Showing papers on "Operator (physics) published in 1986"
TL;DR: In this article, a first-principles theory of the quasiparticle energies in semiconductors and insulators described in terms of the electron self-energy operator is presented.
Abstract: We present a first-principles theory of the quasiparticle energies in semiconductors and insulators described in terms of the electron self-energy operator. The full dielectric matrix is used to evaluate the self-energy operator in the GW approximation: the first term in an expansion of the self-energy operator in terms of the dynamically screened Coulomb interaction (W) and the dressed Green's function (G). Quasiparticle energies are calculated for the homopolar materials diamond, Si, and Ge as well as for the ionic compound LiCl. The results are in excellent agreement with available experimental data. In particular, the indirect band gap is calculated as 5.5, 1.29, and 0.75 eV as compared with experimental gaps of 5.48, 1.17, and 0.744 eV for diamond, Si, and Ge, respectively. The Ge results include relativistic effects. The calculated direct gap for LiCl is within 5% of experiment. Viewed as a correction to the density-functional eigenvalues calculated with the local-density approximation, the present results show a correction dominated by a large jump at the gap. It is found that because of the charge inhomogeneity, the full dielectric screening matrix must be included, i.e., local-field effects are essential. The dynamical effects are also found to be crucial. The required dielectric matrices are obtained within the density-functional approach for the static case and extended to finite frequency with use of a generalized plasmon-pole model based on sum rules. The model reproduces the \ensuremath{\omega} and ${\ensuremath{\omega}}^{\mathrm{\ensuremath{-}}1}$ moments of the exact many-body response function. The qualitative features of the electron self-energy operator are discussed. Using the static Coulomb-hole--screened-exchange approximation for illustration, the role of local fields in the self-energy operator are explained. The role of dynamical renormalization is illustrated. The same qualitative features are observed in both the homopolar and ionic materials.
3,893 citations
TL;DR: In this article, it was shown that a near constant conductivity of a two-dimensional body can be uniquely determined by steady state direct current measurements at the boundary of the body.
Abstract: We show that a near constant conductivity of a two-dimensional body can be uniquely determined by steady state direct current measurements at the boundary. Mathematically, we show that the coefficient γ in the operator ∇.γ∇ is uniquely determined by its Dirichlet integrals.
250 citations
TL;DR: A unified theory of time-domain and frequency-domain four-wave mixing processes, based on the nonlinear response function R(t3, t2, t1), is developed in this paper.
Abstract: A unified theory of time-domain and frequency-domain four-wave mixing processes, which is based on the nonlinear response function R(t3, t2, t1), is developed. The response function is expressed in terms of the four-point correlation function of the dipole operator F(τ1, τ2, τ3, τ4) and is evaluated explicitly for a stochastic model of line broadening that holds for any correlation time of the bath. Our results interpolate between the fast-modulation limit, in which the optical Bloch equations are valid, and the static limit of inhomogeneous line broadening. As an example of the relationship between time-domain and frequency-domain four-wave mixing, we compare the capabilities of steady-state and transient coherent anti-Stokes Raman spectroscopy experiments to probe the vibrational dynamics in ground and excited electronic states.
207 citations
TL;DR: In this paper, a domaine regulier borne strictement convexe dans R n et V:Ω→R une fonction convexe non negative is presented.
Abstract: Soit Ω un domaine regulier borne strictement convexe dans R n et V:Ω→R une fonction convexe non negative. Soient λ 1 et λ 2 les 2 premieres valeurs propres non nulles de l'equation -Δf+Vf=λf, f/ ∂Ω ≡o. Alors λ 2 -λ 1 ≥Π 2 /d 2 , ou d est le diametre de Ω
59 citations
TL;DR: Calculations of magnetic moments for closed shell plus (or minus) one nucleon using this effective current operator recover the Schmidt values, thus resolving a longstanding problem with relativistic models of nuclear structure.
