Capacitance fluctuations in quantum dots

We discuss fluctuations of the charging energy E_C and gate voltage spacings between Coulomb oscillation conductance peaks, as computed within spin density functional theory for a realistic GaAs–AlGaAs dot. We explicitly exhibit the fluctuations in the portion of the total free energy which incorporate the interaction between the dot and its surroundings. These variations in the dot capacitance show a dispersion which is typically greater than the dispersion of the total dot charging energy.     

Level statistics of near-yrast states in rapidly rotating nuclei

The nearest neighbour level spacing distribution and the Δ₃ statistic of level fluctuations associated with very high spin states (I ≳ 30) in rare-earth deformed nuclei are analysed by means of a cranked shell model. The many particle-many hole configurations created in the rotating Nilsson potential are mixed by the surface-delta two-body residual interaction. The levels in the near-yrast region show a Poisson-like level spacing distribution. As the intrinsic excitation energy U increases, the level statistics shows a gradual transition from order to chaos, reaching at U ≳ 2 MeV the Wigner distribution typical-of the Gaussian orthogonal ensemble of random matrices. This transition is caused by the residual two-body interaction. On the other hand, the level spacings between the yrast and the first excited state show a peculiar behaviour, displaying a Wigner-like distribution instead of the Poisson-like distribution seen for the other near-yrast rotational states. The lowest spacings reflect the properties of the single-particle orbits in the mean-field, and are only weakly affected by the residual two-body interaction.     

Double donor in a spherical quantum dot

We present a variational calculation for the ground state of the double donor in a spherical GaAs–Ga_1–x Al _x As quantum dot. The binding energies for the ionized and neutral centres are calculated for several barrier height values as a function of the radius of the dot. Compared with a square well structure, there is a stronger confinement and a larger binding energy for the double donors in a spherical quantum dot.     

The Ising Model on a Quenched Ensemble of c=−5 Gravity Graphs

We study with Monte Carlo methods an ensemble of c=–5 gravity graphs, generated by coupling a conformal field theory with central charge c=–5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent _s and the intrinsic fractal dimension d _H. We find _s=–1.5(1) and d _H=3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=–5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, with a total central charge of the matter sector c=–5.     

Neutron resonances in 185Re and 187Re

In a search for intermediate structure, neutron time-of-flight spectra corresponding to 1 and 4 MeV capture γ-ray thresholds were measured for the target isotopes ^{185, 187}Re. The data were analyzed from the point of view of level spacings as well as intermediate structure. A method was developed for estimating the neutron widths of the resonances even in those cases where the neutron widths are comparable to the γ-widths. On the basis of this analysis it was decided which resonances were most likely to be due to p-wave capture. While some unusual behavior was observed, there is no conclusive evidence for intermediate structure. The statistics of level spacings agree with the long range ordering described in the theory of Dyson and Mehta, and are inconsistent with an uncorrelated Wigner distribution. Energies, estimated neutron widths and p-wave probabilities (if over 10 %) for 488 resonances in ¹⁸⁵Re and 335 resonances in ¹⁸⁷Re are tabulated for the energy range 24 eV to 2 keV.     

The Stochastic Traveling Salesman Problem: Finite Size Scaling and the Cavity Prediction

We study the random link traveling salesman problem, where lengths l _ij between city i and city j are taken to be independent, identically distributed random variables. We discuss a theoretical approach, the cavity method, that has been proposed for finding the optimum tour length over this random ensemble, given the assumption of replica symmetry. Using finite size scaling and a renormalized model, we test the cavity predictions against the results of simulations, and find excellent agreement over a range of distributions. We thus provide numerical evidence that the replica symmetric solution to this problem is the correct one. Finally, we note a surprising result concerning the distribution of k th-nearest neighbor links in optimal tours, and invite a theoretical understanding of this phenomenon.     

Statistical tests applied to proton resonances in57Co

Statistical tests are applied to a sequence of 1/2⁺ resonances observed in⁵⁶Fe(p,p) and the results are compared with predictions of the random matrix model. The target nucleus and proton energy were chosen to yield favorable level densities, strength functions, and Coulomb penetrabilities. In addition, the TUNL high resolution system provides excellent sensitivity to small resonances. These points combine to yield a fairly pure and complete sequence, as indicated by the DysonF statistic and the Dyson-MehtaΔ ₃ statistic. Good agreement is found with the orthogonal ensemble predictions for the long and short range spacing correlations, and for the widths of thek-th nearest neighbor spacing distributions fork=0 to 10.

