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.     

On the fragmentation functions of heavy quarks into hadrons

An explicit form for the charmed quark fragmentation function D^C_c(z) into hadrons has been obtained with the help of the “reciprocity relation” and the c-quark distribution function in charmed mesons (the function calculated in terms of the Kuti-Weisskopf model). D^C_c(z) turns out to peak mainly at z close to 1. The analysis of new data on muon pair production in neutrino reactions points to such a behaviour of the D^C_c(z) function. The obtained fragmentation function, contrary to those, used earlier, leads to a charmed particle (average) multiplicity in e⁺e^?-annihilation independent of energy.     

Cross section of ion excitation in ion-ion collision

The “effective Feynman diagram” technique introduced in a previous paper is used to express the cross section of ion excitation in ion-ion collisions $\text{(A + B → A}{}^1\text{+ B)}$ in terms of the corresponding photon resonance absorption $\text{(hv + A → A}{}^1\text{)}$ and Thomson-scattering (hv + B → hv + B) cross sections. The result is checked for the process He⁺ + H(1s) → He⁺ + H(2p) with experiment and very good agreement is obtained.     

Retardation effects: Localized excitations of a soliton in a model of a one-dimensional electron-phonon (Peierls) system

A set of localized mixed electron-phonon excitations has been found in the “quantum” regime M < K²/2C(g²+2KB) = M_c. We suggest that the spectrum is related to possible bound states of ions in the Coulomb field of the charge soliton for sufficiently light ions.     

First observation of the production and decay of the Σc+

An event with the decay chain Σ_c⁺ → Λ_c⁺ + π⁰, Λ_c⁺ → K^? + p + π⁺, has been observed in an exposure of BEBC, equipped with a track sensitive target, to the wide band neutrino beam from the SPS at CERN. The event has a unique three constraint kinematic fit to the ΔS = ?ΔQ reaction v + p → μ^? + p + K^? + π⁺ + π⁺ + π⁰ with both gammas from the π⁰ decay detected. The proton and other final state particles are identified. The masses are M(Λ_c⁺) = 2290 ± 3 MeV/c², M(Σ_c⁺) = 2457 ± 4 MeV/c² and M(Σ_c⁺) ? M(Λ_c⁺) = 168 ± 3 MeV/c². Including other data one obtains M (Σ_c⁺⁺) ? M(Σ_c⁺) = 0 ± 4 MeV/c².     

Structure and magnetotransport properties of the new quasi-two-dimensional molecular metal β″-(BEDT-TTF)4H3O[Fe(C2O4)3] · C6H4Cl2

The β″-(BEDT-TTF)₄A^I[M^III(C₂O₄)₃] · G(A^I=NH ₄ ⁺ , H₃O⁺, K⁺, Rb⁺; M^III=Fe, Cr; G = “guest” solvent molecule) family of layered molecular conductors with magnetic metal oxalate anions exhibits a pronounced dependence of the conducting properties on the type of neutral solvent molecules introduced into the complex anion layer. A new organic dichlorobenzene (C₆H₄Cl₂)-containing conductor of this family, namely, β″-(BEDT-TTF)₄H₃O[Fe(C₂O₄)₃] · C₆H₄Cl₂, is synthesized. The structure of the synthesized single crystals studied by X-ray diffraction is characterized by the following parameters: a = 10.421(1) Å, b= 19.991(2) Å, c= 35.441(3) Å, β = 92.87(1)°, V= 7374(1) ų, space groupC2/c, and Z = 4. In the temperature range 0.5&;2-300 K, the conductivity of the crystals is metallic without changing into a superconducting state. The magnetotransport properties of the crystals are examined in magnetic fields up to 17 T at T = 0.5 K. In fields higher than 10 T, Shubnikov-de Haas oscillations are detected, and the Fourier spectrum of these oscillations contains two frequencies with maximum amplitudes of about 80 and 375 T. The experimental results are compared with the related data obtained for other phases of this family. The possible structural mechanisms of the effect of a guest solvent molecule on the transport properties of the β″-(BEDT-TTF)₄A^I[M^III(C₂O₄)₃] · G crystals are analyzed.     

