Computable upper bounds for the adiabatic approximation errors

For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.     

Conversion coefficients and E0 transitions in102, 104, 106Pd

In in-beam (p, p′) experiments, electron and γ-spectra were measured in the electron energy range of 500-1840 keV for¹⁰²Pd and¹⁰⁴Pd, and 600–1580 keV for¹⁰⁶Pd. The conversion coefficients of all transitions in this range were obtained with accuracies of about 20%, in some favourable cases 10%. Special attention was given to 0⁺′-0⁺ transitions from the two-phonon triplets to the ground states with the following results for the branching ratios 0⁺′-0⁺ (ground state) to 0⁺′-2⁺ (one-phonon state):¹⁰²Pd:T _k (E0)/T _γ (E2)<(2.1±3.6)·10^{?7 104}Pd:T _k (E0)/T _γ (E2)=(6.0±1.4)·10^{?5 106}Pd:T _k (E0)/T _γ (E2)=(6.0±2.0)·10^?4     

Applications of exact solution for strongly interacting one-dimensional Bose-Fermi mixture: Low-temperature correlation functions, density profiles, and collective modes

We consider one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in current experiments with ultracold Bose-Fermi mixtures. We apply the Bethe ansatz technique to find the exact ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We use it to prove the absence of the demixing, contrary to prediction of a mean-field approximation. Combining exact solution with local density approximation in a harmonic trap, we calculate the density profiles and frequencies of collective modes in various limits. In the strongly interacting regime, we predict the appearance of low-lying collective oscillations which correspond to the counterflow of the two species. In the strongly interacting regime, we use exact wavefunction to calculate the single particle correlation functions for bosons and fermions at low temperatures under periodic boundary conditions. Fourier transform of the correlation function is a momentum distribution, which can be measured in time-of-flight experiments or using Bragg scattering. We derive an analytical formula, which allows to calculate correlation functions at all distances numerically for a polynomial time in the system size. We investigate numerically two strong singularities of the momentum distribution for fermions at k_f and k_f + 2k_b. We show, that in strongly interacting regime correlation functions change dramatically as temperature changes from 0 to a small temperature ∼E_f/γ ? E_f, where E_f = (π?n)²/(2m), n is the total density and γ = mg/(?²n) ? 1 is the Lieb-Liniger parameter. A strong change of the momentum distribution in a small range of temperatures can be used to perform a thermometry at very small temperatures.     

E1-M2-E3 mixing of the 1241.7 keV transition in147Yb

The half-life of theI,K ^π=2, 2^? state at 1318 keV in¹⁷⁴Yb has been measured in the¹⁷³Yb(n, γ) reaction to be 0.486±0.015 ns. This half-life determines the absolute transition probabilities of the gamma-ray transitions to the ground state rotational band yielding the following hindrance factors relative to the Weisskopf estimate:F _W(M 2; 2, 2^?→0, 0⁺)=350;F _W(M2; 2, 2^?→2, 0⁺)≧77F _W(M 2;2, 2^?→4, 0⁺)>740;F _W(E 1; 2, 2^?→2, 0⁺)=4.5×10⁶;F _W(E 3; 2, 2^?→2, 0⁺)≈0.1;F _W(E 3; 2, 2^?→4, 0⁺)≈0.4. These data are compared to analogous transitions in neighboring nuclei.     

Leading role pseudovector and vector mesons in quasielastic pion electroproduction on a nucleon by longitudinal photons at comparatively high virtual momenta in the range 0.4 ≤ |k| ≤ 1 GeV/c

It is shown that, under kinematical conditions of quasielastic knockout, the differential cross section for the exclusive process p(e, e′π ⁺)n induced by longitudinal virtual photons γ* _L changes its physical nature as the recoil momentum |k| of the spectator nucleon grows from values in the range |k| ～ 0.1–0.4 GeV/c, which are typical in studying the pion cloud of the nucleon, to values around |k| ～ 1 GeV/c. Calculations within the ³ P ₀ quark microscopic model reveal that the amplitudes for the deexcitation of vector and pseudovector mesons via the processes ρ ⁺ + γ* _L → π ⁺ and b ₁ ⁺ + γ* _L → π ⁺ become dominant here. Concurrently, the effective momentum distributions develop a substantial angular anisotropy of about 50% with respect to the angle between the momentum of the photon γ* _L and the recoil momentum of the spectator nucleon, the longitudinal differential cross sections undergoing respective changes. In this region, the energy of knock-on pions is expected to be about 5 GeV under conditions of quasilastic kinematics.     

