Terms Of Perturbation Theory Research Articles

Cluster approach to the charge density plateaux int–J ladders

We study the ground state properties of thet–J model on two and three leg ladders. The phase diagram of the anisotropic couplingsalong the rungs and legs is investigated to find the opening of a charge transfergap which appears as a charge density plateau. In a perturbative approach westart from isolated rungs at zero leg couplings. Then the stability of the chargedensity plateau is examined by first order perturbation theory in terms of aneffective Hamiltonian using the numerical Lanczos method on finite size ladders. Theresults of this approach are compared with the exact diagonalization of finitesystems. We have found that an improvement of our results depends on the initialclusters for zeroth order perturbation which cannot be recovered by higher orderperturbation in rung clusters. For the two leg ladder case the application of 4-site(2 × 2) plaquettes helped us to overcome earlier flaws when the charge density is greater thanone-half. We have also addressed the generalization of our method to trace phaseseparation in this model, where a linear dependence of ground state energy versus chargedensity gives evidence of a phase separated state.

Massless Boundary Sine-Gordon Model Coupled to External Fields

We investigate a generalization of the massless boundary sine-Gordon model with conformal invariance, which has been used to describe an array of D-branes (or rolling tachyon). We consider a similar action whose couplings are replaced with external fields depending on the boundary coordinate. Even in the presence of the external fields, this model is still solvable, though it does not maintain the whole conformal symmetry. We obtain, to all orders in perturbation theory in terms of the external fields, a simpler expression of the boundary state and the disc partition function. As a by-product, we fix the relation between the bare couplings and the renormalized couplings which has been appeared in papers on tachyon lump and rolling tachyon.

Low x particle spectra in the modified leading logarithm approximation

We show that the higher moments of the evolution obtained from the Modified Leading Logarithm Approximation may be regarded as spurious higher order terms in perturbation theory, and that neglecting them leads to a good description of the data around and above the peak in $\xi=\ln (1/x)$. Furthermore, we use this study of the moments to show that at high energy the Limiting Spectrum with Local Parton-Hadron Duality may also be derived from the Modified Leading Logarithm Approximation without any non-perturbative assumptions.

High‐Temperature Heat Capacity and Lattice Anharmonicity of LiGaO2.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Irreducible Brillouin conditions and contracted Schrödinger equations for n-electron systems. IV. Perturbative analysis.

The k-particle irreducible Brillouin conditions IBCk and the k-particle irreducible contracted Schrödinger equations ICSEk for a closed-shell state are analyzed in terms of a Møller-Plesset-type perturbation expansion. The zeroth order is Hartree-Fock. From the IBC2(1), i.e., from the two-particle IBC to first order in the perturbation parameter mu, one gets the leading correction lambda2(1) to the two-particle cumulant lambda2 correctly. However, in order to construct the second-order energy E(2), one also needs the second-order diagonal correction gammaD(2) to the one-particle density matrix gamma. This can be obtained: (i) from the idempotency of the n-particle density matrix, i.e., essentially from the requirement of n-representability; (ii) from the ICSE1(2); or (iii) by means of perturbation theory via a unitary transformation in Fock space. Method (ii) is very unsatisfactory, because one must first solve the ICSE3(2) to get lambda3(2), which is needed in the ICSE2(2) to get lambda2(2), which, in turn, is needed in the ICSE1(2) to get gamma(2). Generally the (k+1)-particle approximation is needed to obtain Ek correctly. One gains something, if one replaces the standard hierarchy, in which one solves the ICSEk, ignoring lambda(k+1) and lambda(k+2), by a renormalized hierarchy, in which only lambda(k+2) is ignored, and lambda(k+1) is expressed in terms of the lambdap of lower particle rank via the partial trace relation for lambda(k+2). Then the k-particle approximation is needed to obtain E(k) correctly. This is still poorer than coupled-cluster theory, where the k-particle approximation yields E(k+1). We also study the possibility to use some simple necessary n-representability conditions, based on the non-negativity of gamma(2) and two related matrices, in order to get estimates for gammaD(2) in terms of lambda2(1). In general these estimates are rather weak, but they can become close to the best possible bounds in special situations characterized by a very sparse structure of lambda2 in terms of a localized representation. The perturbative analysis does not encourage the use of a k-particle hierarchy based on the ICSEk (or on their reducible counterparts, the CSEk), it rather favors the approach in terms of the unitary transformation, where the k-particle approximation yields the energy correct up to E(2k-1). The problems that arise are related to the unavoidable appearance of exclusion-principle violating cumulants. The good experience with perturbation theory in terms of a unitary transformation suggests that one should abandon a linearly convergent iteration scheme based on the ICSEk hierarchy, in favor of a quadratically convergent one based on successive unitary transformations.

