Nonperturbative Treatment Research Articles

Complements to nonperturbative treatment of radiative damping effect in dielectronic recombination: Δn=2 transition in C IV

The primary purpose of the present work is to provide new refined results from nonperturbative treatment of the radiative damping effect in dielectronic recombination. The present results are used to test and confirm previously reported method [V. Stancalie, Phys. Plasmas 12, 043301 (2005)] taking full account of the electron collision and radiative processes in a consistent way, when radiation field is considered to all orders. This work refers to the 1s22s5s(S1) and 1s22p7s(P01) configurations, embedded in the electric dipole field of the 2s–2p core transition in Li-like C ion. Comparisons with previously reported results are shown. This data are believed to be the first demonstration of Δn=2 channel in dielectronic recombination of Li-like into Be-like C and are important in plasma diagnostics.

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2-106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.

Noncompact KK theory of gravity: Stochastic treatment for a nonperturbative inflaton field in a de Sitter expansion

We study a stochastic formalism for a nonperturbative treatment of the inflaton field in the framework of a noncompact Kaluza–Klein (KK) theory during an inflationary (de Sitter) expansion, without the slow-roll approximation.

Coherent Inelastic Backscattering of Intense Laser Light by Cold Atoms

We present a nonperturbative treatment of coherent backscattering of intense laser light from cold atoms and predict a nonvanishing backscattering signal even at very large intensities, due to the constructive (self-)interference of inelastically scattered photons.

Ab initiostudy of high-order harmonic generation ofH2+in intense laser fields: Time-dependent non-Hermitian Floquet approach

We present a time-dependent non-Hermitian Floquet approach for the precision three-dimensional nonperturbative calculations of high-order harmonic generation (HHG) rates of the hydrogen molecular ions subject to intense laser fields. The procedure involves an extension of the complex-scaling generalized pseudospectral method for nonuniform spatial discretization of the Hamiltonian and non-Hermitian time propagation of the time-evolution operator. The approach is designed for effective and high-precision nonperturbative treatment of high-order multiphoton processes in very intense and/or low-frequency laser fields, which are generally more difficult to treat using the conventional time-independent non-Hermitian Floquet matrix techniques. The method is applied to the multiphoton ionization (MPI) and HHG calculations of $\mathrm{H}_{2}{}^{+}$ for the wavelength $532\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ at the equilibrium internuclear separation $(R=2.0\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.})$ and several laser intensities, as well as at the laser intensity $5\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$ and various internuclear distances in the range between 3.0 and $17.5\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ We found that both the MPI and HHG rates are strongly dependent on $R$. Further, at some internuclear separations $R$, the HHG productions are strongly enhanced and this phenomenon can be attributed to the resonantly enhanced MPI at these $R$. Finally, the enhancement of higher harmonics is found to take place mainly at larger $R$. Detailed study of the correlation between the behavior of MPI and HHG phenomena is presented.

Non-perturbative flow equations from continuous unitary transformations

The goal of this thesis is the development and implementation of a non-perturbative solution method for Wegner's flow equations. We show that a parameterization of the flowing Hamiltonian in terms of a scalar function allows the flow equation to be rewritten as a nonlinear partial differential equation. The implementation is non-perturbative in that the derivation of the PDE is based on an expansion controlled by the size of the system rather than the coupling constant. We apply this method to the Lipkin model and obtain very accurate results for the spectrum, expectation values and eigenstates for all values of the coupling and in the thermodynamic limit. New aspects of the phase structure, made apparent by this non-perturbative treatment, are also investigated. The Dicke model is treated using a two-step diagonalization procedure which illustrates how an effective Hamiltonian may be constructed and subsequently solved within this framework.

Optimizing the photoassociation of cold atoms by use of chirped laser pulses

Photoassociation of ultracold atoms induced by chirped picosecond pulses is analyzed in a non-perturbative treatment by following the wavepackets dynamics on the ground and excited surfaces. The initial state is described by a Boltzmann distribution of continuum scattering states. The chosen example is photoassociation of cesium atoms at temperature T=54 $\mu K$ from the $a^3 \Sigma_u^+(6s,6s)$ continuum to bound levels in the external well of the $0_g^-(6s+6p_{3/2})$ potential. We study how the modification of the pulse characteristics (carrier frequency, duration, linear chirp rate and intensity) can enhance the number of photoassociated molecules and suggest ways of optimizing the production of stable molecules.

Nonperturbative Coulomb correlations generated by simultaneous excitation of excitonic and band-to-band continuum transitions

We investigate theoretically the nonlinear optical response of a semiconductor for excitation conditions where simultaneously all kinds of correlated two-pair transitions contribute to the dynamics. This includes transitions to biexcitons, exciton-exciton scattering states, two free electron-hole pairs as well as two-pair states involving an exciton and a free electron-hole pair. For certain excitation conditions two-pair correlations give rise to a complex line shape of four-wave-mixing spectra with an emission spread over the whole range between the exciton line and the band-edge. Even a strong suppression of the signal at the exciton line can be achieved while the emission is still concentrated between the exciton and the band-edge. The dependence of these features on the excitation conditions and on the strength of the Coulomb interaction is discussed. Comparing a nonperturbative treatment of the Coulomb interaction with the Born approximation and the mean-field theory clearly reveals the importance of nonperturbative Coulomb correlations even for excitations involving the continuum of free electron-hole pairs.

High-resolution degenerate four-wave-mixing spectroscopy of OH in a flame with a novel single-mode tunable laser

The first application of a novel single-mode tunable laser system to nonlinear spectroscopy is reported. The device uses a modeless dye laser, pumped by a single longitudinal mode (SLM) Q-switched Nd:YAG laser, as a narrow-bandwidth amplifier of the output of a SLM diode laser. The system provides pulses of 5-ns duration, 30-mJ energy and 165-MHz spectral line width tunable in the range 632–639 nm at 10-Hz repetition rate. The frequency-doubled output of the laser is used to record spectral line shapes of degenerate four wave mixing (DFWM) signals from the P1(15) line of the A2Σ–X2Π (0,0) band of OH in a methane/oxygen flame. Pressure broadening of the DFWM line shape is studied for the first time in a low-pressure flame and a pressure-broadening rate of 1.31±0.09×10-4 cm-1/Torr is derived from the data. Power-broadening effects are measured and compared with predictions of the standard perturbative model and of an analytical solution derived from a non-perturbative treatment of DFWM with arbitrary pump and probe intensities.

Dressed bosons theory for nuclear structure

The structure of nuclei of even number of nucleons is investigated in the boson-dynamic correlation model where valence-particle-excitation as well as core-excitation modes coexist. The model is nonperturbative and does not employ effective operators. The eigenstates of the model are the self-consistent solution of a set of nonlinear dynamical equations, which represents valence-particle pairs dressed by their interactions with the nuclear medium. The model is applied to medium mass as well as light nuclei. Our study of 18O reveals that the inclusion and the nonperturbative treatment of core excitations are the principal reasons for obtaining a correct ordering of the energy levels, a more complete spectrum and a much better agreement with the experimental low-lying as well as high-lying states than other published calculations. Our study of light nuclei 6He and 6Li shows that the halo formation in these nuclei is also a consequence of the excitation of the core protons and that halo can also be associated with valence proton–neutron pairs. The calculated matter distributions of these two nuclei reproduce well the differential cross sections obtained in proton elastic scattering experiments. The cluster-factorization method that expedites nonperturbative calculations is elucidated.

Nonperturbative treatment of medium-energy proton scattering under shadowing-blocking conditions in Al(110)

Measurements of the energy spectrum for 98 keV protons backscattered from Al(110) under shadowing-blocking conditions have been performed with high resolution. The corresponding energy losses at central collisions are dominated by ionization of the Al inner shells. In connection with coupled-channel calculations for the electronic energy loss in individual atomic collisions, we discuss the influence of higher-order effects and surface relaxation in the simulation of the strongly asymmetric surface peak.