Thermal evolution of vacancy defects induced in sintered UO2 disks by helium implantation

A slow positron beam coupled with Doppler broadening (DB) spectrometer was used to measure the low- and high-momentum annihilation fractions, S and W, respectively, as a function of positron energy in UO₂ disks implanted with different 1 MeV ³He fluences and annealed in ArH₂ or in vacuum. The S(E) and W(E) behaviors indicate that for fluences in the range from 2 × 10¹⁴ to 2 × 10¹⁶³He cm⁻², the vacancy defects distribution evolves with the annealing temperature in the range from 264 to 700 °C under ArH₂. This evolution is found to be dependent on the ³He fluence implanted in the sintered UO₂ disks. For the lowest fluence of 2 × 10¹⁴³He cm⁻², the S(W) plot with positron energy as the running parameter suggests that only the concentration of vacancy defects decreases when annealing temperature increases. For the highest implantation fluences (from 5 × 10¹⁵ to 2 × 10¹⁶³He cm⁻²) the S(W) plot suggests that the nature of the vacancy defects changes in the annealing temperature range from 260 to 400 °C. Measurements performed in implanted UO₂ disks annealed in vacuum have revealed a partial recovery of the vacancy defects possibly due to their recombination with mobile oxygen interstitials. The role of the hydrogen infusion into the disk is also discussed.     

Long Time,Large Scale Limit of the Wigner Transform for a System of Linear Oscillators in One Dimension

We consider the long time, large scale behavior of the Wigner transform W _? (t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile et al. in Phys. Rev. Lett. 96 (2006) to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile et al. in Arch. Rat. Mech. 195(1):171–203 (2009). In the present paper we prove that in the unpinned case there exists γ ₀>0 such that for any γ∈(0,γ ₀] the weak limit of W _? (t/? ^3/2γ ,x/? ^γ ,k), as ??1, satisfies a one dimensional fractional heat equation \(\partial_{t} W(t,x)=-\hat{c}(-\partial_{x}^{2})^{3/4}W(t,x)\) with \(\hat{c}>0\). In the pinned case an analogous result can be claimed for W _? (t/? ^2γ ,x/? ^γ ,k) but the limit satisfies then the usual heat equation.     

169Tm NMR study of the high-Tc superconductor TmBa2Cu3O6.92

The ground state of Tm³⁺ ion (4t²,³H₆) in a crystal electric field (CEF) of TmBaCuO is a singlet, separated from the lowest excited states by an energy gap of 100÷130 cm^?1. The pulsed NMR of¹⁶⁹Tm nuclei (spinI=1/2) in a magnetically-oriented TmBa₂Cu₃O_6.92 power is studied at temperatures 1.5÷4.2 K. Two sorts of Tm nuclei are observed: rapidly relaxing Tm1 (≥80% of total amount, having relaxation timesT ₁ ⁽¹⁾ ≈35 ms,T ₂ ⁽¹⁾ =80÷250 μs) and slowly relaxing Tm2 nuclei (≦20%,T ₁ ⁽²⁾ =300÷1000 μs). The¹⁶⁹Tm NMR spectra are described by the spin-Hamiltonian ?₁ = ??Σγ _i H _i I _i (i = x,y,z), where |γ _x ⁽¹⁾/2π| = 5.3(1), |γ _y ⁽¹⁾/2π| = 6.6(1), |γ _x ⁽²⁾/2π| = |γ _y ⁽²⁾/2π| = 5.1(1), |γ _z ⁽¹⁾/2π| = |γ _z ⁽²⁾/2π| = 2.3(1) kHz/Oe, and axesx, y, z coincide with the crystal axesa, b, c. The Tm1 and Tm2 nuclei are identified as those belonging to orthorhombic (CEF of D_2h symmetry) and tetragonal (D_4h) phases of the TmBaCuO compound, respectively. Two-exponential and nearly temperature-independent nuclear relaxation is observed at temperatures 1.5÷4.2 K. The smallestT ₂ ⁽¹⁾ -values (≈80 μs) found for the orthorhombic (superconducting) phase in an external field H perpendicular to the crystalc-axis agree fairly well with those one could expect due to the dipole-dipole interaction of thulium nuclei. However, the slowing down of this rapid relaxation of the nuclear transverse magnetization in a field H‖c as well as the origin of unusually largeT ₂ ⁽²⁾ -values remain unclear.     

