Instantaneous Coulomb Interaction Research Articles

Optical response of laser-driven charge-transfer complex described by Holstein-Hubbard model coupled to heat baths: Hierarchical equations of motion approach.

We investigate the optical response of a charge-transfer complex in a condensed phase driven by an external laser field. Our model includes an instantaneous short-range Coulomb interaction and a local optical vibrational mode described by the Holstein-Hubbard (HH) model. Although characterization of the HH model for a bulk system has typically been conducted using a complex phase diagram, this approach is not sufficient for investigations of dynamical behavior at finite temperature, in particular for studies of nonlinear optical properties, where the time irreversibility of the dynamics that arises from the environment becomes significant. We therefore include heat baths with infinite heat capacity in the model to introduce thermal effects characterized by fluctuation and dissipation to the system dynamics. By reducing the number of degrees of freedom of the heat baths, we derive numerically "exact" hierarchical equations of motion for the reduced density matrix of the HH system. As demonstrations, we calculate the optical response of the system in two- and four-site cases under external electric fields. The results indicate that the effective strength of the system-bath coupling becomes large as the number of sites increases. Excitation of electrons promotes the conductivity when the Coulomb repulsion is equivalent to or dominates the electron-phonon coupling, whereas excitation of optical vibrations always suppresses the conductivity.

Long-range Coulomb interaction effects on the topological phase transitions between semimetals and insulators

Topological states may be protected by a lattice symmetry in a class of topological semi-metals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space defines a chirality concretely, so a protecting symmetry may be referred to as a chiral symmetry. Prime examples include Dirac semi-metal (DSM) in a distorted spinel, BiZnSiO$_4$, protected by a mirror symmetry and DSM in Na$_3$Bi, protected by a rotational symmetry. In these states, topology and a chiral symmetry are intrinsically tied. In this work, we investigate characteristics interplay between a chiral symmetry order parameter and instantaneous long-range Coulomb interaction with the standard renormalization group method. We show that a topological transition associated with a chiral symmetry is stable under the presence of the Coulomb interaction and the electron velocity always becomes faster than one of a chiral symmetry order parameter. Thus, the transition {\it must not} be relativistic, which implies a supersymmetry is intrinsically forbidden by the long-range Coulomb interaction. {Asymptotically exact} universal ratios of physical quantities such as energy gap ratio are obtained, and connections with experiments and recent theoretical proposals are also discussed.

An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling.

An atomic mean-field (AMF) spin-orbit (SO) approach within exact two-component theory (X2C) is reported, thereby exploiting the exact decoupling scheme of X2C, the one-electron approximation for the scalar-relativistic contributions, the mean-field approximation for the treatment of the two-electron SO contribution, and the local nature of the SO interactions. The Hamiltonian of the proposed SOX2CAMF scheme comprises the one-electron X2C Hamiltonian, the instantaneous two-electron Coulomb interaction, and an AMF SO term derived from spherically averaged Dirac-Coulomb Hartree-Fock calculations of atoms; no molecular relativistic two-electron integrals are required. Benchmark calculations for bond lengths, harmonic frequencies, dipole moments, and electric-field gradients for a set of diatomic molecules containing elements across the periodic table show that the SOX2CAMF scheme offers a balanced treatment for SO and scalar-relativistic effects and appears to be a promising candidate for applications to heavy-element containing systems. SOX2CAMF coupled-cluster calculations of molecular properties for bismuth compounds (BiN, BiP, BiF, BiCl, and BiI) are also presented and compared with experimental results to further demonstrate the accuracy and applicability of the SOX2CAMF scheme.

Two-component relativistic coupled-cluster methods using mean-field spin-orbit integrals

A novel implementation of the two-component spin-orbit (SO) coupled-cluster singles and doubles (CCSD) method and the CCSD augmented with the perturbative inclusion of triple excitations [CCSD(T)] method using mean-field SO integrals is reported. The new formulation of SO-CCSD(T) features an atomic-orbital-based algorithm for the particle-particle ladder term in the CCSD equation, which not only removes the computational bottleneck associated with the large molecular-orbital integral file but also accelerates the evaluation of the particle-particle ladder term by around a factor of 4 by taking advantage of the spin-free nature of the instantaneous electron-electron Coulomb interaction. Benchmark calculations of the SO splittings for the thallium atom and a set of diatomic 2Π radicals as well as of the bond lengths and harmonic frequencies for a set of closed-shell diatomic molecules are presented. The basis-set and core-correlation effects in the calculations of these properties have been carefully analyzed.

