Long-Range Orders in Models of Itinerant Electrons Interacting with Heavy Quantum Fields

The Falicov–Kimball model consists of itinerant lattice fermions interacting with Ising spins by an on-site potential of strength U. Kennedy and Lieb proved that at half filling there is a low temperature phase with chessboard long range order on ^d , d2, for all non-zero values of U. Here we investigate the stability of this phase when small quantum fluctuations of the Ising spins are introduced in two different ways. The first one corresponds to replace the classical spins by quantum two level systems attached to each site of the lattice. In the second one we interpret the spins as occupation numbers of localized f-electrons or heavy ions which have a small kinetic energy. This leads to the so-called asymmetric Hubbard model. For both models we prove that for all non-zero values of U the long range order of the original Falicov–Kimball model remains stable if the additional quantum fluctuations are small enough. This result is proved by non-perturbative methods based on a chessboard estimate and the principle of exponential localisation. In order to derive the chessboard estimate the phase factors in the kinetic energy of fermions must have a flux equal to . We also investigate the models where the fermions are replaced by hard-core bosons and prove the same result for large U. For hard core bosons the kinetic term is the conventional one with zero phase factors. For small U and hard-core bosons we find that there is an off-diagonal long range order for low enough temperature and any strength of the additional quantum fluctuations. Open problems are discussed.     

Hartree–Fock versus quantum Monte Carlo study of persistent current in a one-dimensional ring with single scatterer

We calculate the persistent current of interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We use the self-consistent Hartree–Fock method and the quantum Monte Carlo method which gives fully correlated solutions. Our Hartree–Fock method treats the non-local Fock term in a local approximation and also exactly (if the ring is not too large). Treating the Fock term exactly we attempt to support our previous Hartree–Fock result obtained in the local approximation, in particular the persistent current behaving like I∝L^-1-α, where L is the ring length and α>0 is the power depending only on the electron–electron interaction. Finally, we use the Hartree–Fock solutions as an input for our quantum Monte Carlo calculation. The Monte Carlo results exhibit only small quantitative differences from the Hartree–Fock results.     

Phase transition of directed polymer in random potentials on 4+1 dimensions

Finite-temperature-directed polymer in random potentials is described by a transfer matrix method. On 4+1 dimensions, the evidence for a finite-temperature phase transition is found at T_c≈0.18, where the free energy fluctuation grows logarithmically as a function of time t. When TT_c, the fluctuation of the free energy grows as t^ω with ω≈0.156. The phase transition of the restricted solid-on-solid model, which is closely related to the directed polymer problem through the Kardar–Parisi–Zhang equation, is also discussed.     

Boundary G/G Theory and Topological Poisson–Lie Sigma Model

We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G ^* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky.     

Ion beam mixing and sputtering of Kr-irradiated TiN films measured with RBS,RNRA, and PIXE

Thin titanium nitride films of 10–300 nm thickness were irradiated with ⁸⁴Kr ions of 80–700 keV energy and fluences ranging from 10¹⁶ cm² to 2×10¹⁷ cm². Sputter yields (Y=0.4–1.0) and mixing rates (k=0.05–0.5 nm⁴) were determined using the depth profiling methods RBS, RNRA, and PIXE. While the sputter yields agree well with the modified Sigmund theory, the energy dependence of the mixing rates cannot be explained by standard models.     

On Quantum Phase Transition. I. Spinless Electrons Strongly Correlated with Ions

We study a large class F of models of the quantum statistical mechanics dealing with two types of particles. First the spinless electrons are quantum particles obeying to the Fermi statistics, they can hop. Secondly the ions which cannot move, are classical particles. The Falicov–Kimball (FK) model⁽¹⁾ is a well known model belonging to F, for which the existence of an antiferomagnetic phase transition was proven in the seminal paper of Kennedy and Lieb.⁽²⁾ This result was extended by Lebowitz and Macris.⁽³⁾ A new approach to this problem based on quantum selection of the ground states was proposed in ref. 4. In this paper we extend this approach to show that, under the strong insulating condition, any hamiltonian of the class F admits, at every temperature, an effective hamiltonian, which governs the behaviour of the ions interacting through forces mediated by the electrons. The effective hamiltonians are long range many body Ising hamiltonians, which can be computed by a cluster expansion expressed in term of the quantum fluctuations. Our main result is that we can apply the powerfull results of the classical statistical mechanics to our quantum models. In particular we can use the classical Pirogov–Sinai theory to establish a hierarchy of phase diagrams, we can also study of the behaviour of the quantum inter- faces,⁽²⁹⁾ and so on...     