| m | Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef _|m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off _|m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f _|m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off _|m|(θ) on the positive real |m| axis.     

Liquid Madelung energy and Schottky defect energy related to liquid structure and melting temperature for alkali halides

Motivated by the work of Reiss et al in which the melting temperature T_m of alkali halides is correlated with Coulomb energy, we consider the cohesive energy W of ionic melts and Schottky defect energy E_s in the hot crystal, relative to the thermal energy k_BT_m It is shown here that W is accurately approximated by the liquid Madelung energy and hence that Wk_BT_m relates to the charge-charge direct correlation function c_QQ(r) at r = 0 The existence of a “Madelung constant” for the liquid at T_m is thereby demonstrated through the alkali halide series An estimate of the ratio E_s/k_BT_m then considered, the basic additional ingredient being argued to be the static dielectric constant of the solid The BarrDawson-Lidiard empirical correlation between E_s, and k_BT_m can be understood in this way.     

Calculation of chemisorption energies of oxygen on narrow-gap semiconductors

Newns' self-consistent model for hydrogen chemisorption on transition metals is extended to calculate the chemisorption energy ΔE of oxygen on Si, Ge and III–V compounds. ΔE is found to depend on the widths of the energy gap and valence band, the crystal work function and the crystal plane, |ΔE₍₁₀₀₎|>|ΔE₍₁₁₁₎|. In general, larger ΔE's are associated with wider energy gaps.     

Estimate of the probability of K+→μ+νμγ decay

About 100 000 K⁺-decays were observed in a magnetic spectrometer with streamer chambers. The estimation for the radiative decay K⁺→μ⁺ν_μγ, R^exp = [W(K⁺→μ⁺ν_μγ)]/[W(K⁺→all)]=(5.8±3.5) x 10^?3, at E_γ ? 9 MeV was obtained and the ratio R = [W(K⁺→π⁺π°)]/[W(K⁺→μ⁺ν_μ)] = 0.328 ± 0.005 was measured.     

Breit-Wigner parameters of the <Emphasis Type="Italic">S</Emphasis><Subscript>11</Subscript>(1535) nucleon resonance

The results of a partial-wave analysis of the angular distributions for the process γp → ηp over the energy range up to 2 GeV are presented. Reliable estimates of the Breit-Wigner parameters of the S₁₁(1535) resonance, as well as the energy dependence of the real and imaginary parts of the electric dipole amplitude E₀₊ and its phase, are derived from the energy dependence of the regression coefficient a₀(W).     

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.     