Editors' Choice—A Quantum Electrodynamics Formulation of Energy Transfer between Two Optically Active Ions

We have visited the nonradiative electron transfer process between optically active ions in luminescent materials. In contrast to the earlier formulations using multipolar expansion of instantaneous coulomb interaction between electrons, we have utilized a quantum electrodynamics (QED) approach to study the process of energy transfer from an excited ion to another. Such energy transfers occur in both sensitized luminescence and cross relaxations in the excited state. We have here investigated the nonradiative energy transfer processes specifically mediated by electric dipole moment-magnetic dipole moment and magnetic electric dipole moment-magnetic dipole moment interactions using a Feynman diagrammatic method. We have shown how experimentally relevant transfer rates could be obtained using a QED formulation involving discrete energy levels and spectral line shape function for emission and absorption profiles of interactive ions. Additional features of the dependence of the energy transfer rates on the interionic distance arising from retarded interaction potential have been pointed out.

Keldysh functional renormalization group for electronic properties of graphene

We construct a nonperturbative nonequilibrium theory for graphene electrons interacting via the instantaneous Coulomb interaction by combining the functional renormalization group method with the nonequilibrium Keldysh formalism. The Coulomb interaction is partially bosonized in the forward scattering channel resulting in a coupled Fermi-Bose theory. Quantum kinetic equations for the Dirac fermions and the Hubbard-Stratonovich boson are derived in Keldysh basis, together with the exact flow equation for the effective action and the hierarchy of one-particle irreducible vertex functions, taking into account a possible non-zero expectation value of the bosonic field. Eventually, the system of equations is solved approximately under thermal equilibrium conditions at finite temperature, providing results for the renormalized Fermi velocity and the static dielectric function, which extends the zero-temperature results of Bauer~\textit{et~al.}, Phys.\ Rev.\ B {\bf 92}, 121409 (2015).

Critical behavior of reduced QED4,3 and dynamical fermion gap generation in graphene

The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced QED$_{4,3}$ with $N$ four component fermions ($N=2$ for graphene), where photons are $(3+1)$-dimensional and mediate a fully retarded interaction among $(2+1)$-dimensional fermions. A correspondence between reduced QED$_{4,3}$ and QED$_3$ allows us to derive an exact gap equation for QED$_{4,3}$ up to next-to-leading order. Our results show that a dynamical gap is generated for $\alpha > \alpha_c$ where $1.03 < \alpha_c < 1.08$ in the case $N=2$ or for $N < N_c$ where $N_c$ is such that $\alpha_c \to \infty$ and takes the values $3.24 < N_c < 3.36$. The striking feature of these results is that they are in good agreement with values found in models with instantaneous Coulomb interaction. At the fixed point: $\alpha = 1/137 \ll \alpha_c$, and the system is therefore in the semi-metallic regime in accordance with experiments.

Elimination of theA-Square Problem from Cavity QED

We generalize the Power-Zineau-Woolley transformation to obtain a canonical Hamiltonian of cavity quantum electrodynamics for arbitrary geometry of boundaries. This Hamiltonian is free from the A-square term and the instantaneous Coulomb interaction between distinct atoms. The single-mode models of cavity QED (Dicke, Tavis-Cummings, Jaynes-Cummings) are justified by a term by term mapping to the proposed microscopic Hamiltonian. As one straightforward consequence, the basis of no-go argumentations concerning the Dicke phase transition with atoms in electromagnetic fields dissolves.

