Showing papers by "International School for Advanced Studies published in 1994"

Macroscopic polarization in crystalline dielectrics : the geometric phase approach

Abstract: The macroscopic electric polarization of a crystal is often defined as the dipole of a unit cell. In fact, such a dipole moment is ill defined, and the above definition is incorrect. Looking more closely, the quantity generally measured is differential polarization, defined with respect to a "reference state" of the same material. Such differential polarizations include either derivatives of the polarization (dielectric permittivity, Born effective charges, piezoelectricity, pyroelectricity) or finite differences (ferroelectricity). On the theoretical side, the differential concept is basic as well. Owing to continuity, a polarization difference is equivalent to a macroscopic current, which is directly accessible to the theory as a bulk property. Polarization is a quantum phenomenon and cannot be treated with a classical model, particularly whenever delocalized valence electrons are present in the dielectric. In a quantum picture, the current is basically a property of the phase of the wave functions, as opposed to the charge, which is a property of their modulus. An elegant and complete theory has recently been developed by King-Smith and Vanderbilt, in which the polarization difference between any two crystal states---in a null electric field---takes the form of a geometric quantum phase. The author gives a comprehensive account of this theory, which is relevant for dealing with transverse-optic phonons, piezoelectricity, and ferroelectricity. Its relation to the established concepts of linear-response theory is also discussed. Within the geometric phase approach, the relevant polarization difference occurs as the circuit integral of a Berry connection (or "vector potential"), while the corresponding curvature (or "magnetic field") provides the macroscopic linear response.

Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

Abstract: We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of theN=2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons theory. Using the mirror map this leads to computation of the ‘number’ of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingN=2 theory. Relations withc=1 strings are also pointed out.

Interatomic Potentials from First-Principles Calculations: The Force-Matching Method

Abstract: We present a new scheme to extract numerically optimal interatomic potentials from large amounts of data produced by first-principles calculations. The method is based on fitting the potential to ab initio atomic forces of many atomic configurations, including surfaces, clusters, liquids and crystals at finite temperature. The extensive data set overcomes the difficulties encountered by traditional fitting approaches when using rich and complex analytic forms, allowing to construct potentials with a degree of accuracy comparable to that obtained by ab initio methods. A glue potential for aluminium obtained with this method is presented and discussed.

The Contribution of the obscuring torus to the x-ray spectrum of Seyfert galaxies: A Test for the unification model

Abstract: The presence of an obscuring torus around the nucleus of a Seyfert galaxy, as supposed in the popular unification scheme, can strongly modify the X-ray spectrum for both type 1 and type 2 Seyfert galaxies. We study this problem by means of Monte Carlo simulations, finding that, if the torus is Compton-thick, it can scatter at small angles a significant fraction of the nuclear radiation, and contribute to the continuum of Seyfert 1 galaxies above ∼10 keV, and to the fluorescence iron line at 6.4 keV. At large inclination angles and for large torus column densities, the spectrum is attenuated by photoabsorption and Compton scattering, while the iron fluorescence line produced by the torus can have large equivalent widths

Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells

Abstract: A sum rule for electronic intersubband transitions has been derived following Kane's model, beyond the quadratic dispersion relations The sum rule takes into account the effects of nonparabolicity and the different effective masses in the well and barrier materials; it depends on the property of the ground state of the system and, as such, on the shape of the potential The boundaries of the validity of matrix element computations are also discussed in the case where only the conduction band is included Experimental results are presented for bound-to-bound and bound-to-continuum intersubband transitions in various types of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/${\mathrm{Ga}}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$As quantum well systems (single wells, coupled wells and quantum wells with Bragg confinement); the agreement with theory is excellent In the last section of the paper, the effect of the electric field on the sum rule is investigated

Electron-vibron interactions in charged fullerenes. I. Berry phases.

Abstract: A simple model for electron-vibron interactions on charged fullerenes ${\mathrm{C}}_{60}^{\mathit{n}\mathrm{\ensuremath{-}}}$, n=1,...,5, is solved both at weak and strong couplings. We consider a single ${\mathit{H}}_{\mathit{g}}$ vibrational multiplet interacting with ${\mathit{t}}_{1\mathit{u}}$ electrons. At strong coupling the semiclassical dynamical Jahn-Teller theory is valid. The Jahn-Teller distortions are unimodal for n=1,2,4,5 electrons, and bimodal for 3 electrons. The distortions are quantized as rigid-body pseudorotators which are subject to geometrical Berry phases. These impose ground-state degeneracies and dramatically change zero-point energies. Exact diagonalization shows that the semiclassical level degeneracies and ordering survive well into the weak-coupling regime. At weak coupling, we discover an enhancement factor of 5/2 for the pair binding energies over their classical values. This has potentially important implications for superconductivity in fullerides, and demonstrates the shortcoming of Migdal-Eliashberg theory for molecular crystals.

A notion of total variation depending on a metric with discontinuous coefficients

Abstract: Given a function u : Ω ⊆ _ ℝ n → ℝ , we introduce a notion of total variation of u depending on a possibly discontinuous Finsler metric. We prove some integral representation results for this total variation, and we study the connections with the theory of relaxation.

Intracellular immunization with cytosolic recombinant antibodies.

Abstract: We report the application of a strategy to inactivate cellular proteins in vertebrate cells based on the intracellular expression of immunoglobulin genes. We have selected, in this instance, the p21 protein, encoded by the ras proto-oncogene, as a target protein. The variable regions of the neutralizing anti-p21ras monoclonal antibody Y13-259 were cloned in vectors for the expression of either the whole antibody molecule or its single-chain Fv fragment (ScFv) derivative. In order to target the recombinant antibodies to the cytosol, their hydrophobic leader sequence for secretion was mutated or deleted. When these proteins are expressed in the cytosol of Xenopus laevis oocytes they colocalize with the endogenous p21ras protein in the cytoplasmic face of the oocyte plasma membrane, and they markedly inhibit the H1 kinase activity induced by insulin. Moreover, cytosolic anti-p21ras ScFv fragments block the ensuing meiotic maturation. Thus the intracellular expression of both whole antibodies and antibody domains can be used to block a biological function.

Local interface composition and band discontinuities in heterovalent heterostructures.

Abstract: The local Zn/Se relative concentration at the interface in ZnSe-GaAs(001) heterostructures synthesized by molecular beam epitaxy was found to be controlled by the Zn/Se flux ratio employed during the early growth stage of ZnSe on GaAs. Correspondingly, the valence band discontinuity varies from 1.20 eV (Zn-rich interface) to 0.58 eV (Se-rich interface). Comparison with the results of first-principles calculations suggests that the observed trend in band offsets is related to the establishment of neutral interfaces with different atomic configurations.

Structural Phase Transformations via First-Principles Simulation

Abstract: We present a new simulation scheme for structural phase transitions via first-principles molecular dynamics. The method is obtained by combining the Car-Parrinello method for ab initio simulation with the Parrinello-Rahman method to account for variable cell shape. We demonstrate the validity of our approach by simulating the spontaneous transformation of silicon from diamond to simple hexagonal phase under high pressure.

Layering transition in confined molecular thin films : nucleation and growth

Abstract: When a fluid is confined between two molecularly smooth solid surfaces (e.g., mica surfaces) it tends to form layers of molecular thickness parallel to the surfaces. We study the process of the squeezing out of a monolayer as a function of an applied normal pressure. We estimate the pressure necessary to ``nucleate'' the thickness transition (n\ensuremath{\rightarrow}n-1, where n is the number of monolayers) and study the ``growth'' or ``spreading'' of the removal process after the nucleation has occurred.

Transient expression of a novel type of GABA response in rat CA3 hippocampal neurones during development.

Abstract: 1. Intracellular recordings were used to study the effects of gamma-aminobutyric acid (GABA) on rat CA3 hippocampal neurones during the first two weeks of postnatal life. 2. In the presence of tetrodotoxin (TTX, 1 microM), from postnatal day 0 (P0) to P12 both associated with an increase in input conductance whereas baclofen (30-100 microM) produced a membrane hyperpolarization. 3. Bicuculline (50 microM) reduced the effects of GABA and abolished the response to isoguvacine without affecting the response to baclofen. 4. This novel bicuculline-insensitive GABA response was chloride dependent and was blocked by picrotoxin (10-100 microM) in an uncompetitive way. In bicuculline and picrotoxin, a GABAB-mediated hyperpolarization appeared. 5. Towards the end of the second postnatal week, bicuculline blocked the GABA-induced depolarization and revealed a small hyperpolarizing response which was blocked by the GABAB antagonist CGP 35348 (0.5-1 mM). 6. It is suggested that, during development, the GABA response was mediated through the conventional GABAA and GABAB receptors as well as a new bicuculline-baclofen-insensitive type of receptor.