Associated average charged particle multiplicities in K+p interactions at 32 GeV/c

The average charged particle multiplicities, 〈n_R(M_X²)〉, in the reactions K⁺p → π^?X and K⁺p → K⁰X at 32 GeV/c are studied as functions of the mass squared M_X² of the “associated” system X. A comparison with the corresponding results obtained at lower incident momenta is presented.     

Properties of the φ and f′ produced in the channel Kp → KpKK̄ at 10 GeV/c

Data are presented and cross sections given for ф and f′ production in the channel K⁺p → K⁺pKK? at 10 Gev/c. The resonance parameters obtained from a fit to the KK? effective mass distribution are M = (1020.4 ± 0.5) MeV/c² and Γ = (5.0 ± 1.3) MeV/c² for the ф meson and M = (1514 ± 4) MeV/c² and Γ = (28 ± 15) MeV/c² for the f′. The resonance widths are corrected for experimental resolution. The branching fraction for the rate (ф → K⁰₁K⁰₂)/(ф → K⁺K⁻) is determined to be 1.15 ± 0.15. The angular distributions for the decay of the f′ have unnormalized moments _H(2,0) and H(4,0) different from the values for the nearby background, indicating spin 2 or greater for the f′.     

Observation of a doubly charged charmed baryon in the reaction υp→μ−Σ++c

Evidence for the quasi-elastic production of the doubly charged charmed barron Σ⁺⁺_c has been observed in a vp interaction in BEBC. The mass of the Σ⁺⁺_c and of its decay product, the Λ⁺_c, are 2454±5 MeV and 2288±5 MeV, respectively. The mass difference M(Σ⁺⁺_c)? M(Λ⁺_c) is 166±1 MeV. Combining the Λ⁺_c mass value obtained here with the values obtained in the two Λ⁺_c events previously observed in this experiment, thevalue M(Λ⁺_c)=2283±3 MeV is deduced.     

200 MeV Ag ion irradiation created columnar defects and enhanced critical current density of La-2125 type superconducting thin films

We have deposited c-axis oriented thin films of La_1.5Dy_0.5CaBa₂Cu₅O_z (La-2125) tetragonal superconductor on LaAlO₃(001) substrates by pulsed laser deposition. These films were irradiated with 200 MeV Ag⁺¹⁵ ions. Atomic force microscopy and elastic recoil detection analysis indicate that the irradiation has created columnar defects through the entire thickness (2000 Å) of these films. With ion irradiation up to 1×10¹¹ ions/cm², the critical current density (J_c(H)) enhances by fivefold, which is attributed to the augmented flux pinning by the columnar defects. A further increase in irradiation to 1×10¹² ions/cm² causes reduction in J_c(H) due to distorted morphology of the film. Our work shows that the enhancement in J_c(H) of the irradiated La-2125 film is comparable to that in irradiated RE-123 (RE = rare earth ion). Also, as the La-2125 type films have greater chemical stability than RE-123, La-2125 type superconductors are potential candidates for applications. It is interesting to note that there are partial flux jumps observed to occur symmetrically in the magnetic hysteresis of irradiated La-2125 thin films with enhanced J_c(H).     