Photoinduced dynamics in a molecule metal nanoparticle complex: Mean–field approximation versus exact treatment of the interaction

Photoexcitation of a molecule placed in the proximity of a metal nanoparticle (MNP) is described theoretically. For a sufficient small spatial extension of the whole system the molecule-MNP coupling is given by the instantaneous Coulomb-interaction. The coupling can also be considered in terms of a local field to which an external field has been transferred due to the presence of the MNP. It is known that such an approach can explain a number of observations. However, it fails to describe molecular excited state quenching. By considering the exact molecule-MNP Coulomb-coupling and a related mean field approximation which directly leads to a local field description we investigate this disappearance of excited state quenching in detail. Laser pulse induced dynamics in the molecule-MNP system are studied and the importance of higher multipole excitations in a spherical MNP is underlined. The equivalence of the mean field approximation with the exact approach when calculating spectra of linear absorption is also demonstrated.

Quantum critical behavior in a graphenelike model

We present the results of numerical simulations of a $(2+1)$-dimensional fermion field theory based on a recent proposal for a model of graphene consisting of ${N}_{f}$ four-component Dirac fermions moving in the plane and interacting via an instantaneous Coulomb interaction. In the strong-coupling limit we identify a critical number of flavors ${N}_{fc}=4.8(2)$ separating an insulating from a conducting phase. This transition corresponds to the location of a quantum critical point, and we use a fit to the equation of state for the chiral order parameter to estimate the critical exponents. Next we simulate ${N}_{f}=2$ corresponding to real graphene and approximately locate a transition from strong- to weak-coupling behavior. Strong correlations are evident in the weak-coupling regime.

Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction

Motivated by the physics of graphene, we consider a model of $N$ species of $2+1$ dimensional four-component massless Dirac fermions interacting through a three dimensional instantaneous Coulomb interaction. We show that in the limit of infinitely strong Coulomb interaction, the system approaches a quantum critical point, at least for sufficiently large fermion degeneracy. In this regime, the system exhibits invariance under scale transformations in which time and space scale by different factors. The elementary excitations are fermions with dispersion relation $\ensuremath{\omega}\ensuremath{\sim}{p}^{z}$, where the dynamic critical exponent $z$ depends on $N$. In the limit of large $N$, we find $z=1\ensuremath{-}4∕({\ensuremath{\pi}}^{2}N)+O({N}^{\ensuremath{-}2})$. We argue that due to the numerically large Coulomb coupling, graphene (freely suspended) in a vacuum stays near the scale-invariant regime in a large momentum window, before eventually flowing to the trivial fixed point at very low momentum scales.

An interaction Lagrangian for two spin-1/2 elementary Dirac particles

The kinematical formalism for describing spinning particles developed by the author is based upon the idea that an elementary particle is a physical system with no excited states. It can be annihilated by the interaction with its antiparticle but, if not destroyed, its internal structure can never be modified. All possible states of the particle are just kinematical modifications of any one of them. The kinematical state space of the variational formalism of an elementary particle is necessarily a homogeneous space of the kinematical group of spacetime symmetries. By assuming Poincaré invariance we have already described a model of a classical spinning particle which satisfies Dirac's equation when quantized. We have recently shown that the spacetime symmetry group of this Dirac particle is larger than the Poincaré group. It also contains spacetime dilations and local rotations. In this work we obtain an interaction Lagrangian for two Dirac particles, which is invariant under this enlarged spacetime group. It describes a short- and long-range interaction such that when averaged, to suppress the spin content of the particles, describes the instantaneous Coulomb interaction between them. As an application, we analyse the interaction between two spinning particles, and show that the existence is possible of metastable bound states for two particles of the same charge, when the spins are parallel and provided some initial conditions are fulfilled. The possibility of formation of bound pairs is due to the zitterbewegung spin structure of the particles because when the spin is neglected, the bound states vanish.

