. For parabolic and biparabolic spherical bands the result is discussed explicitly.     

Systems with separable many-particle interactions. I

In this paper we give an exact evaluation of the free energy per particle for systems with separable many-particle interactions described by a hamiltonian of the type ? = ∑_kT(k) + NP (N^-1 ∑_kV(k)), where P is an arbitrary polynomial. In the proof use is made of a fundamental theorem due to Bogoliubov Jr. for ferromagnetic quadratic operators. The free energy can be obtained from a trial hamiltonian, which is linear in the operators T and V.     

Investigation of the two-photon absorption spectrum of 3,4-benzopyrene by means of a tunable dye laser

The two-photon absorption of the solid solution of 3,4-benzopyrene in methyl polymetacrylate, induced by a tunable dye laser has been investigated. An absorption spectrum in the range of 530–750 nm has been obtained. The dependence of the fluorescence intensity I_F upon the laser power I_F, I_FλI^k_L and the relation k=k(λ) has been i investigated.     

A simple accurate formula for the energy levels of oscillators with a quartic potential

In this note we present a simple analytical formula which reproduces the energy eigenvalues E_k(λ) of the pure quartic and quartic anharmonic oscillators with high accuracy for all values of the anharmonicity parameter λ and the level number k.     

The Threshold Effects for the Two-Particle Hamiltonians on Lattices

For a wide class of two-body energy operators h(k) on the d-dimensional lattice ℤ^d, d≥3, k being the two-particle quasi-momentum, we prove that if the following two assumptions (i) and (ii) are satisfied, then for all nontrivial values k, k≠0, the discrete spectrum of h(k) below its threshold is non-empty. The assumptions are: (i) the two-particle Hamiltonian h(0) corresponding to the zero value of the quasi-momentum has either an eigenvalue or a virtual level at the bottom of its essential spectrum and (ii) the one-particle free Hamiltonians in the coordinate representation generate positivity preserving semi-groups.     

On spectral invariance of single scattering albedo for water droplets and ice crystals at weakly absorbing wavelengths

The single scattering albedo ω_0λ in atmospheric radiative transfer is the ratio of the scattering coefficient to the extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, thus the single scattering albedo, are functions of wavelength λ and droplet size r. This note shows that for water droplets at weakly absorbing wavelengths, the ratio ω_0λ(r)/ω_0λ(r₀) of two single scattering albedo spectra is a linear function of ω_0λ(r). The slope and intercept of the linear function are wavelength independent and sum to unity. This relationship allows for a representation of any single scattering albedo spectrum ω_0λ(r) via one known spectrum ω_0λ(r₀). We provide a simple physical explanation of the discovered relationship. Similar linear relationships were found for the single scattering albedo spectra of non-spherical ice crystals.     

The exponential interaction in Rn

We prove that the Schwinger functions for the ultraviolet cut-off exponential interaction with euclidean measure exp {;?λ∫Λ:e^αξk(x):dx} dμ₀(ξ/ ∫ exp{?λ∫Λ:e^αξk(x):dx} dμ₀(ξ), λ > 0, converge as the ultraviolet cut-off is removed. The limits are the free Schwinger functions in the case of space-time dimension n ? 3. In the case n = 2 this holds for |α| sufficiently big, whereas for |α| < 2 √π, one has the well-known nontrivial Schwinger functions of the exponential interaction.     

On the rate of quantum ergodicity I: Upper bounds

One problem in quantum ergodicity is to estimate the rate of decay of the sums $$S_k (\lambda ;A) = \frac{1}{{N(\lambda )}}\sum\limits_{\sqrt {\lambda _j } \leqq \lambda } {\left| {(A\varphi _j ,\varphi _j ) - \bar \sigma _A } \right|^k } $$ on a compact Riemannian manifold (M, g) with ergodic geodesic flow. Here, {λ _j ,? _j } are the spectral data of the Δ of(M, g), A is a 0-th order ψDO, $\bar \sigma _A $ is the (Liouville) average of its principal symbol and $N(\lambda ) = \# \{ j:\sqrt {\lambda _j } \leqq \lambda \} $ . ThatS _k (λ;A)=o(1) is proved in [S, Z.1, CV.1]. Our purpose here is to show thatS _k (λ;A)=O((logλ) ^?k/2 ) on a manifold of (possibly variable) negative curvature. The main new ingredient is the central limit theorem for geodesic flows on such spaces ([R, Si]).     

Elektromagnetische Übergänge imSU(3)-Modell

A method is developed how to calculate electromagnetic transition probabilities and selection rules forSU(3)-classified wave functions. For this purpose the transition operators of electric multipole radiation are expanded inSU(3)-tensors. The calculations are explicitly carried out forE1- andE2-radiation. ForB(E2)-values in (λ,0)-bands an analytic expression is obtained independent of the special form of the interaction. The results ofSU(3)-theory are compared with those of Hartree-Fock-calculations performed by other authors. An astonishing agreement is found.     

The 2+-2+ transition of 879 keV in160Dy investigated by electron-gamma directional correlation

e-γ directional correlation measurements of 2⁺(879 keV)2⁺(87 keV)0⁺ cascade in¹⁶⁰Dy have been made and the magnitude of electric monopole to quadrapole mixing ratio for 879 keV transition was found to beq _k =?0.03(10) for λ=0 (λ-according to Hager-Saltzer definition).     

Ground states in two-dimensional boson quantum field-theory

We consider λ:P(?):₂ models of Euclidean quantum field theory, P(?) = Σ_k=1²ⁿa_k?^k and define for them translation-invariant ground states. It appears that the number of them is not more than two provided $\text{λ}\text{m}{}_0{}^2$ is large.     

Fractional supersymmetric Liouville theory and the multi-cut matrix models

We point out that the non-critical version of the k-fractional superstring theory can be described by k  -cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p,q)$(p,q)$ minimal fractional superstring theories appear in the Zk${\mathbb{Z}}_k$-symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators.