Lowest-order Perturbation Theory Research Articles

Study of Multiple Quantum Beats in Atomic Wavepackets

A theoretical model consisting of 5 energy levels in coupled four-wave mixing processes was proposed to analyze the coherent characteristics of atomic wavepackets using perturbative theory. The equations of motions of the density matrix were derived and the third-order density matrix elements were presented. Under the condition that the duration of laser pulses is sufficiently short, the system response was treated as impulse response. Moreover, in the lowest order perturbation theory, the third-order nonlinear polarization was obtained using rotating-wave approximation. The results show that multiple quantum beats are embedded in the coupled four-wave mixing signals, and coherent dynamics of wavepackets can be retrieved from the quantum beat dynamics.

First-principles quantum transport with electron-vibration interactions: A maximally localized Wannier functions approach

We present an ab initio inelastic quantum transport approach based on maximally localized Wannier functions. Electronic-structure properties are calculated with density-functional theory in a planewave basis, and electron-vibration coupling strengths and vibrational properties are determined with density-functional perturbation theory. Vibration-induced inelastic transport properties are calculated with non-equilibrium Green's function techniques, which are based on localized orbitals. For this purpose we construct maximally localized Wannier functions. Our formalism is applied to investigate inelastic transport in a benzene molecular junction connected to mono-atomic carbon chains. In this benchmark system the electron-vibration self-energy is calculated either in the self-consistent Born approximation or by lowest-order perturbation theory. It is observed that upward and downward conductance steps occur, which can be understood using multi-eigenchannel scattering theory and symmetry conditions. In a second example where the mono-atomic carbon chain electrode is replaced by a (3; 3) carbon nanotube, we focus on the non-equilibrium vibration populations driven by the conducting electrons using a semi-classical rate equation.

Two-Photon Detachment Cross Section of the Positronium Negative Ion

The two-photon detachment cross section of positronium negative ion is calculated within the lowest-order perturbation theory for the final-state energies below the Ps(n = 2) threshold. A coupled-channel method with positronium orbital expansion is used to prepare the wavefunctions. The resonance structure below the threshold is clearly seen.

Pumping through a Luttinger liquid ring threaded by a time-varying magnetic field

We consider a quantum ring laterally connected to open one-dimensional leads described within the Luttinger liquid (LL) model and subject to a time-dependent driving magnetic field o(t ). The closed loop is obtained by connecting two points of the LL by a weak link, which is treated exactly to lowest order in perturbation theory. Analytical results for the current across the weak link, as well as in the external circuit and inside the loop, are obtained. We pay special attention to the case of smooth magnetic pulses such that the response of the system is approximately adiabatic. We find that the response to the flux o is linear only if o is a small fraction of a flux quantum o0. By inserting whole quanta, a current goes in the external wires as two bunches, separated by a time proportional to the length of the loop, and a net pumped current in the external wires is produced. This kind of pumping is consistent with the predictions of the corresponding tight-binding model in the uncorrelated limit, but is not destroyed by electron-electron interactions.

Chiral restoration effects on the shear viscosity of a pion gas

We investigate the shear viscosity of a pion gas in relativistic kinetic theory, using the Nambu-Jona-Lasinio model to construct the pion mass and the pi-pi interaction at finite temperature. Whereas at low temperatures the scattering properties and, hence, the viscosity are in agreement with lowest-order chiral perturbation theory, we find strong medium modifications in the crossover region. Here the system is strongly coupled and the scattering lengths diverge, similarly as for ultra-cold Fermi gases at a Feshbach resonance. As a consequence, the ratio eta/s is found to be strongly reduced as compared to calculations without medium-modified masses and scattering amplitudes. However, the quantitative results are very sensitive to the details of the applied approximations.

Application of discrete variable representation to planar ${\rm H}_2^+$H2+ in strong xuv laser fields

We present an efficient and accurate grid method to study the strong field dynamics of planar H(2)(+) under Born-Oppenheimer approximation. After introducing the elliptical coordinates to the planar H(2)(+), we show that the Coulomb singularities at the nuclei can be successfully overcome so that both bound and continuum states can be accurately calculated by the method of separation of variables. The time-dependent Schrödinger equation (TDSE) can be accurately solved by a two-dimensional discrete variable representation (DVR) method, where the radial coordinate is discretized with the finite-element discrete variable representation for easy parallel computation and the angular coordinate with the trigonometric DVR which can describe the periodicity in this direction. The bound states energies can be accurately calculated by the imaginary time propagation of TDSE, which agree very well with those computed by the separation of variables. We apply the TDSE to study the ionization dynamics of the planar H(2)(+) by short extreme ultra-violet (xuv) pulses, in which case the differential momentum distributions from both the length and the velocity gauge agree very well with those calculated by the lowest order perturbation theory.