Irreducible Brillouin conditions and contracted Schrödinger equations for n-electron systems. III. Systems of noninteracting electrons.

We analyze the structure and the solutions of the irreducible k-particle Brillouin conditions (IBCk) and the irreducible contracted Schrödinger equations (ICSEk) for an n-electron system without electron interaction. This exercise is very instructive in that it gives one both the perspective and the strategies to be followed in applying the IBC and ICSE to physically realistic systems with electron interaction. The IBC1 leads to a Liouville equation for the one-particle density matrix gamma1=gamma, consistent with our earlier analysis that the IBC1 holds both for a pure and an ensemble state. The IBC1 or the ICSE1 must be solved subject to the constraints imposed by the n-representability condition, which is particularly simple for gamma. For a closed-shell state gamma is idempotent, i.e., all natural spin orbitals (NSO's) have occupation numbers 0 or 1, and all cumulants lambdak with k> or =2 vanish. For open-shell states there are NSO's with fractional occupation number, and at the same time nonvanishing elements of lambda2, which are related to spin and symmetry coupling. It is often useful to describe an open-shell state by a totally symmetric ensemble state. If one wants to treat a one-particle perturbation by means of perturbation theory, this mainly as a run-up for the study of a two-particle perturbation, one is faced with the problem that the perturbation expansion of the Liouville equation gives information only on the nondiagonal elements (in a basis of the unperturbed states) of gamma. There are essentially three possibilities to construct the diagonal elements of gamma: (i) to consider the perturbation expansion of the characteristic polynomial of gamma, especially the idempotency for closed-shell states, (ii) to rely on the ICSE1, which (at variance with the IBC1) also gives information on the diagonal elements, though not in a very efficient manner, and (iii) to formulate the perturbation theory in terms of a unitary transformation in Fock space. The latter is particularly powerful, especially, when one wishes to study realistic Hamiltonians with a two-body interaction.

High‐temperature heat capacity and lattice anharmonicity of LiGaO2

AbstractThe first three even moments of the phonon density of states of LiGaO2 and the anharmonic contribution to the heat capacity at constant volume of the compound are estimated from experimental heat capacity data. The effect of lattice anharmonicity is discussed in terms of perturbation theory. The temperature dependent principal Grüneisen functions of LiGaO2 are calculated. The results obtained for LiGaO2 are compared with existing literature for other ternary lithium compounds. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Internal nonlinear resonance of charged drop capillary oscillations in a dielectric medium at multimode initial deformation of the interface

An analytical expression for the generatrix of the shape of a nonlinearly vibrating charged drop of a perfect incompressible conducting fluid immersed in an ideal incompressible dielectric medium is found in the second order of smallness in terms of perturbation theory. The drop experiences multimode initial deformation. The expression contains resonant (small-denominator) terms. With the effect of the environment taken into account, the number of resonant situations becomes dependent on the drop-to-environment density ratio and the resonant self-charge of the drop changes. It is shown that nonlinear vibrations may be of resonant character even if the charge of the drop is far away from exact resonant values. This is because Rayleigh subcritical values of the self-charge affect the frequencies of higher vibration modes insignificantly.

The short-wave limit for nonlinear, symmetric, hyperbolic systems

For general semilinear or quasilinear symmetric, hyperbolic systems, the short-wave approximation is studied by constructing approximate solutions to the initial-value problem associated with the hyperbolic operator by means of a multiscale WKB expansion. In the diffractive optics regime, the components of the leading-order terms of the approximate solutions are shown to satisfy differential equations of KP type. Whether these equations are scalar or not depends on the polarization of the initial datum and on the asymptotic behavior of the branches of the characteristic variety of the hyperbolic operator. The asymptotic stability of the approximate solution is proved. Following J.-L. Joly, G. Métivier, and J. Rauch, the cornerstone of this study is the characteristic variety of the hyperbolic operator. It is examined here in terms of perturbation theory, which yields new proofs of the so-called algebraic lemmas of geometric optics.

Many-Electron Problem in Terms of the Density: From Thomas–Fermi to Modern Density-Functional Theory

In this paper we focus on the use of electron density and current-density as basic variables in describing a many-electron system. We start with a discussion of the seminal Thomas–Fermi theory and its extension by Bloch for time-dependent hamiltonians. We then present modern density-functional theory (for both time-independent and time-dependent hamiltonians) and approximations involved in implementing it. Also discussed is perturbation theory in terms of electron density and its use for calculating various response properties and related quantities. In particular, van der Waals coefficient C6is calculated using density and current density in time-dependent perturbation theory. Throughout the paper, results for alkali-metal clusters are presented to demonstrate the strength of density-based theories.