An extension of the Borel-Weil construction to the quantum groupU q (n)

The Borel-Weil (BW) construction for unitary irreps of a compact Lie group is extended to a construction of all unitary irreps of the quantum groupU _q(n). Thisq-BW construction uses a recursion procedure forU _q(n) in which the fiber of the bundle carries an irrep ofU _q(n–1)×U _q(1) with sections that are holomorphic functions in the homogeneous spaceU _q(n)/U _q(n–1)×U _q(1). Explicit results are obtained for theU _q(n) irreps and for the related isomorphism of quantum group algebras.Supported in part by the National Science Foundation, No. PHY-9008007     

Diffusion of silicon in titanium nitride films. Efficiency of TiN barrier layers

Two kinds of reactively evaporated titanium nitride films with columnar (B ₀ films) and fine-grained film structure (B ₊ films) have been examined as diffusion barriers, preventing the silicon diffusion in silicon devices. The silicon diffusion profiles have been investigated by 2 MeV ⁴He⁺ Rutherford backscattering spectrometry (RBS) after annealing at temperatures up to 900° C, in view of application of high-temperature processes. The diffusivity from 400 to 900° C: D (m² s^–1)=2.5×10^–18 exp[–31 kJ/mol/(RT)] in B ₀ layers and D (m² s^–1)=3×10^–19 exp[–26 kJ/mol/(RT) in B ₊ TiN layers. The diffusivities determined correspond to grain boundary diffusion, the difference being due to the different microstructure. The very low diffusivity of silicon in B ₊ TiN layer makes it an excellent high-temperature barrier preventing silicon diffusion.     

The factor of nonparaxial Hermite–Gaussian beams and related problems

On the basis of the second-order moment of the power density and in the use of the series expansion, the expressions for the beam width, far-field divergence angle and M² factor of nonparaxial Hermite–Gaussian (H–G) beams are derived and expressed in a sum of the series of the Gamma function. The theoretical results are illustrated with numerical examples. The M² factor of nonparaxial H–G beams depends not only on the beam order m, but also on the waist-width to wavelength ratio w₀/λ. The far-field divergence angles of nonparaxial H–G beams with even and odd orders approach their upper limits θ_max=63.435 and 73.898, respectively, which results in M²<1 as w₀/λ→0. For the special case of m=0 our results reduce to those of nonparaxial Gaussian beams. Some problems related to the characterization of the nonparaxial beam quality are also discussed.     

A Study of Dipolar Interactions and Dynamic Processes of Water Molecules in Tendon byH andH Homonuclear and Heteronuclear Multiple-Quantum-Filtered NMR Spectroscopy

The effect of proton exchange on the measurement of¹H–¹H,¹H–²H, and²H–²H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the¹H–¹H and¹H–²H residual dipolar interactions and the proton exchange rate at a temperature of 24°C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24°C were 300 and 50 Hz and 3000 s⁻¹, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5°C, where the spectra of the H₂O molecules were well resolved, so that the¹H–¹H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5°C, where the proton exchange was in the intermediate regime for the¹H–²H dipolar interaction, confirmed the result obtained at 24°C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T₂) depend on the orientation as the square of the second-rank Legendre polynomial.     

Superconductivity as a Kosterlitz–Thouless transition in the two-dimensional Hubbard model

We investigate a superconducting Kosterlitz–Thouless transition in the two-dimensional (2D) Hubbard model using auxiliary quantum Monte Carlo method for the ground state. The pair susceptibility is computed for both the attractive and repulsive Hubbard model. The numerical results show that the s-wave pair susceptibility scales as χ  L² for the attractive case, in agreement with previous quantum Monte Carlo studies. The scaling χ  L² also holds for the d-wave pair susceptibility for the repulsive Hubbard model if we adjust the band parameter t′.     

The Constants in the Central Limit Theorem for the One-Dimensional Edwards Model

The Edwards model in one dimension is a transformed path measure for one-dimensional Brownian motion discouraging self-intersections. We study the constants appearing in the central limit theorem (CLT) for the endpoint of the path (which represent the mean and the variance) and the exponential rate of the normalizing constant. The same constants appear in the weak-interaction limit of the one-dimensional Domb–Joyce model. The Domb–Joyce model is the discrete analogue of the Edwards model based on simple random walk, where each self-intersection of the random walk path recieves a penalty e ^–2. We prove that the variance is strictly smaller than 1, which shows that the weak interaction limits of the variances in both CLTs are singular. The proofs are based on bounds for the eigenvalues of a certain one-parameter family of Sturm–Liouville differential operators, obtained by using monotonicity of the zeros of the eigen-functions in combination with computer plots.     