     

A symmetry relating certain processes in 2-and 4-dimensional space-times and the value α0 = 1/4π of the bare fine structure constant

The symmetry manifests itself in exact relations between the Bogoliubov coefficients for processes induced by an accelerated point mirror in 1 + 1 dimensional space and the current (charge) densities for the processes caused by an accelerated point charge in 3 + 1 dimensional space. The spectra of pairs of Bose (Fermi) massless quanta emitted by the mirror coincide with the spectra of photons (scalar quanta) emitted by the electric (scalar) charge up to the factor e ²/ħc. The integral relation between the propagator of a pair of oppositely directed massless particles in 1 + 1 dimensional space and the propagator of a single particle in 3 + 1 dimensional space leads to the equality of the vacuum-vacuum amplitudes for the charge and the mirror if the mean number of created particles is small and the charge e = √ħc. Due to the symmetry, the mass shifts of electric and scalar charges (the sources of Bose fields with spin 1 and 0 in 3 + 1 dimensional space) for the trajectories with a subluminal relative velocity β₁₂ of the ends and the maximum proper acceleration w ₀ are expressed in terms of the heat capacity (or energy) spectral densities of Bose and Fermi gases of massless particles with the temperature w ₀/2π in 1 + 1 dimensional space. Thus, the acceleration excites 1-dimensional oscillation in the proper field of a charge, and the energy of oscillation is partly deexcited in the form of real quanta and partly remains in the field. As a result, the mass shift of an accelerated electric charge is nonzero and negative, while that of a scalar charge is zero. The symmetry is extended to the mirror and charge interactions with the fields carrying spacelike momenta and defining the Bogoliubov coefficients α^B,F. The traces trα^B,F, which describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector, were found in analytic form for two mirror trajectories with subluminal velocities of the ends. The symmetry predicts one and the same value e ₀ = √ħc for the electric and scalar charges in 3 + 1 dimensional space. Arguments are adduced in favor of the conclusion that this value and the corresponding value α₀ = 1/4π of the fine structure constant are the bare, nonrenormalized values. The text was submitted by the author in English.     

Fine structure of excitons in self-assembled In0.60Ga0.40As quantum dots: Zeeman-interaction and exchange energy enhancement

The fine structure of the ground state exciton has been studied by magnetophotoluminescence spectroscopy of self-assembled In_0.60Ga_0.40As single quantum dots. This was realized by using lithography for fabricating mesa structures which contain only a single dot. Due to a dot geometry-induced symmetry breaking we are able to observe the dark exciton states in magnetic field besides the bright excitons. From the spin-splitting data values for the corresponding exciton g-factors are obtained. In addition, the electron–hole exchange energies are determined, which are compared to detailed numerical calculations.     

Systematic treatment of the anderson localization on the basis of the projection operator formalism

A derivation within the projection operator technique is given for the density and current response functions of a system of independent particles moving in a random potential. The essential point is the derivation of kinetic equations for the current relaxation kernel instead of for the density propagator as in a previous treatment on the basis of the projection operator formalism. In these equations the divergent contributions from the 2k _F -scattering mechanism can be systematically separated from those of diffusional scattering. Especially, both the self-consistent current relaxation theory, developed by Götze and the self-consistent treatment of Vollhardt and Wölfle are rederived from simple approximations of the kinetic equations. The outlined method represents a systematic approach to the Anderson localization. It may be applicable also to more realistic models for the Anderson localization as well as extended to the evaluation of general transport coefficients on a level far beyond the usual perturbation theories.     

Electric-field gradients at Ta donor impurities in Cr2O3(Ta) semiconductor

We report perturbed-angular-correlation (PAC) experiments on ¹⁸¹Hf(→¹⁸¹Ta)-implanted corundum Cr₂O₃ powder samples in order to determine the magnitude and symmetry of the electric-field gradient (EFG) tensor at Ta donor impurity sites of this semiconductor. These results are analyzed in the framework of ab initio full-potential augmented-plane wave plus local orbitals (FP−APW+lo) calculations. The results are also compared with EFG results coming from PAC experiments in isomorphous α-Al₂O₃ and α-Fe₂O₃ doped with ¹¹¹In→¹¹¹Cd and ¹⁸¹Hf→¹⁸¹Ta tracers. This combined analysis enables us to quantify the magnitude of the lattice relaxations induced by the presence of the impurity and to determine the charge state of the impurity donor level introduced by Ta in the band gap of the semiconductor.     