Smeared spin-flop transition in random antiferromagnetic Ising chain

At T = 0 and in a sufficiently large field, the nearest-neighbor antiferromagnetic Ising chain undergoes a first-order spin-flop transition into the ferromagnetic phase. We consider its smearing under the random-bond disorder such that all independent random bonds are antiferromagnetic (AF). It is shown that the ground-state thermodynamics of this random AF chain can be described exactly for an arbitrary distribution P(J) of AF bonds. Moreover, the site magnetizations of finite chains can be found analytically in this model. We consider a continuous P(J) that is zero above some ?J ₁ and behaves near it as (?J ₁?J)^λ, λ > ?1. In this case, the ferromagnetic phase emerges continuously in a field H > H _c = 2J ₁. At 0 > λ > ?1, it has the usual second-order anomalies near H _c with the critical indices obeying the scaling relation and depending on λ. At λ > 0, higher-order transitions occur (third, fourth, etc.), marked by a divergence of the corresponding nonlinear susceptibilities. In the chains with an even number of spins, the intermediate “bow-tie” phase with linearly modulated AF order exists between the AF and ferromagnetic phases at J ₁ < H < H _c . Its origin can be traced to the infinite correlation length of the degenerate AF phase from which it emerges. This implies the existence of similar inhomogeneous phases with size- and form-dependent order in a number of other systems with infinite correlation length. The possibility to observe the signs of the “bow-tie” phase in low-T neutron diffraction experiments is discussed.     

On the intercalation and deintercalation mechanisms for ammoniated titanium disulfide

The redox mechanism associated with ammonia intercalation of TiS₂ has been clearly demonstrated, with essentially the only reaction products being (NH₄⁺)_y′(NH₃)_y″TiS₂^y′- and N₂, (NH₄⁺)_y′(NH₃) _y′(NiS₂^y′- undergoes thermal deintercalation by the sequential removal of NH₃ and “NH₄⁺” at progressively higher temperatures. Only small amounts of polysulfides and H₂S were observed during intercalation and deintercalation, respectively, indicating the near quantitative nature of the above mechanisms.     

Indirect exciton dispersion in III–V semiconductors: “Camel's back” in GaP

A new perturbation approach to exciton dispersion in indirect gap semiconductors is developed. For GaP and AlSb existence of the “camel's back” in exciton dispersion is confirmed, and a precise value of the “camel's back” parameter for X^c₁-minima in GaP is reported: E(X^c₁)?E_min(Δ^c₁)=3.5±0.3 meV. At the X-point the 21.44 and 19.48 meV exciton binding energies in GaP are obtained. The corresponding valley-anisotropy splitting is 1.96 meV.     

A new method for estimating the critical current density of a superconductor from its hysteresis loop

The critical current density J_c of some of the superconducting samples, calculated on the basis of the Bean’s model, shows negative curvature for low magnetic field with a downward bending near H = 0. To avoid this problem Kim’s expression of the critical current density, J_c = k/(H₀ + H), where J_c has positive curvature for all H, has been employed by connecting the positive constants k and H₀ with the features of the hysteresis loop of a superconductor. A relation between the full penetration field H_p and the magnetic field H_min, at which the magnetization is minimum, is obtained from the Kim’s theory. Taking the value of J_c at H = H_p according to the actual loop width, as in the Bean’s theory, and at H = 0 according to an enhanced loop width due to the local internal field, values of k and H₀ are obtained in terms of the magnetization values M⁺(?H_min), M^?(H_min), M⁺(H_p) and M^?(H_p). The resulting method of estimating J_c from the hysteresis loop turns out to be as simple as the Bean’s method.     

Anilinium Ions: Relations Between pK, σ and Intensity of the UV Transition

Spectroscopists have often assumed, based only on the UV spectrum of the anilinium ion (φNH₃ ⁺), that ammonium groups cannot bring a “mesomeric” effect upon π systems. This assumption^(1–3) which could be justified for the anilinium ion itself, whose OO band of the secondary transition (towards 260 nm) is very weak, has been unduly extended to all the ammonium groups. Actually, the interaction between a π system and (NX_aX_bX_c)⁺ groups has been studied by several authors^(4–8) and we have shown that contrary to what had been assumed by spectroscopists, such an interaction induces strong effects on the UV spectrum of the benzene chromophore^(9–11). Using the MNDO and the CNDO methods, we have studied the quantum factors which play a part in the long range interaction, between: an ω group X on the one hand, N on the other hand, and then φ, in φNH₂ ⁺CH₂X, φNH⁺ (CH₂X_a) CH₂X_b and φNH⁺ (C₂H₄)₂X.     