Far-infrared giant dipole resonances in neutral quantum dots

A resonance behaviour of the far-infrared absorption probability at a frequency N^1/4 is predicted for clusters of N electron–hole pairs (2N110) confined in disk-shaped quantum dots. For radially symmetric dots, the absorption is dominated by a giant dipole resonance, which accounts for more than 98% of the energy-weighted photoabsorption sum rule.     

TIGHT MACH-STYLE CONNECTION BETWEEN THE EINSTEIN MASS-ENERGY AND INERTIA-GRAVITY EQUIVALANCES. REMARKS ON A RECENT EXPERIMENT BY MIKHAILOV

Equivalence of the two famous Einstein equivalences is, U denoting the cosmological potential, expressed à la Mach as U=c ². The electrostatic analog is induction of an extra mass –c ^–2eV (esu) in an electron immersed in the constant Coulomb potential c=Q/R enclosed in a charged sphere. This effect has been evidenced in a recent experiment by Mikhailov.     

Effect of localized spins in coherent transport through quantum dots

The effect of localized spins on the quantum coherence in solids is discussed. A quantum dot with an odd number of electrons can be a model system for a localized spin. It is experimentally shown that a spin flip scattering by a quantum dot pulls the trigger of quantum decoherence. On the other hand, spin flip scattering is the basic process to construct the Kondo singlet state around a magnetic impurity. Through an interference effect of the Kondo state (the Fano–Kondo effect) in a side-coupled dot system, we show experimentally that the Kondo singlet state is quantum mechanically coherent. The analysis of the Fano–Kondo lineshape indicates the locking of the phase shift to π/2, which is in agreement with theoretical predictions. The Fano–Kondo effect is also observed in an Aharonov–Bohm ring, in which a quantum dot is embedded, and also indicates the phase shift locking to π/2.     

Electronic properties of a large quantum dot at a finite temperature

The physical properties of a two-dimensional parabolic quantum dot composed of large number of interacting electrons are numerically determined by the Thomas–Fermi (TF) method at a finite temperature. Analytical solutions are given for zero temperature for comparative purposes. The exact solution of the TF equation is obtained for the non-interacting system at finite temperatures. The effect of the number of particles and temperature on the properties are investigated both for interacting and non-interacting cases. The results indicate that the effect of e–e interaction on the density profile shows different temperature dependencies above and below a certain temperature T_c.     

Noncommutative theories, the axial anomaly, Fujikawa's method and the Atiyah–Singer index

Fujikawa's method is employed to compute at first order in the noncommutative parameter the U(1)_A anomaly for noncommutative SU(N). We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θ^μν, which is of “magnetic” type. Our results for SU(N) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.     

Generalized beam propagation factor of hard-edged circular apertured diffracted Bessel–Gaussian beams

Based on the truncated second-order moments method on the cylindrical coordinate systems and the incomplete gamma function, an analytical expression of the generalized beam propagation factor (M_G² factor) of hard-edged circular apertured diffracted Bessel–Gaussian beams is derived and illustrated numerically. It is shown that the M_G² factor of hard-edged diffracted BGBs mainly depends on the truncation parameter δ and the beam parameters m and η. The results can be reduced to that for the non-truncated Bessel–Gaussian beams case and that for the truncated fundamental Gaussian beams case under certain conditions, respectively. The power fraction is also discussed analytically and numerically.     

New Exact Ground States for One-Dimensional Quantum Many-Body Systems

We consider one-dimensional quantum many-body systems with pair interactions in external fields and (re)investigate the conditions under which exact ground-state wave functions of product type can be found. Contrary to a claim in the literature that an exhaustive list of such systems is already known, we show that this list can still be enlarged considerably. In particular, we are able to calculate exact ground-state wave functions for a class of quantum many-body systems with Ax ^–2+Bx ² interaction potentials and external potentials given by sixth-order polynomials.     

Consolidation of hydrogenation–disproportionation–desorption–recombination processed Nd–Fe–B magnets by spark plasma sintering

We have successfully consolidated hydrogenation–disproportionation–desorption–recombination (HDDR) processed Nd–Fe–Co–Zr–B–Ga powder by spark plasma sintering (SPS). The field compacted samples were sintered at different temperatures (T_S) from 550 to 600 °C with compressive pressure of 80 MPa for 20 min. Microstructural investigations by transmission electron microscopy indicated that the sintered specimen exhibits Nd₂Fe₁₄B grains of ~300 nm with Nd-rich grain boundary phase. The optimum magnetic properties of B_r: 1.22 T, H_c: 928 kA/m, _BH_c: 600 kA/m, (BH)_max: 210 kJ/m³ were obtained in the sample sintered at 550 °C. The strategy for further improving the coercivity and remanence is discussed based on the microstructure-property relationships.