Recovering Asymptotics of Short Range Potentials

Any compact smooth manifold with boundary admits a Riemann metric of the form near the boundary, where x is the boundary defining function and h' restricts to a Riemannian metric, h, on the boundary. Melrose has associated a scattering matrix to such a metric which was shown by he and Zworski to be a Fourier integral operator. It is shown here that the principal symbol of the difference of the scattering matrices for two potentials at fixed energy determines a weighted integral of the lead term of V ₁ - V ₂ over all geodesics on the boundary. This is used to prove that the entire Taylor series of the potential at the boundary is determined by the scattering matrix at a non-zero fixed energy for certain manifolds including Euclidean space. Received: 3 January 1997 / Accepted: 15 August 1997     

Conformal invariance in incommensurate phases

We study finite-size corrections to the free energy of free-fermion models on a torus with periodic, twisted, and fixed boundary conditions. Inside the critical (striped-incommensurate) phase, the free energy densityf(N, M) on anN×M square lattice with periodic (or twisted) boundary conditions scales asf(N, M)=f _–A(s)/(NM)+.... We derive exactly the finite-size-scaling (FSS) amplitudesA(s) as a function of the aspect ratios=M/N. These amplitudes are universal because they do not depend on details of the free-fermion Hamiltonian. We establish an equivalence between the FSS amplitudes of the free-fermion model and the Coulomb gas system with electric and magnetic defect lines. The twist angle generates magnetic defect lines, while electric defect lines are generated by competition between domain wall separation and system size. The FSS behavior of the free-fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec=l. For instance, the FSS amplitude on an infinite cylinder with fixed boundary conditions is found to be one-quarter of that with periodic boundary conditions. Finally, we conjecture the exact form of the FSS amplitudes for an interacting-fermion model on a torus. Numerical calculations employing the Bethe Ansatz confirm our conjecture in the infinite-cylinder limit.     

White light emitting from single phased K2Ca1−x−yP2O7: xEu, yMn phosphors under UV excitation

A single phased white light emitting phosphors K₂Ca_1−x−yP₂O₇: xEu²⁺, yMn²⁺ were synthesized by solid state reaction method. The Effective energy transfer occurs in this phosphor due to the large spectral overlap between the emission of Eu²⁺ and the excitation of Mn²⁺. The emission hue of K₂Ca_1−x−yP₂O₇: xEu²⁺, yMn²⁺ from blue to white light can be obtained by tuning the Eu²⁺/Mn²⁺ content ratio. The energy transfer mechanism from Eu²⁺ to Mn²⁺ in this phosphor was carefully investigated and demonstrated to be via the dipole–quadrupole interaction.     

Perturbation theory of polar hard Gaussian overlap fluid mixtures

A perturbation theory of polar hard Gaussian overlap fluid mixture is discussed. Explicit analytic expressions for the second and third varial coefficients are given. Numerical results are estimated for the thermodynamic properties of quadrupolar hard Gaussian overlap fluid and fluid mixture. It is found that the excess free energy and internal energy depend on concentrationsc ₁,c ₂, molecular diameter ratioR, shape parameterK and the quadrupole momentsQ*₁,Q*₂.     

Phase shift analysis of the <Superscript>6</Superscript>He+<Superscript>208</Superscript>Pb and the <Superscript>6</Superscript>He+<Superscript>197</Superscript>Au systems

We present the elastic scattering of the ⁶He+²⁰⁸Pb and the ⁶He+¹⁹⁷Au systems at the laboratory energy of E _lab=27 MeV within the framework of the McIntyre parametrization, and systematically investigate χ ²/N analysis of both systems to obtain an excellent agreement between the theoretical results and the experimental data. We find large diffusivity parameters indicating long range absorption mechanisms. We also show that both systems lack both the nuclear and the Coulomb rainbow scattering for obtained S-matrix parameters.     

Efficient approach to metal/metal oxide interfaces within variable charge model

A modified procedure of calculating the energy of metal/oxide interfaces and surfaces in the frame of the CTIP + EAM model (charge transfer ionic potential + embedded atom method) has been developed. According to the proposed approach, local charges and positions of atoms are determined only in a restricted zone surrounding the interface, while in the remaining region they are fixed. As a result, the number of variables undergoes a significant reduction, which enables carrying out efficient calculations for metal/oxide systems. The modified procedure has been applied to studying the relaxation of the α-Al₂O₃ surface. Using three different forms of the CTIP + EAM model present in literature, it has been shown that the correctness of the obtained results is conditioned by the appropriate relation between the CTIP and EAM components. Finally, the relaxation of the Ni/α-Al₂O₃ interface has been examined.     