Distorted-wave calculation of cross sections for inner-shell ionization by electron and positron impact

The relativistic distorted-wave Born approximation is used to calculate differential and total cross sections for inner shell ionization of neutral atoms by electron and positron impact. The target atom is described within the independent-electron approximation using the self-consistent Dirac-Fock-Slater potential. The distorting potential for the projectile is also set equal to the Dirac-Fock-Slater potential. For electrons, this guarantees orthogonality of all the orbitals involved and simplifies the calculation of exchange T-matrix elements. The interaction between the projectile and the target electrons is assumed to reduce to the instantaneous Coulomb interaction. The adopted numerical algorithm allows the calculation of differential and total cross sections for projectiles with kinetic energies ranging from the ionization threshold up to about ten times this value. Algorithm accuracy and stability are demonstrated by comparing differential cross sections calculated by our code with the distorting potential set to zero with equivalent results generated by a more robust code that uses the conventional plane-wave Born approximation. Sample calculation results are presented for ionization of K- and L-shells of various elements and compared with the available experimental data.

Inquiry for the π+- π− bound state conversion into two π0's as being due to the Weinberg π-π interaction

In this paper the decay of the pionium, i.e. the ( π + π −) bound state into π 0's, is studied, with the ππ interaction causing this transition described by the underlying Weinberg Lagrangian. The calculation with such a ππ-Lagrangian being carried out, the π-meson size r 0 emerges unavoidably to be drawn into consideration. The bound π + π − system itself is presumed to be due to the instantaneous Coulomb interaction and is treated as a consistently non-relativistic one, the Bethe-Salpeter equation being used. In the calculations the terms to the lowest orders in the fine structure constant α and the terms ∼ ln( r 0) are retained. The obtained pionium lifetime τ is thought to be compatible with conceivable future experimental data. The dependence of the results on the effective Lagrangian parameters is discussed. The investigation carried out tells us that it is the complete form of the genuine ππ-interaction that determines the pionium lifetime, not just simply the ππ scattering lengths. The inquiry into the pionium decay helps to ascertain the validity of the various ππ-interaction descriptions.

Coulomb-Gauge in QCD: Renormalization and Confinement

We review the Coulomb gauge in QCD and report some recent results. The minimal Coulomb gauge is defined and the fundamental modular region, a region without Gribov copies, is described. The Coulomb gauge action is expressed in terms of the dynamical degrees of freedom with an instantaneous Coulomb interaction, and its physical meaning is discussed. The local Coulomb gauge action with phase-space and ghost variables is derived, and its BRS-invariance and renormalizability are reviewed. It is shown that the instantanteous part $V(R)$ of $g^2 D_{00}(R, t)$, the time-time component of the gluon propagator, is a renormalization-group invariant $V(R) = f(R\Lambda_{QCD})/R$, and that the contribution of $V(R)$ to the Wilson loop exponentiates. It is conjectured that $V(R) \sim \kappa_{coul}R$ at large $R$, and that $\kappa_{coul}$ provides an order parameter for confinement of color even in the presence of dynamical quarks.

Calculating theQQ¯potential in(2+1)-dimensional light-front QCD

Pure glue QCD is formulated on a (2+1)-dimensional transverse lattice, using discrete light-front quantization. The transverse component of the gauge fields is taken to be compact, but in a linearized approximation with an effective potential. The (rest-frame) Q{bar Q} potential is evaluated numerically using Lanzcos matrix diagonalization. We first discuss the strong coupling limit analytically and then present numerical results beyond the strong coupling limit. The physical origin of confinement on a transverse lattice depends on the orientation of the external charges: For longitudinally separated charges, confinement arises from the instantaneous Coulomb interaction and for transversely separated quarks a string of link-fields forms. In the general case one obtains a superposition of both effects. Despite the asymmetry in the microscopic mechanism, already a very simple ansatz for the effective link-field potential provides an almost rotationally invariant Q{bar Q} potential. The momentum carried by the glue depends strongly on the orientation of the external charges, which might have observable consequences. {copyright} {ital 1997} {ital The American Physical Society}

Atomic Dirac-Fock-Breit self-consistent field calculations

The frequency-independent Breit interaction, which gives the leading correction to the instantaneous Coulomb interaction, is treated self-consistently in matrix Dirac–Fock–Breit self-consistent field (SCF) calculations. Calculations were done on He, He-like ions, Be, Be-like ions, Ne, and Ar. Basis sets of even- and well-tempered Gaussian functions were used to expand the large and small components of Dirac 4-spinors. The results of the variational calculations are compared with Desclaux's benchmark numerical perturbative calculations.