Experimentelle Untersuchungen am Elektroneneinfang des Mangan 54 und Zink 65

The electron capture decay of Mn 54 and Zn 65 was investigated using Na I(Tl)-detectors. Spectroscopic-coincidence techniques were employed to examine theK-electron capture rates of Mn 54 and Zn 65, the branching ratio and positron rate of Zn 65. The experimental results are:P _k ω _k (Mn)=0.2492±0.0017,P _k ω _k (Zn)=0.3927±0.0026,EC ^* /EC ⁰(Zn)=53.2±1.0/46.8±1.0,γ/β ⁺=35.1±1.7,K ⁰/β ⁺=27.7±1.5. Thus electron capture to the excited state of Cu 65 occurs to the extent of 52.4±1.0% while electron capture and positron decay to the ground state were found to be associated with 46.1±1.0% and 1.49±0.05% of the disintegrations. These data partly disagree significantly from measurements of other authors. Using the fluorescence yieldsω _k (Cr)=0.279 andω _k (Cu)=0.4425, deduced from other measurements, values ofL+M/K of electron capture to the excited state could be derived:L+M/K(Mn 54)=0.120±0.015 andL+M/K(Zn 65)=0.127±0.015. These ratios agree with the calculations ofBahcall. The half-lives of Mn 54 and Zn 65 have been determined to beT _1/2(Mn 54)=312±5d,T _1/2(Zn 65)=243±4d The energy of the Zn 65-γ-rays was measured with a Ge(Li)-counter:E ^γ=1115.5±0.5 keV.     

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.     

The polarization of protons from the 2H(d, p)3H reaction for deuteron energies below 1 MeV

The angular distribution of proton polarization P^γ' (θ) from the ${}^2\text{H}\text{(}\text{d,}\text{p}\text{)}{}^3\text{H}$ reaction has been measured at 975 keV deuteron energy. Moreover, the energy dependence of P^γ′(E_d) was measured at 45°(lab) for deuteron energies between 250 and 975 keV. The values of σ₀(θ)P^γ' (θ) were fitted in terms of an associated Legendre polynomial expansion. The measured energy dependence of P^γ' (E_d) has been analyzed in terms of barrier-penetration parameters.     

On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

Calculation of the wave functions of the ground and weakly excited states of helium II

The wave functions of the ground (Ψ₀) and the first excited (Ψ_k) states of He II in the second-order approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions Ψ₀ and Ψ_k = ψ_kΨ₀ are determined as the eigenfunctions of the N-particle Schrödinger equation from a system of coupled equations for Ψ₀, Ψ_k, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the first-order approximation), and (2) Ψ₀ and ψ_k are derived from a model potential of interaction between He⁴ atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V ₀ of the potential barrier is a free parameter. Except for V ₀, the model does not have any free parameters or functions. The calculated values of the structure factor, the ground-state energy E ₀, and the quasiparticle spectrum E(k) of He II are in agreement with the experimental values for V ₀ ≈ 100 K. The second-order correction to the logarithm of Ψ₀ significantly affects the value of E ₀ and provides the asymptotics E(k → 0) = ck, while the second-order correction to ψ_k slightly affects the E(k). The second-order corrections to Ψ₀ and ψ_k have a smaller effect on the results compared with the first-order corrections, whereby the theory is in agreement with experiment; therefore, one may assume that the truncated Ψ₀ and ψ_k well describe the microstructure of He II. Thus, the series for Ψ₀ and Ψ_k can be truncated in spite of the fact that the expansion parameter is not very small (～1/2).     

The long-time behaviour of the electric-field autocorrelation function in a finite photon gas

We investigate an autocorrelation function of a soluble three-dimensional system, namely the temporal coherence functionC _E(t)∝<E(0)E(t)> of the thermal radiation field in a cube-shaped cavity for the stochastic electrical fieldE. In the thermodynamic limit,C _E(t) relaxes exponentially at intermediate times, but a “long-tail” behaviourC ₀(t)=At^?4 withA<0 is predominant for long times. In the case of a finite, but not too small, cavity lengthL obeyingΛ=hc/k _BT?L and at timest withct?L, C _E(t) is described by an asymptotic expansion in powers ofL ^?1 using generalized Riemann zeta functions. Surface-and shape-effects enhance the long-tail. In the case of very small cavities withL«Λ, we calculate an expansion ofC _E(t) in terms of exp(?L ^?1) and cosines. An oscillatory, but not strictly periodic, long-time behaviour is observed in this case.