Brownian motion with restoring drift: The petit and micro-canonical ensembles

Letf(Q) be odd and positive near +∞. Then the non-linear wave equation ?² Q/?t ²??² Q/?x ²?f(Q)=0, considered on the circle 0≤x<L, can be written in Hamiltonian formQ ^⊙ =?H/?P, P ^⊙ =??H/?Q with $$P = Q^\cdot and H = \tfrac{1}{2}\mathop \smallint \limits_0^L (Q')^2 + \mathop \smallint \limits_0^L F(Q) + \tfrac{1}{2}\mathop \smallint \limits_0^L P^2 ;$$ the corresponding flow preserves the (suitably interpreted) “petit ensemble”e ^?H d ^∞ Qd ^∞ P; and forL↓∞,Q settles down to the stationary diffusion with infinitesimal operator 1/2 ?²/?Q ²+m(Q)?/?Q,m being the logarithmic derivative of the ground state of ?d ²/dQ ² ‖F(Q). This diffusion is the “Brownian motion with restoring drift”; see McKean-Vaninsky [1993(1)]. For reasons suggested by the paper of Lebowitz-Rose-Speer [1988] on NLS, it is interesting to study the “micro-canonical ensemble” obtained by restricting to the sphere $\int\limits_0^L {Q^2 } = N$ and makingL↓∞ with fixedD=N/L. Now, forF(Q)/Q ²→∞, the same type of diffusion appears, but with drift arising from the modified potentialF(Q)+cQ ²,c being chosen so that the mean ofQ ² is the assigned numberD. The proof employs Döblin's method of “loops” [1937] and steepest descent. The same is true forF(Q)=m ² Q ², only now the proof is elementary. The outcome is also the same ifF(Q)/Q ²→0, providedD is smaller than the petit canonical mean ofQ ²; forD larger than this mean, the matter is more subtle and the outcome is unknown.     

Isometric immersions of pseudo-Riemannian space forms

In this paper we study local isometric immersions f:M_sⁿ(K)→N_s+q²ⁿ⁻¹(c) of a time-like n-submanifold M_sⁿ(K) with constant sectional curvature K and index s into a pseudo-Riemannian space form N_s+q²ⁿ⁻¹(c) with constant sectional curvature c and index s+q, where q≥0, 1≤s≤n−1 and K≠c. We first prove the existence of Chebyshev coordinates of a time-like submanifold M_sⁿ(K) in certain conditions. Afterwards, we generalize the classical Bäcklund theorem for space-like (or time-like) submanifolds in N_n−1²ⁿ⁻¹(c) and N₁²ⁿ⁻¹(c). Finally as an application, in the Chebyshev coordinates, we use the Bäcklund theorem to give a Bäcklund transformation and a permutability formula between the generalized sine-Laplace equation and the generalized sinh-Laplace equation.     

Influence of the surface electric field in ion-beam-surface interaction at grazing incidence

We have measured the polarization of light emitted after ion surface scattering at small angle of incidence. The measurements are carried out with H⁺-, H ₂ ⁺ - and He⁺-ions under UHV-conditions with mono- and polycrystalline targets. We explain the typical variation of the polarization as “post collision Stark interaction” (PCSI) in the surface electric field, which can force transitions between nearly degenerate terms. The electric field is composed of two different contributions, a strong but short range surface field which is “seen” by atomsand ions and a long range but weak field due to the image charge which is “seen” to first orderonly by ions. The influence of the electric field on H-Balmer radiation is negligible at typical survival distances r_s≧0.35nm. But in contrast to H-atoms He⁺-ions feel the additional influence of the image field leading to a strong alteration of the polarization of the emitted light. The polarization of the Balmer-radiation stemming from Coulomb exploding H ₂ ⁺ -beams is observed to be modified by the electric field of the “spectator proton”.