Numerical results for ground states of spin glasses on Bethe lattices

The average ground state energy and entropy for ±J spin glasses on Bethe lattices of connectivities k + 1 = 3..., 26 at T = 0 are approximated numerically. To obtain sufficient accuracy for large system sizes (up to n = 2¹²), the Extremal Optimization heuristic is employed which provides high-quality results not only for the ground state energies per spin e_k+1 but also for their entropies s_k+1. The results indicate sizable differences between lattices of even and odd connectivities. The extrapolated ground state energies compare very well with recent one-step replica symmetry breaking calculations. These energies can be scaled for all even connectivities k + 1 to within a fraction of a percent onto a simple functional form, e _{k + 1} = E _SK - (2E _SK + )/, where E _SK = - 0.7633 is the ground state energy for the broken replica symmetry in the Sherrington-Kirkpatrick model. But this form is in conflict with perturbative calculations at large k + 1, which do not distinguish between even and odd connectivities. We also find non-zero entropies per spin s_k+1 at small connectivities. While s_k+1 seems to vanish asymptotically with 1/(k + 1) for even connectivities, it is numerically indistinguishable from zero already for odd k + 1 ≥ 9. Received 9 August 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: sboettc@emory.edu www.physics.emory.edu/faculty/boettcher     

Computing activation energies of non-thermal reactions

The chemistry in bulk gases involves reactions of nascent radicals that are almost invariably non-thermal. The energy requirements of reactions involving radicals depend on the reactions that produce them and the intra- and inter-molecular energy transfer they may undergo. Here, we extend the generalised Tolman activation energy (GTEa) method to non-thermal reactions in molecular dynamics (MD) simulations. We compute the energy requirements, which we refer to as chemical-activation energies (CE _a), of reactions of radicals formed by the decomposition of hydrogen peroxide. The equipartition theorem is adapted to compute average energies of small isolated systems with internal degrees of freedom in MD simulations with periodic boundary conditions, which is necessary for application of the GTEa method to non-thermal reactions. To illustrate the applicability of the GTEa method to non-thermal reactions, we present CE _a results for H₂O₂?+?OH → H₂O?+?HO₂, a key reaction in hydrogen combustion, as described by the ReaxFF force field. The OH radicals are the products of the self-dissociation of H₂O₂ and subsequent reactions. We define the chemical-activation energy for a back reaction (BCE _a) as the difference between the energy of the products and the average energy of the system. We show that the BCE _a and CEa are linearly correlated.     

Differential real-space renormalization of thed-Dimensional Gaussian model

With the aid of the differential real-space method we derive exact renormalization group (RG) equations for the Gaussian model ind dimensions. The equations involved + 1 spatially dependent nearest-neighbor interactions. We locate a critical fixed point and obtain the exact thermal critical indexy _T = 2. A special trajectory of the full nonlinear RG transformation is found and the free energy of the corresponding initial state calculated.Supported by Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 130 Ferroelektrika.     

Profiling the binding motif between Be and Mg in the ground state via a single-reference coupled cluster method

We present a study on the performance of our iterative triples correction for the coupled cluster singles and doubles excitations (CCSDT-1a+d) method for computation of potential energy surface (PES), spectroscopic constants, and vibrational spectrum for the ground state (X¹Σ⁺) BeMg, where the ostensible inadequacy of the CCSD and CCSD(T) methods is quite expected. We compare our results with those obtained using state-of-the-art multireference configuration interaction (MRCI) investigations reported earlier by Kerkines and Nicolaides. Our estimated dissociation energy (417.37 cm^?1), equilibrium distance (3.285 Å), and vibrational frequency (82.32 cm^?1) are in good agreement with recent results of advanced MRCI calculations for X¹Σ⁺ BeMg PES, which exhibits a shallow well of 469.4 cm^?1 with a minimum at 3.241 Å and a harmonic vibrational frequency of 85.7 cm^?1. Very weakly bound nature of X¹Σ⁺ BeMg is clearly reflected from these values. In accord with MRCI studies, a comparison of BeMg with iso-valence weakly bound ground-state species, Be₂ and Mg₂, suggests that its characteristics do not exhibit any resemblance to Be₂ rather, it shows a close kinship to Mg₂. The agreement of our derived vibrational levels with those obtained via the high-level MRCI calculations is very encouraging reflecting the potential of the suitably modified single-reference coupled cluster (SRCC) method, CCSDT-1a+d as a tool for the study of multireference van der Waals systems.     

Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature

We study the effect of an external field on (1 + 1) and (2 + 1) dimensional elastic manifolds, at zero temperature and with random bond disorder. Due to the glassy energy landscape the configuration of a manifold changes often in abrupt, “first order”-type of large jumps when the field is applied. First the scaling behavior of the energy gap between the global energy minimum and the next lowest minimum of the manifold is considered, by employing exact ground state calculations and an extreme statistics argument. The scaling has a logarithmic prefactor originating from the number of the minima in the landscape, and reads ΔE ₁∼L ^θ[ln(L _z L ^{- ζ})]^-1/2, where ζ is the roughness exponent and θ is the energy fluctuation exponent of the manifold, L is the linear size of the manifold, and L_z is the system height. The gap scaling is extended to the case of a finite external field and yields for the susceptibility of the manifolds ∼L ^{2D + 1 - θ}[(1 - ζ)ln(L)]^1/2. We also present a mean field argument for the finite size scaling of the first jump field, h ₁∼L ^{d - θ}. The implications to wetting in random systems, to finite-temperature behavior and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are discussed. Received December 2000 and Received in final form April 2001     

Where do the H atoms reside in PdH x systems?

We present an ab initio density-functional theory study of PdH _x systems. We evaluated the total energy of PdH _x systems with the H atoms occupying interstitial (octahedral and tetrahedral) sites of a Pd supercell, allowing for the relaxation of the coordinates and supercell dimensions. The majority of our calculations were based on supercells consisting of four Pd atoms, and up to four H atoms, covering the range from x = 0.25 to x = 1. In addition some larger calculations are reported. In order to compare the relative stability of systems at different values of x (at fixed pressure and temperature T = P = 0), we computed the enthalpy of formation ΔH _f (x) of the (non)stoichiometric systems. In the regime x = 0 → 1, the ΔH _f (x) decrease in a manner indicative of the existence of attractive interactions between the dissolved H atoms. Ideal-solution theory cannot be applied to this system. Furthermore, we find that tetrahedral occupation is favoured over octahedral occupation at high x, leading to the formation of a zincblende structure at x = 1. A preliminary vibrational analysis of normal modes has been performed. Inclusion of vibrational zero-point energies in a harmonic approximation leads us to conclude, tentatively, that the observed stability of octahedral site occupation is due to more favourable zero-point energies of the H atoms in those sites. The results indicate that a proper understanding of this system must take into account the quantum nature of the dissolved hydrogen.     

On the layering transition of an SOS surface interacting with a wall. I. Equilibrium results

We consider the model of a 2D surface above a fixed wall and attracted toward it by means of a positive magnetic fieldh in the solid-on-solid (SOS) approximation when the inverse temperature is very large and the external fieldh is exponentially small in . We improve considerably previous results by Dinaburg and Mazel on the competition between the external field and the entropic repulsion with the wall, leading, in this case, to the phenomenon of layering phase transitions. In particular, we show, using the Pirogov-Sinai scheme as given by Zahradník, that there exists a unique critical valueh _k ^* () in the interval (1/4e ^–4k , 4e ^–4k ) such that, for allh(h _k+1 ^* ,h _k ^* ) and large enough, there exists a unique infinite-volume Gibbs state. The typical configurations are small perturbation of the ground state represented by a surface at heightk+1 above the wall. Moreover, for the same choice of the thermodynamic parameters, the influence of the boundary conditions of the Gibbs measure in a finite cube decays exponentially fast with the distance from the boundary. Whenh=h _k ^* () we prove instead the convergence of the cluster expansion for bothk andk+1 boundary conditions. This fact signals the presence of a phase transition. In the second paper of this series we will consider a Glauber dynamics for the above model and we will study the rate of approach to equilibrium in a large finite cube with arbitrary boundary conditions as a function of the external fieldh. Using the results proven in this paper, we will show that there is a dramatic slowing down in the approach to equilibrium when the magnetic field takes one of the critical values and the boundary conditions are free (absent).     

Effective mass theory of a two-dimensional quantum dot in the presence of magnetic field

The effective mass of electrons in low-dimensional semiconductors is position-dependent. The standard kinetic energy operator of quantum mechanics for this position-dependent mass is non-Hermitian and needs to be modified. This is achieved by imposing the BenDaniel-Duke (BDD) boundary condition. We have investigated the role of this boundary condition for semiconductor quantum dots (QDs) in one, two and three dimensions. In these systems the effective mass m _i inside the dot of size R is different from the mass m _o outside. Hence a crucial factor in determining the electronic spectrum is the mass discontinuity factor β = m _i/m _o. We have proposed a novel quantum scale, σ, which is a dimensionless parameter proportional to β ² R ² V ₀, where V ₀ represents the barrier height. We show both by numerical calculations and asymptotic analysis that the ground state energy and the surface charge density, (ρ(R)), can be large and dependent on σ. We also show that the dependence of the ground state energy on the size of the dot is infraquadratic. We also study the system in the presence of magnetic field B. The BDD condition introduces a magnetic length-dependent term (√ħ//eB) into σ and hence the ground state energy. We demonstrate that the significance of BDD condition is pronounced at large R and large magnetic fields. In many cases the results using the BDD condition is significantly different from the non-Hermitian treatment of the problem.     