Exact Wigner Surmise Type Evaluation of the Spacing Distribution in the Bulk of the Scaled Random Matrix Ensembles

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices, respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form a(s)e^–b(s) for a simply related to a Painlevé transcendent and b its anti-derivative. A formula consisting of the sum of two such terms is given for the symplectic case (Hermitian matrices with real quaternion elements).     

NH3 self-broadening coefficients in the ν2 and ν4 bands and line intensities in the ν2 band

Self-broadening coefficients of NH₃ in the ν₂ and ν₄ bands and absolute line intensities in the ν₂ band have been measured at room temperature for some selected lines in the P- and R-branches. Using a Fourier transform spectrometer, line intensities and collisional widths were obtained by fitting Voigt profiles to the measured shapes of the lines. The results of self-broadening coefficients are in reasonable agreement with calculated linewidths using a semiclassical model which reproduce rather well the systematic experimental J and K quantum numbers dependencies. Satisfactory agreement was also obtained for line intensities with previous measurements in the ν₂ band. From the intensity measurements, we have determined effective transition dipole moments as well as Herman–Wallis parameters for the ν₂ band.     

Spin glass and ferromagnetism in Kondo lattice compounds

The Kondo lattice model has been analyzed in the presence of a random inter-site interaction among localized spins with non zero mean J₀ and standard deviation J. Following the same framework previously introduced by us, the problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields. The static approximation and the replica symmetry ansatz have allowed us to solve the problem at a mean field level. The resulting phase diagram displays several phase transitions among a ferromagnetically ordered region,a spin glass one, a mixed phase and a Kondo state depending on J₀, J and its relation with the Kondo interaction coupling J_K. These results could be used to address part of the experimental data for the CeNi _{1 - x} Cu _x compound, when x ⩽ 0.8. Received 24 June 2002 Published online 31 December 2002     

Band model analysis of the H2O2ν6(b) band

A Mayer-Goody random band model with a Voigt line profile is used to derive interval absorption coefficients, mean line spacings, and pressure-broadening coefficients for the ν₆(b) H₂O₂ band centered at 1265 cm^?1 at 285°K.     

Electronic structure calculation of CuMn alloy

We have used a fully self-consistent multiple scatteringX _α method within the local density formalism to study the charge distribution, bonding characteristics and the density of states in CuMn alloy. The charge distribution shows almost no ionic character but significant hybridization ofs andd states is observed near the Fermi level. The crystal field splittings, ionization energies and the excitation energies are calculated and compared with experiments wherever available.     

Eigenvalues and eigenfunctions of a clover plate

We report a numerical study of the flexural modes of a plate using semi-classical analysis developed in the context of quantum systems. We first introduce the Clover billiard as a paradigm for a system inside which rays exhibit stable and chaotic trajectories. The resulting phase space explored by the ray trajectories is illustrated using the Poincare surface of section, and shows that it has both integrable and chaotic regions. Examples of the stable and the unstable periodic orbits in the geometry are presented. We numerically solve the biharmonic equation for the flexural vibrations of the Clover shaped plate with clamped boundary conditions. The first few hundred eigenvalues and the eigenfunctions are obtained using a boundary elements method. The Fourier transform of the eigenvalues show strong peaks which correspond to ray periodic orbits. However, the peaks corresponding to the shortest stable periodic orbits are not stronger than the peaks associated with unstable periodic orbits. We also perform statistics on the obtained eigenvalues and the eigenfunctions. The eigenvalue spacing distribution P(s) shows a strong peak and therefore deviates from both the Poisson and the Wigner distribution of random matrix theory at small spacings because of the C_4v symmetry of the Clover geometry. The density distribution of the eigenfunctions is observed to agree with the Porter-Thomas distribution of random matrix theory. Received 12 February 2001 and Received in final form 17 April 2001     

On the basic properties of the A = 48 isobars

Binding energies of the A = 48 isobars and their charge radii are defined on the basis of self-consistent calculations and using the concept of isobaric symmetry in nuclei. The text was submitted by the authors in English.