Abstract: A Landau-Migdal approach to relativistic mean field theory of nuclear matter is used to define the single particle isoscalar current. By virtue of the near cancellation of scalar and vector potentials, this current is very close to the standard nonrelativistic isoscalar current; and hence the single particle isoscalar magnetic moment operator gives results in agreement with the nonrelativistic shell model. Calculations of magnetic moments for closed shell plus (or minus) one nucleon using this effective current operator recover the Schmidt values, thus resolving a longstanding problem with relativistic models of nuclear structure.
56 citations
TL;DR: In this article, a microscopic correlation function expression for the signal in four-wave mixing is developed and conditions under which the correlation function may be factorized into a product of two four-point, single-particle correlation functions are specified.
Abstract: A microscopic correlation function expression for the signal in four-wave mixing is developed. Both stationary and transient (i.e., photon-echo) experiments with coherent or incoherent radiation fields are considered. In general, these observables are described by an eight-point correlation function of the dipole operator involving two particles, and the signal cannot be written as an amplitude squared. Conditions under which the correlation function may be factorized into a product of two four-point, single-particle correlation functions are specified. In this case the conventional approach, based on calculating a nonlinear polarization and substituting it as a source in Maxwell's equations, is justified. However, in the presence of long-range spatial correlations in the sample (e.g., near critical points) the conventional formulation breaks down and the present theory should be used.
47 citations
TL;DR: A method for calculating center-of-mass corrections to hadron properties in soliton models and the method to the soliton bag model is presented and three ''virial theorems'' are used to test the approximate solution.
Abstract: We present a method for calculating center-of-mass corrections to hadron properties in soliton models and we apply the method to the soliton bag model. A coherent state is used to provide a quantum wave function corresponding to the mean-field approximation. This state is projected onto a zero-momentum eigenstate. States of nonzero momentum can be constructed from this with a Lorentz boost operator. Hence center-of-mass corrections can be made in a properly relativistic way. The energy of the projected zero-momentum state is the hadron mass with spurious center-of-mass energy removed. We apply a variational principle to our projected state and use three ``virial theorems'' to test our approximate solution. We also study projection of general one-mode states. Projection reduces the nucleon energy by up to 25%. Variation after projection gives a further reduction of less than 20%. Somewhat larger reductions in the energy are found for meson states.
44 citations
TL;DR: In this paper, the authors used the symmetrized split operator fast Fourier transform method to compute the time evolution of the vibrational wave packet involved in the time dependent formula of Raman scattering.
Abstract: Resonance Raman overtone progressions of I2 in an Ar crystal are computed using the time dependent formula of Raman scattering which has been known to possess distinct computational advantages over the Kramers–Heisenberg–Dirac sum‐over‐states method, especially when treating condensed phase systems. The symmetrized split operator fast Fourier transform method, which provides a simple and accurate algorithm, is applied to computing the time evolution of the vibrational wave packet involved in the time dependent formula. Our calculated result based on Heller’s time dependent formula is in qualitative agreement with the experimental one of Grzybowski and Andrews, but there are some discrepancies between them (for example, the overtone enhancement with the 530.9 nm excitation is not so strong as the experimental one). Those discrepancies are ascribed to the adopted assumption that the line shape for a vibronic transition is a Lorentzian and it is independent of the vibrational level in the excited electronic state. The use of an incident frequency dependent line shape proves to resolve the disagreements to a great extent, which implies that to obtain perfect agreement one needs to explicitly deal with the motion of the trapped molecule and its neighboring host atoms.
42 citations
TL;DR: Using the Green's-function approach to steady-state nonlinear transport recently developed for an interacting system of electrons, impurities, and phonons, a generalized Langevin equation for the current operator is obtained and the numerical results of the transient currents obtained from the quantum and the classical limits are presented.
Abstract: Using the Green's-function approach to steady-state nonlinear transport recently developed for an interacting system of electrons, impurities, and phonons, we obtain, in the linear approximation, a generalized Langevin equation for the current operator. From this equation, the time-dependent current, the current fluctuation, the noise associated with both current and voltage fluctuations, and the time-dependent diffusion constant are explicitly derived and are cast into numerically tractable forms. All of the involved correlation and retarded Green's functions are obtained microscopically without ad hoc assumptions as is usually done in a conventional Langevin treatment of the motion of a Brownian particle. In the classical and high-temperature limits, all the above-mentioned quantities can be evaluated analytically. They reduce exactly to the well-known results in the existing literature. The numerical results of the transient currents obtained from the quantum and the classical limits are presented and compared at (1) zero temperature for a two-dimensional interacting electron system with charged impurities and (2) high temperature for a three-dimensional electron system with nonpolar optical phonons.
Book Chapter•
1 Jan 1986
TL;DR: In this article, the authors show how groups and the inversion operator generate maps between the representations of ideal continuum models (fluids, plasmas, elasticity, etc.) using the theory of momentum maps and reduction.
Abstract: Ideal continuum models (fluids, plasmas, elasticity, etc.)
can be studied using a variety of representations, each of which has a Hamiltonian structure. This paper shows how groups (typified by the group of particle relabelling symmetries) and the inversion operator which swaps the reference and current particle positions generate maps between the representations. These maps, derived using the theory of momentum maps and reduction, are all Poisson (or canonical) maps which carry the brackets in one representation to those in another. the results
are developed abstractly in the framework of reduction of a pair of principal bundles by left and right group actions. Examples are given treating the motion of an incompressible fluid with surface tension, the heavy top, and ideal compressible (barotropic) flow.
TL;DR: The behavior of spin-1 2 AX 3 and A 2 X 2 systems evolving under cross-polarization (CP) and isotropic mixing (IM) is analyzed in detail by computing the time development of the density operator by commutator algebra.
Journal Article•
TL;DR: In this paper, a stochastic finite element solution method utilizing a Neumann expansion of the operator matrix involved and at the same time, devises an efficient Monte Carlo method consistent with the solution method are presented.
Abstract: This paper develops a stochastic finite element solution method utilizing a Neumann expansion of the operator matrix involved and at the same time, devises an efficient Monte Carlo method consistent with the solution method. These analytical and Monte Carlo methods both utilize the successive nature of approximation. The methods demand inversion of the 'average' operator matrix only once, achieve successive improvements of the solution by means of a stationary operator, and require no evaluation of the partial derivatives of the operator matrix. The generic system deviator formulation, which is analogous to that of a static case, is illustrated in order to avoid lengthy algebraic expressions. The computational steps for natural extension to steady-state and transient response analyses are then indicated.
TL;DR: In this article, the canonical operator theory of paraxial optics is generalized to address the case of misaligned optics, and the formal group structure is extended from the aligned case in terms of Heisenberg-Weil and inhomogeneous canonical transforms and the associated 3 × 3 augmented ray matrices.
Abstract: Canonical operator theory of paraxial optics is generalized to address the case of misaligned optics. The formal group structure is extended from the aligned case in terms of Heisenberg–Weil and inhomogeneous canonical transforms and the associated 3 × 3 augmented ray matrices. Certain misalignment phase shifts that are often mistreated and ignored have been derived and incorporated into the theory.
TL;DR: In this paper, the isoscalar electromagnetic current operator for the two-nucleon system is studied in the Skyrme model using the factorized two-soliton ansatz.
TL;DR: In this paper, the decomposition method is applied to integro-differential operator equations and is shown to be applicable to nonlinear stochastic operator equations as well as nonlinear Stochastic Operator Equations.
TL;DR: The general problem of relativistic corrections to the kinetic energy in quasirelativistic theories is discussed and related formulas are developed in this paper, where it is shown that the well-known mass-velocity operator, Hmv = (−α2/8)p4, is incorrect and does not provide any proper relativistically corrections.
Abstract: The general problem of relativistic corrections to the kinetic energy in quasirelativistic theories, is discussed and related formulas are developed. It is shown that the well-known mass-velocity operator, Hmv = (−α2/8)p4, is incorrect and does not provide any proper relativistic corrections.
TL;DR: The Hamiltonian formulation of U(1) lattice gauge theory is studied in a basis of eigenstates of the electric-field operator, and exact ground-state properties of the theory in three space dimensions are calculated.