Path integral approach for superintegrable potentials on spaces of non-constant curvature: II. Darboux spaces <Emphasis Type="Italic">D</Emphasis><Subscript>III</Subscript> and <Emphasis Type="Italic">D</Emphasis><Subscript>IV</Subscript>

This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze five and four superintegrable potentials in the spaces D _III and D _IV, respectively; these potentials were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green’s functions, the discrete and continuous wavefunctions, and the discrete energy spectra. In some cases, however, the discrete spectrum cannot be stated explicitly because it is determined by a higher-order polynomial equation. We also show that the free motion in a Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We can state the corresponding energy spectrum and the wavefunctions. The text was submitted by the authors in English.     

On the Initial Boundary Value Problems for the Enskog Equation in Irregular Domains

The paper is concerned with the Enskog equation with a constant high density factor for large initial data in L ¹(R ⁿ). The initial boundary value problem is investigated for bounded domains with irregular boundaries. The proof of an H-theorem for the case of general domains and boundary conditions is given. The main result guarantees the existence of global solutions of boundary value problems for large initial data with all v-moments initially finite and domains having boundary with finite Hausdorff measure and satisfying a cone condition. Existence and uniqueness are first proved for the case of bounded velocities. The solution has finite norm where q = (t ₀, x) is taken on all possible n-dimensional planes Q(v) in R ^n+l intersecting a fixed point and orthogonal to vectors (1, v), v R ⁿ.     

Orthogonality theorem for a one-dimensional-electron gas with a bounded spectrum

The overlap between the ground-state wave functions of a one-dimensional electron gas with the Hamiltonians Ĥ ₀ and , where is the impurity potential, is calculated. It is shown that in the limit of an infinite potential the overlap vanishes as M ^−1/8 as M→∞, where M is the number of filled levels, while in the case of a weak potential this overlap differs little from 1. A relation is found between the magnitude of the overlap and the behavior of the density of states near the Fermi energy (statistics of the levels). The possibility of linearization of the spectrum and the possibility of performing a bosonization procedure are discussed in light of the results obtained. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 57–60 (10 July 1996)     

Hearing the zero locus of a magnetic field

We investigate the ground state of a two-dimensional quantum particle in a magnetic field where the field vanishes nondegenerately along a closed curve. We show that the ground state concentrates on this curve ase/h tends to infinity, wheree is the charge, and that the ground state energy grows like (e/h)^2/3. These statements are true for any energy level, the level being fixed as the charge tends to infinity. If the magnitude of the gradient of the magnetic field is a constantb ₀ along its zero locus, then we get the precise asymptotics(e/h) ^2/3 (b ₀) ^2/3 E _* +O(1) for every energy level. The constantE _* .5698 is the infimum of the ground state energiesE() of the anharmonic oscillator family .     

On the layering transition of an SOS surface interacting with a wall. II. The Glauber dynamics

We continue our study of the statistical mechanics of a 2D surface above a fixed wall and attracted towards it by means of a very weak positive magnetic fieldh in the solid on solid (SOS) approximation, when the inverse temperature is very large. In particular we consider a Glauber dynamics for the above model and study the rate of approach to equilibrium in a large cube with arbitrary boundary conditions. Using the results proved in the first paper of this series we show that for allh(h _k+1 ^* ,h _k ^* ) ({h _k ^* } being the critical values of the magnetic field found in the previous paper) the gap in the spectrum of the generator of the dynamics is bounded away from zero uniformly in the size of the box and in the boundary conditions. On the contrary, forh=h _k ^* and free boundary conditions, we show that the gap in a cube of sideL is bounded from above and from below by a negative exponential ofL. Our results provide a strong indication that, contrary to what happens in two dimensions, for the three dimensional dynamical Ising model in a finite cube at low temperature and very small positive external field, with boundary conditions that are opposite to the field on one face of the cube and are absent (free) on the remaining faces, the rate of exponential convergence to equilibrium, which is positive in infinite volume, may go to zero exponentially fast in the side of the cube.Work partially supported by grant SC1-CT91-0695 of the Commission of European Communities.