PCT-Invariance of Generalized de Broglie-Bargmann-Wigner Equations

Generalized de Broglie-Bargmann-Wigner (GBBW)-equations are part of the derivation of effective theories for composite particles based on a nonlinear spinor field model with canonical quantization, relativistic invariant selfregularization and probability interpretation. Owing to the close connection between the model itself and its GBBW-equations the behavior of both is studied under PCT-transformations leading to the proof of invariance against such tranformation of the field Hamiltonian as well as of the GBBW-equations. Finally the algebraic formulation of the operators of these transformations in general state spaces is derived as the nonperturbative algebraic treatment of the model is referred to such spaces which are inequivalent to the Fock space representation of perturbation theory.

Asymptotic safety of gravity coupled to matter

Nonperturbative treatments of the UV limit of pure gravity suggest that it admits a stable fixed point with positive Newton's constant and cosmological constant. We prove that this result is stable under the addition of a scalar field with a generic potential and nonminimal couplings to the scalar curvature. There is a fixed point where the mass and all nonminimal scalar interactions vanish while the gravitational couplings have values which are almost identical to the pure gravity case. We discuss the linearized flow around this fixed point and find that the critical surface is four-dimensional. In the presence of other, arbitrary, massless minimally coupled matter fields, the existence of the fixed point, the sign of the cosmological constant and the dimension of the critical surface depend on the type and number of fields. In particular, for some matter content, there exist polynomial asymptotically free scalar potentials, thus providing a solution to the well-known problem of triviality.

Nonperturbative QCD treatment of $J/\Psi$ photoproduction

We present a nonperturbative QCD calculation of elastic $J/\psi$ meson production in photon-proton scattering at high energies. Using light cone wave functions of the photon and vector mesons, and the framework of the model of the stochastic QCD vacuum, we calculate the differential and integrated elastic cross sections for $\gamma p \goto J/\psi p $ . With an energy dependence following the two-pomeron model we are able to give a consistent description of the integrated cross sections and the differential cross sections at low $|t|$ in the range from 20 GeV up to the highest HERA energies. We discuss different approaches to introduce saturation and find no specific effects up to energies presently available. We also calculate and compare to experiments the cross section for $\upsilon$ photoproduction.

Coherent suppression of plasmon-phonon oscillations in a semiconductor using two ultrashort optical pulses

An ultrafast optical pulse can create an electron-hole plasma in the depletion layer of a polar semiconductor, such as GaAs, and excite plasmon-phonon modes. We show that another optical pulse, which arrives later, always suppresses the excited plasmon-phonon modes and the suppression rate varies dramatically with the delay. The energy of the oscillations transfers to free-streaming currents which are not sustained by any electric field. The free-streaming currents consist of counter-directed streams of the carriers created by the first and second pulses. Our predictions are based on an analytical solution of the coupled equations for plasmon-phonon modes with nonperturbative treatment of plasma density.

Problems with the use of line shifts in plasmas

In this work a nonperturbative semiclassical treatment with proper account of penetrating collisions and monopoles is used to illustrate the relative importance of penetration, close collisions and monopoles to the line shift. The main result of this work is that shifts are very sensitive, not linear in the density and even the sign of shifts may be affected by fairly fine effects, such as small deviations from thermal behavior.

Non-perturbative treatment of quantum dots coupled to light and phonons

We present an exact solution for the dynamics of a quantum dot (QD) coupled to phonons and excited by ultra-short light pulses. The solution is non-perturbative with respect to both carrier-phonon and carrier-light coupling, and accounts for an arbitrary number of pulses. Explicit expressions for the one and two pulse solutions are used to obtain the non-linear four-wave-mixing optical response by a single QD as well as by disordered QD arrays. Phonon emission by the excited QD is shown to be qualitatively different from that in the phonon assisted carrier relaxation.