Analysis of an unstable particle with the maximum entropy method inO(4)φ4theory on the lattice

We explore applications of the maximum entropy method (MEM) to determine properties of unstable particles using the four-dimensional O(4) $\phi^4$ theory as a laboratory. The spectral function of the correlation function of the unstable $\sigma$ particle is calculated with MEM, and shown to yield reliable results for both the mass of $\sigma$ and the energy of the two-pion state. Calculations are also made for the case in which $\sigma$ is stable. Distinctive differences in the volume dependence of the $\sigma$ mass and two-pion energy for the stable and unstable cases are analyzed in terms of perturbation theory.

Two-slit interference in strong-field photodetachment of H−

The evolution of multiphoton detachment of H− with laser intensity reveals striking interference features in the angular distribution of the detached photoelectrons. Using femtosecond infrared laser pulses we show that the two-photon detachment angular distribution changes from a d-wave pattern, predicted in terms of perturbation theory in the limit of low intensities, to preferential emission perpendicular to the laser polarization at higher intensities, when the electron energy decreases due to the ponderomotive shift. At intensities where the two-photon channel closes and the electron energy approaches zero, the expected s-wave distribution is observed, as required by the Wigner threshold law. We discuss these observations in terms of the analytical KFR-type theory proposed by Gribakin and Kuchiev. Their saddle-point analysis has recently been shown to quantitatively predict the electron spectra for photodetachment of H− in a strong laser field. Here we discuss an intuitive two-slit interference picture predicted by this theory in the limit of low electron energies.

Deeply virtual Compton scattering off nuclei

We consider the hard leptoproduction of a photon off nuclei up to spin-1. As a new result we present here the general azimuthal angular dependence of the differential cross section for a spin-1 target. Its twist-two Fourier coefficients of the interference and squared deeply virtual Compton scattering amplitude are evaluated in leading order approximation of perturbation theory in terms of generalized parton distributions, while the pure Bethe--Heitler cross section is exactly calculated in terms of electromagnetic form factors. Relying on a simple model for the nucleon generalized parton distribution $H$, which describes the existing DVCS data for a proton target, we estimate the size of unpolarized cross sections, beam and longitudinal target spin as well as unpolarized charge asymmetries for present fixed target experiments with nuclei. These estimates are confronted with preliminary HERMES data for deuterium and neon.

Nonperturbative effects from the resummation of perturbation theory

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect I argue that the nonperturbative effect associated with the perturbation theory should have a branch cut only along the positive real axis in the complex coupling plane. The component in the weak coupling expansion of the nonperturbative amplitude that gives rise to the branch cut can be calculated in principle from the perturbation theory combined with the exactly calculable properties of the nonperturbative effect. The realization of this mechanism is demonstrated in the double well potential and the two-dimensional $O(N)$ nonlinear sigma model. In these models the leading term in the weak coupling expansion of the nonperturbative effect can be obtained with a good accuracy from the first terms of perturbation theory. Applying this mechanism to the infrared renormalon induced nonperturbative effect in QCD, I suggest some of the QCD condensate effects can be calculated in principle from the perturbation theory.

Schr$ouml$dinger equation for joint bidirectional motion in time

The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the description of joint, and interactive, forward and backward time evolution within a physical system. [...] Three applications are studied: (1) a formal theory of collisions in terms of perturbation theory; (2) a relativistically invariant quantum field theory for a system that kinematically comprises the direct sum of two quantized real scalar fields, such that one field evolves forward and the other backward in time, and such that there is dynamical coupling between the subfields; (3) an argument that in the latter field theory, the dynamics predicts that in a range of values of the coupling constants, the expectation value of the vacuum energy of the universe is forced to be zero to high accuracy. [...]

Condensates in quantum chromodynamics

The paper presents the short review of our to-day knowledge of vacuum condensates in QCD. The condensates are defined as vacuum averages of the operators which arise due to nonperturbative effects. The important role of condensates in determination of physical properties of hadrons and of their low-energy interactions in QCD is underlined. The special value of quark condensate, connected with the existence of baryon masses is mentioned. Vacuum condensates induced by external fields are discussed. QCD at low energy is checked on the basis of the data on hadronic tau-decay. In the theoretical analysis the terms of perturbation theory (PT) up to alpha^3_s are accounted, in the operator product expansion (OPE) - those up to dimension 8. The total probability of the decay tau->hadrons (with zero strangeness) and of the tau-decay structure functions are best described at alpha_s(m^2_tau) = 0.330+-0.025. It is shown that the Borel sum rules for tau-decay structure functions along the rays in the q^2-complex plane are in agreement with the experiment with the accuracy ~2% at the values of the Borel parameter |M^2|> 0.8 GeV^2. The magnitudes of dimensions 6 and 8 condensates were found and the limitations on gluonic condensates were obtained. The sum rules for the charmed quark vector currents polarization operator was analysed in 3 loops (i.e., in order alpha^2_s). The value of charmed quark mass (in MS-bar regularization scheme) was found to be: m_c(m_c) = 1.275+-0.015 GeV and the value of gluonic condensate was estimated: <(alpha_s/pi)G^2> = 0.009+-0.007 GeV^4. The general conclusion is: QCD described by PT + OPE is in a good agreement with experiment at Q^2 >~ 1 GeV^2.