Erratum: Reduction of the Breit Coulomb equation to an equivalent Schrödinger equation, and investigation of the behavior of the wave function near the origin

The Breit equation for two equal-mass spin-1/2 particles interacting through an attractive Coulomb potential is separated into its angular and radial parts, obtaining coupled sets of first-order differential equations for the radial wave functions. The radial equations for the /sup 1/J/sub J/, /sup 3/J/sub J/, and /sup 3/P/sub 0/ states are further reduced to a single, one-dimensional Schroedinger equation with a relatively simple effective potential. No approximations, other than the initial one of an instantaneous Coulomb interaction, are made in deriving this equation; it accounts for all relativistic effects, as well as for mixing between different components of the wave function. Approximate solutions are derived for this Schroedinger equation, which gives the correct O(..cap alpha../sup 4/) term for the 1 /sup 1/S/sub 0/ energy and for the n/sup 1/J/sub J/ energies, for J>0. The radial equations for the /sup 3/(J +- 1)/sub J/ states are reduced to two second-order coupled equations. At small r, the Breit Coulomb wave functions behave as r/sup ..nu..//sup -1/, where ..nu.. is either ..sqrt..J(J+1)+1-..cap alpha../sup 2//4 or ..sqrt..J(J+1)-..cap alpha../sup 2//4 . The /sup 1/S/sub 0/ and /sup 3/P/sub 0/ wave functions therefore diverge at the origin as r/sup //sup ..sqrt..//sup 1-//sup ..cap alpha..//sup <2//4 -1$.more » This divergence of the J = 0 states, however, does not occur when the spin-spin interaction, -(..cap alpha../r)..cap alpha..x..cap alpha.., is added to the Coulomb potential.« less

Effect of dissipation on macroscopic quantum tunneling in thin superconducting wires

Macroscopic quantum tunnelings in thin superconducting wires are discussed within the framework of the time-dependent Ginzburg-Landau equation. The dissipation is described by introducing the reservoir oscillators of infinite degrees of freedom and eliminating them in the path integral representation of the partition function. The instantaneous Coulomb interaction is shown to maintain the charge neutrality due to a kind of Debye shielding in superconductors, according to which the formulation of the tunneling probability is greatly simplified. The derived temperature dependence of the tunneling rate is compatible with recently observed phenomena in thin indium wires near the critical temperature.

Virtual-pair effects in atomic structure theory.

A modified perturbation procedure for computing relativistic atomic bound-state energies is described, in which the instantaneous Coulomb interaction is included in the unperturbed QED Hamiltonian and the effect of virtual electron-positron pairs and of virtual transverse photons is treated as the perturbation. To illustrate the method in the context of a simple model, a one-electron atom is considered and a ``one-pair'' approximation is analyzed in detail. The approach is based on the resolvent-operator formulation of many-body time-independent perturbation theory. The removal of divergent vacuum-to-vacuum matrix elements is easily accomplished in this formulation, and it leads rather directly to the derivation of a modified Dirac equation in which all perturbative effects are contained in an effective one-electron potential. A set of integral equations for the evaluation of the effective potential in the one-pair model is derived. These equations have the same structure as the Dyson-Schwinger equations of covariant QED and serve a similar purpose. That is, they allow for the isolation of the divergent self-energy and vertex parts, leaving a finite kernel (the K matrix) which contains the effects of multiparticle intermediate states. In the one-pair model considered here the intermediate states consist of an electron and a virtual pair interacting Coulombically. It is shown that the K matrix can be constructed with the aid of a rigorous minimum principle of the Rayleigh-Ritz type. That such a minimum principle exists appears to be an advantage of the noncovariant Hamiltonian procedure. The inapplicability of standard renormalization methods is, however, a distinct disadvantage. While some progress (the removal of vacuum divergences and the isolation of divergent parts in the integral equation) is reported, a full resolution of the renormalization problem in the Hamiltonian formulation remains to be developed.