New lower semicontinuity results for polyconvex integrals

Abstract: We study integral functionals of the formF(u, Ω)=∫Ωf(▽u)dx, defined foru ∈ C1(Ω;Rk), Ω⊑R n . The functionf is assumed to be polyconvex and to satisfy the inequalityf(A) ≥c0¦ℳ(A)¦ for a suitable constant c0 > 0, where ℳ(A) is then-vector whose components are the determinants of all minors of thek×n matrixA. We prove thatF is lower semicontinuous onC1(Ω;Rk) with respect to the strong topology ofL1(Ω;Rk). Then we consider the relaxed functional ℱ, defined as the greatest lower semicontinuous functional onL1(Ω;R k ) which is less than or equal toF on C1(Ω;Rk). For everyu ∈ BV(Ω;Rk) we prove that ℱ (u,Ω) ≥ ∫Ωf(▽u)dx+c0¦Dsu¦(Ω), whereDu=▽u dx+Dsu is the Lebesgue decomposition of the Radon measureDu. Moreover, under suitable growth conditions onf, we show that ℱ (u,Ω)=∫Ωf(▽u)dx for everyu ∈ W1,p(Ω;Rk), withp ≥ min{n,k}. We prove also that the functional ℱ (u, Ω) can not be represented by an inte- gral for an arbitrary functionu ∈ BVloc(Rn;Rk). In fact, two examples show that, in general, the set functionΩ → ℱ (u, Ω) is not subadditive whenu ∈ BVloc(Rn;Rk), even ifu ∈ W loc 1,p (Rn;Rk) for everyp < min{n,k}. Finally, we examine in detail the properties of the functionsu ∈ BV(Ω;Rk) such that ℱ (u, Ω)=∫Ωf(▽u)dx, particularly in the model casef(A)=¦ℳ(A)¦.

Electron-vibron interactions in charged fullerenes. II. Pair energies and spectra.

Abstract: The ground-state energy shifts and excitation spectra of charged fullerenes ${\mathrm{C}}_{60}^{\mathit{n}\mathrm{\ensuremath{-}}}$, n=1,...,5 are calculated. The electron-vibron Hamiltonian of part I is extended to include all ${\mathit{A}}_{\mathit{g}}$ and ${\mathit{H}}_{\mathit{g}}$ modes with experimentally determined frequencies and theoretically estimated coupling constants. Complex splitting patterns of ${\mathit{H}}_{\mathit{g}}$ vibrational levels are found. Our results are relevant to EPR measurements of spin splittings in ${\mathrm{C}}_{60}^{2\mathrm{\ensuremath{-}}}$ and ${\mathrm{C}}_{60}^{3\mathrm{\ensuremath{-}}}$ in solution. Spectroscopic gas-phase experiments will be of interest for further testing of this theory. As found in part I, degeneracies in the electron and vibron Hamiltonians give rise to a dynamical Jahn-Teller effect, and to a considerable enhancement of the electronic pairing interaction. This helps to overcome repulsive Coulomb interactions and has important implications for superconductivity in ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$ and the insulating state in ${\mathrm{K}}_{4}$${\mathrm{C}}_{60}$.

Ale manifolds and conformal field theories

Abstract: We address the problem of constructing the family of (4,4) theories associated with the σ model on a parametrized family ℳζ of asymptotically locally Euclidean (ALE) manifolds. We rely on the ADE classification of these manifolds and on their construction as hyper-Kahler quotients, due to Kronheimer. By so doing we are able to define the family of (4,4) theories corresponding to a ℳζ family of ALE manifolds as the deformation of a solvable orbifold C2/Γ conformal field theory, Γ being a Kleinian group. We discuss the relation between the algebraic structure underlying the topological and metric properties of self-dual four-manifolds and the algebraic properties of nonrational (4,4) theories admitting an infinite spectrum of primary fields. In particular, we identify the Hirzebruch signature τ with the dimension of the local polynomial ring associated with the ADE singularity, with the number of nontrivial conjugacy classes in the corresponding Kleinian group and with the number of short representations of the (4,4) theory minus four.

Geometry of 2d topological field theories

Abstract: These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial solutions of WDVV. {Appendix B.} Symmetriies of WDVV. Twisted Frobenius manifolds. {Appendix C.} WDVV and Chazy equation. Affine connections on curves with projective structure. Lecture 2. Topological conformal field theories and their moduli. Lecture 3. Spaces of isomonodromy deformations as Frobenius manifolds. {Appendix D.} Geometry of flat pencils of metrics. {Appendix E.} WDVV and Painlev\'e-VI. {Appendix F.} Branching of solutions of the equations of isomonodromic deformations and braid group. {Appendix G.} Monodromy group of a Frobenius manifold. {Appendix H.} Generalized hypergeometric equation associated to a Frobenius manifold and its monodromy. {Appendix I.} Determination of a superpotential of a Frobenius manifold. Lecture 4. Frobenius structure on the space of orbits of a Coxeter group. {Appendix J.} Extended complex crystallographic groups and twisted Frobenius manifolds. Lecture 5. Differential geometry of Hurwitz spaces. Lecture 6. Frobenius manifolds and integrable hierarchies. Coupling to topological gravity.