Abstract: The Hamiltonian formulation of U(1) lattice gauge theory is studied in a basis of eigenstates of the electric-field operator. The guided-random-walk algorithm of Chin et al. is transcribed to the electric-field basis, and exact ground-state properties of the theory in three space dimensions are calculated. A novel variational scheme is used to compute the potential between two static charges for two space dimensions.
TL;DR: A linear discontinuous Galerkin treatment is developed for the continuous slowing down operator and a synthetic acceleration scheme is developed to accelerate the outer iterations required by this treatment.
Abstract: A linear discontinuous Galerkin treatment is developed for the continuous slowing down operator. Multigroup Legendre coefficients are derived that allow this treatment to be implemented in standard S/sub ETA/ codes. A synthetic acceleration scheme is developed to accelerate the outer iterations required by this treatment. A computational comparison between the diamond difference treatment and the linear discontinuous treatment is given.
TL;DR: In this paper, the spectral asymptotics of a multidimensional Schrodinger operator with potential which behaves nonregularly at infinity were proved for the case where the potential is non-convex.
Abstract: Formulas are proved for the spectral asymptotics of a multidimensional Schrodinger operator with potential which behaves nonregularly at infinity.Bibliography: 17 titles.
TL;DR: In this article, a fundamental framework of thermo field dynamics, including non-equilibrium situations as well as equilibrium stuations, is formulated through a compact axiomatic form, in which no reference to reservoirs is needed, by considering quantum fields.
Abstract: A fundamental framework of thermo field dynamics (TFD), including non-equilibrium situations as well as equilibrium stuations, is formulated through a compact axiomatic form, in which no reference to reservoirs is needed, by considering quantum fields. The semi-free quantum fields in TFD are constructed in a way parallel to that of the usual quantum field theory without thermal degrees of freedom, i.e. in terms of orthonormalization relations among wave functions, the sum rule for wave functions, the divisor operator and the particle-antiparticle conjugation (C-conjugation).
TL;DR: In this paper, a variational derivation technique for the Green's functions and the self-energy is presented, which is formally closed and should be an appropriate starting point for any kind of iteration or approximation.
Abstract: Aiming at a realistic description of highly excited states in semiconductors the derivation of kinetic equations is reformulated where emphasis is laid on the consideration of many-body effects without perturbation expansion arguments. By the variational derivation technique a set of equations for the Green's functions and the self-energy is obtained, which is formally closed and should be an appropriate starting point for any kind of iteration or approximation. The connection of this technique with the diagram technique given by Keldysh and the translation technique for thermodynamic Green's functions according to Kadanoff and Baym is demonstrated. The general equations are then exactly transformed to difference and sum coordinates, enabling an adequate approximation in the case of slowly varuing (in space and time) external fields in terms of local quantities. In linear approximation with respect to the drift operator D a generalized Boltzmann equation is derived, which clearly exhibits many-body effects in all drift and collision contributions.
TL;DR: In this article, a trace formula is given for an abstract pair consisting of a dissipative operator and a selfadjoint operator, and a connection is established between the spectral shift function of this pair and the corresponding scattering matrix.
Abstract: A trace formula is given for an abstract pair consisting of a dissipative operator and a selfadjoint operator, and a connection is established between the spectral shift function of this pair and the corresponding scattering matrix. As a consequence, trace formulas are obtained for a specific dissipative operator arising in the problem of resonance scattering of plane waves on a one-dimensional semi-infinite crystal.Bibliography: 8 titles.
TL;DR: In this article, the authors characterize in terms of the infinitesimal generator those cosine operator functions which are almost periodic or uniformly almost periodic, i.e., almost periodic.
TL;DR: In this paper, the reduction relation for the fixedisospin (T,Tz) average of a general operator in the model space of many fermions is described in two forms with and without recourse to factorization of isospin z components.
Abstract: The reduction relation for the fixed‐isospin (T,Tz) average of a general operator in the model space of many fermions is described in two forms with and without recourse to factorization of isospin z components. Algebraic treatment is developed to deduce various types of expressions for each propagation coefficient that plays the role of the Green’s function in each form of the reduction relation. Propagation coefficients are described also in relation to sum rules as to fixed‐isospin spectroscopic factors. These results lead to novel identities among n‐j symbols and factorials.