Generalized Floquet Formulation of Time‐Dependent Density Functional Theory for Multiphoton Processes in Intense Laser Fields

AbstractWe present a short review article of recent new developments of Floquet formulations of time‐dependent density functional theory (TDDFT) for ab initio nonperturbative treatment of multiphoton and high‐order nonlinear optical processes of many‐electron quantum systems in intense laser fields. In the presence of monochromatic or polychromatic (multi‐color) time‐dependent fields, it is shown that the time‐dependent Kohn‐Sham equation can be exactly reformulated as a time‐independent generalized Floquet matrix eigenvalue problem. The theory has been extended to include the time‐dependent current density functional theory (TDCDFT) as well. In the case of bound‐free transition processes such as multiphoton ionization or dissociation, we show that the complex scaling transformation can be implemented into the Floquet formulation of TDDFT and TDCDFT, and the field‐induced complex quasienergy (dressed) states of many‐electron quantum systems can be determined by means of the solution of a time‐independent non‐Hermitian Floquet matrix eigenvalue problem. To facilitate the exploration of the constraints satisfied by the universal but unknown time‐dependent exchange‐correlation energy functionals, we develop several exact relations and theorems for the quasienergy functionals. Finally we present some initial applications of the Floquet‐TDDFT formalism for the study of multiphoton ionization of neutral atoms and electron angular distribution in multiphoton detachment of negative ions in intense laser fields. The Floquet‐TDDFT/TDCDFT formalism provides a powerful new theoretical foundation and feasible procedures for the exploration of many‐electron atomic and molecular physics in strong fields in the future.

The oblique pulsator model revisited

The oblique pulsator model accounts for most of the pulsation properties of the rapidly oscillating Ap (roAp) stars. The model predicts that modes are seen as equidistant multiplets separated by the angular frequency of rotation. The relative amplitudes of the components may be calculated and directly compared with observations. The effects of rotation introduce amplitude asymmetry, that is peaks corresponding to azimuthal numbers m and are unequal. In this paper we propose improvements to the model that consist of including effects of the centrifugal force and in using a non-perturbative treatment of the magnetic field influence. We show that in roAp stars the centrifugal force is the primary source of the rotational frequency shift. Although the amplitude asymmetry arises from the Coriolis force, its size is strongly affected by the centrifugal force. For dipole modes () we develop a simple geometrical picture of pulsation in the presence of rotation and a magnetic field. We provide some numerical results for a representative model of roAp stars which is applied to the case of HR 3831. We find that the mode that agrees with the observed amplitude ratios in this star significantly departs from alignment with the magnetic axis. We discuss problems posed by the observational data of HR 3831, emphasizing difficulties of the standard oblique pulsator model which assumes that the excited mode is nearly aligned with the magnetic field.

CP breaking in lattice chiral gauge theories

The CP symmetry is not manifestly implemented for the local and doubler-free Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify where the effects of this CP breaking appear. We show that they appear in: (I) Overall constant phase of the fermion generating functional. (II) Overall constant coefficient of the fermion generating functional. (III) Fermion propagator appearing in external fermion lines and the propagator connected to Yukawa vertices. The first effect appears from the transformation of the path integral measure and it is absorbed into a suitable definition of the constant phase factor for each topological sector; in this sense there appears no ``CP anomaly''. The second constant arises from the explicit breaking in the action and it is absorbed by the suitable weights with which topological sectors are summed. The last one in the propagator is inherent to this formulation and cannot be avoided by a mere modification of the projection operator, for example, in the framework of the Ginsparg-Wilson operator. This breaking emerges as an (almost) contact term in the propagator when the Higgs field, which is treated perturbatively, has no vacuum expectation value. In the presence of the vacuum expectation value, however, a completely new situation arises and the breaking becomes intrinsically non-local, though this breaking may still be removed in a suitable continuum limit. This non-local CP breaking is expected to persist for a non-perturbative treatment of the Higgs coupling.