Quantum field theory of dilute homogeneous Bose-Fermi mixtures at zero temperature: General formalism and beyond mean-field corrections

We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We introduce a new relevant object, the renormalized boson-fermion T-matrix which we determine to second order in the boson-fermion s-wave scattering length. We also discuss how to incorporate the usual boson-boson T-matrix in mean-field approximation to obtain the total ground state properties of the system. The next order term beyond mean-field stems from the boson-fermion interaction and is proportional to $a_{\scriptsize BF}k_{\scriptsize F}$. The total ground-state energy-density reads $E/V = \epsilon_{\scriptsize F} + \epsilon_{\scriptsize B} + (2\pi\hbar^{2}a_{\rm BF}n_{\scriptsize B}n_{\scriptsize F}/m) [1 + a_{\scriptsize BF}k_{\scriptsize F}f(\delta)/\pi]$. The first term is the kinetic energy of the free fermions, the second term is the boson-boson mean-field interaction, the pre-factor to the additional term is the usual mean-field contribution to the boson-fermion interaction energy, and the second term in the square brackets is the second-order correction, where $f(\delta)$ is a known function of $\delta= (m_{\scriptsize B} - m_{\scriptsize F})/(m_{\scriptsize B} + m_{\scriptsize F})$. We discuss the relevance of this new term, how it can be incorporated into existing theories of boson-fermion mixtures, and its importance in various parameter regimes, in particular considering mixtures of $^{6}$Li and $^{7}$Li and of $^{3}$He and $^{4}$He.

The Effect of Substituents on the Thermochemical Properties of Alternant Radicals

The effect of substituents on the dissociation energy of the C—H bond in the molecules of mono- and disubstituted toluenes was analyzed in terms of perturbation theory. It was shown that the variation of the thermochemical characteristics in the alternant radicals is described in second-order perturbation theory by a quadratic dependence on the substituent constants.

Enhanced resonant backscattering of light from quantum-well excitons

The angle-dependent resonant Rayleigh scattering of light from excitons in a disordered quantum well is studied theoretically. An enhancement of the scattered intensity peaked on the backscattering direction is predicted, for values of the parameters corresponding to realistic GaAs/AlGaAs heterostructures. It is shown that this effect can be isolated by measuring the differential enhancement between two different scattering directions. An analysis in terms of perturbation theory provides a simple analytical approximation of the measurable quantity.

Glueballs in a Hamiltonian light-front approach to pure-glue QCD

We calculate a renormalized Hamiltonian for pure-glue QCD and diagonalize it. The renormalization procedure is designed to produce a Hamiltonian that will yield physical states that rapidly converge in an expansion in free-particle Fock-space sectors. To make this possible, we use light-front field theory to isolate vacuum effects, and we place a smooth cutoff on the Hamiltonian to force its free-state matrix elements to quickly decrease as the difference of the free masses of the states increases. The cutoff violates a number of physical principles of light-front pure-glue QCD, including Lorentz covariance and gauge covariance. This means that the operators in the Hamiltonian are not required to respect these physical principles. However, by requiring the Hamiltonian to produce cutoff-independent physical quantities and by requiring it to respect the unviolated physical principles of pure-glue QCD, we are able to derive recursion relations that define the Hamiltonian to all orders in perturbation theory in terms of the running coupling. We approximate all physical states as two-gluon states, and use our recursion relations to calculate to second order the part of the Hamiltonian that is required to compute the spectrum. We diagonalize the Hamiltonian using basis-function expansions for the gluons' color, spin, and momentum degrees of freedom. We examine the sensitivity of our results to the cutoff and use them to analyze the nonperturbative scale dependence of the coupling. We investigate the effect of the dynamical rotational symmetry of light-front field theory on the rotational degeneracies of the spectrum and compare the spectrum to recent lattice results. Finally, we examine our wave functions and analyze the various sources of error in our calculation.