Jump shocks in molecular clouds: speed limits and excitation levels

Abstract: Below a speed limit, hydromagnetic jump shocks propagate through the interstellar medium without dissociating the molecules. The resulting excitation of the molecules is modelled here, where several factors, including the shock shape and magnetic field strength (i.e. the Alfven speed), are explored. The speed limit for molecular hydrogen is in the range ∼ 24-39 km s −1 for low Alfven speeds but reaches 50 km s −1 for an Alfven speed of 10 km s −1 . High Alfven speeds may well occur within active regions, such as already found for HH 34, where the results of multiple outflow events are being observed. Origins for the low but significant level of pre-shock ionization, a prerequisite for a jump shock, are considered.

Density-functional theory of the dielectric constant: Gradient-corrected calculation for silicon

Abstract: We study the screening of a macroscopic electric field in a crystalline dielectric. Density-functional perturbation theory provides the static dielectric constant (or tensor) as a bulk property; we give a formulation which extends the local-density approximation, and specifically we discuss its implementation within gradient-corrected schemes. We briefly consider the relevance (if any) of the so-called ``gap problem'' to static linear response. As a case study, we perform an an initio calculation of the dielectric constant in silicon within a popular gradient-corrected local-density scheme. We find that the gradient corrections reduce the discrepancy found so far between local-density predictions and experiments in covalently bonded materials. The amount of this reduction is sizable if the calculations are performed at the experimental equilibrium lattice constant of the crystal, while, however, it is only marginal when the calculations are carried out, at the calculated lattice constants, consistently within each given theoretical scheme.

Density-functional theory of macroscopic stress : gradient-corrected calculations for crystalline se

Abstract: We generalize the Nielsen-Martin stress theorem beyond the local-density approximation (LDA) and present an alternative derivation of the whole theorem. We show that the exchange-correlation stress becomes anisotropic in the most general case: its explicit form is given within a gradient-corrected (GC) scheme. As a test implementation, we use the generalized theorem to achieve fast structural optimization in crystalline Se. In this material LDA predicts a rather poor structure period. Our GC calculation is in much better agreement with the experiment.

Developmental Changes in Spontaneous GABAA-mediated Synaptic Events in Rat Hippocampal CA3 Neurons

Abstract: Ongoing spontaneous postsynaptic potentials (SPSPs) were intracellularly recorded at 34-36°C from hippocampal CA3 neurons in slices obtained from postnatal days (P) 0 – 6 and 7 – 31. SPSPs occurred randomly, and their frequency distribution was fitted by a single exponential function. They were little affected by kynurenic acid, but were reversibly blocked by bicuculline, implying that they were mediated by GABAA receptors. The mean amplitude was 4.53 ± 0.89 mV in control conditions and 4.07 ± 0.79 mV in kynurenic acid. In kynurenic acid (with CsCl-filled microelectrodes), SPSPs reversed polarity at 2.4 ± 2 mV. When tetrodotoxin (1 μM) was added to kynurenic acid solution, GABAA-mediated miniature postsynaptic potentials (MPSPs) were recorded. Under these conditions large events disappeared. The mean amplitude of MPSPs was 2.51 ± 0.43 mV. The mean frequency decreased from 2.96 ± 1.04 Hz in kynurenic acid to 0.4 ± 0.15 Hz in kynurenic acid plus tetrodotoxin. In contrast with P0 – P6, at P7 – P31 SPSPs were significantly affected by kynurenic acid. The mean amplitude of SPSPs shifted from 4.71 ± 0.82 mV in control conditions to 3.79 ± 0.76 mV in kynurenic acid. At this developmental stage, the reversal potential of GABAA-mediated SPSPs shifted towards more negative values (-23.7 ± 1.3 mV). Addition of tetrodotoxin to kynurenic acid solution abolished larger events and revealed GABAergic MPSPs. The mean amplitude of MPSPs was 2.72 ± 0.5 mV, a value very close to that observed at P0 – P6. Synaptic currents were recorded at 22 – 24°C from voltage-clamped CA3 pyramidal neurons (at P6) using the tight-seal whole-cell recording technique. Cells were dialysed with CsCl solution and held at -70 mV. Spontaneous GABAA-mediated miniature postsynaptic currents (MPSCs) were recorded in the presence of kynurenic acid and tetrodotoxin. The decay time of MPSCs was fitted with a single exponential and was 29 ± 3 ms. No correlation was found between the peak amplitude of individual events and their rise or decay time constant. The mean amplitude distribution of MPSCs was 12 ± 4.3 pA. In outside-out patches from acutely dissociated CA3 hippocampal neurons, GABA (50 μM) activated single-channel events of 24 and 35 pS conductance. Therefore one quantal current represents the simultaneous opening of five to seven GABAA receptor channels on the postsynaptic cell. These data show also that in the immediate postnatal period spontaneous glutamatergic potentials are poorly developed and start appearing towards the end of the first postnatal week concomitant with the shift of GABA from the depolarizing to the hyperpolarizing direction.