Dynamics of Two- and Four-Boson Interactions in Dressed Vacuum States

We analyze the spatial and temporal dynamics of virtual particles in the vacuum states of the one-dimensional ϕ2- and ϕ4-model systems. The properties of the vacuum state for the ϕ2-system can be found analytically, which allows us to compute all spatial and temporal correlations exactly. For large spatial and temporal separations, the correlation functions approach a non-vanishing finite constant associated with the occurrence of multiple vacuum bubbles, in contradiction to lowest-order perturbation theory. Long-range inter-bubble correlations suggest that virtual particles can actually enhance the occurrence of another bubble due to stimulated emission. We argue that many of the vacuum’s properties can be explained in the usual particles terms.

Two-photon double ionization of He(1s2) and He(1s2s1S) by xuv short pulses

This paper addresses the problem of two-photon double ionization (TPDI) of He($1{s}^{2}$) and He($1s2{s}^{1}\phantom{\rule{-0.16em}{0ex}}S$). First, we reconsider TPDI of He($1{s}^{2}$) with a photon energy of 2.1 a.u.; it is well known that TPDI is mainly a sequential process, resulting in an electron spectrum dominated by two peaks. In the past, we have noticed that the peaks are shifted as the pulse duration shortens; they move toward each other. The first objective of the present work is to clarify the origin of the shift and to evaluate it quantitatively. In parallel with the resolution of the time-dependent Schr\odinger equation (TDSE), we have developed a model calculation based on lowest-order perturbation theory for the laser-atom interaction and for the atomic structure representation. The model agrees with TDSE calculations, and it also explains the physical origin of the shifts. Furthermore, it provides a quantitative evaluation of these shifts. The second objective of the present work is to extend our study to TPDI of He($1s2{s}^{1}\phantom{\rule{-0.16em}{0ex}}S$), which has received much less attention until now. We have investigated the cases of photon energies of 1.8 and 2.5 a.u. We show that TPDI is dominated by a sequential process where the first ionization leaves a remaining He${}^{+}(2s)$ ion, which is ionized by a second photon. As in the case of He($1{s}^{2}$), the model agrees with TDSE calculations, and it leads to better insights into the physics underlying the double-ionization process.

Lorentz gauge theory as a model of emergent gravity

We consider a class of Lorentz gauge gravity theories within Riemann-Cartan geometry that admits a topological phase in the gravitational sector. The dynamic content of such theories is determined only by the contortion part of the Lorentz gauge connection. We demonstrate that there is a unique Lagrangian that admits propagating spin-one mode in correspondence with gauge theories of other fundamental interactions. Remarkably, despite the ${R}^{2}$ type of the Lagrangian and noncompact structure of the Lorentz gauge group, the model possesses rather a positive-definite Hamiltonian. This has been proved in the lowest order of perturbation theory. This implies further consistent quantization and leads to renormalizable quantum theory. It is assumed that the proposed model describes possible mechanism of emergent Einstein gravity at very early stages of the Universe due to quantum dynamics of contortion.

Island of Stability for Consistent Deformations of Einstein’s Gravity

We construct deformations of general relativity that are consistent and phenomenologically viable, since they respect, in particular, cosmological backgrounds. These deformations have unique symmetries in accordance with their Minkowski cousins (Fierz-Pauli theory for massive gravitons) and incorporate a background curvature induced self-stabilizing mechanism. Self-stabilization is essential in order to guarantee hyperbolic evolution in and unitarity of the covariantized theory, as well as the deformation's uniqueness. We show that the deformation's parameter space contains islands of absolute stability that are persistent through the entire cosmic evolution.

Modelling large-scale halo bias using the bispectrum

We study the relation between the halo and matter density fields -- commonly termed bias -- in the LCDM framework. In particular, we examine the local model of biasing at quadratic order in the matter density. This model is characterized by parameters b_1 and b_2. Using an ensemble of N-body simulations, we apply several statistical methods to estimate the parameters. We measure halo and matter fluctuations smoothed on various scales and find that the parameters vary with smoothing scale. We argue that, for real-space measurements, owing to the mixing of wavemodes, no scale can be found for which the parameters are independent of smoothing. However, this is not the case in Fourier space. We measure halo power spectra and construct estimates for an effective large-scale bias. We measure the configuration dependence of the halo bispectra B_hhh and reduced bispectra Q_hhh for very large-scale k-space triangles. From this we constrain b_1 and b_2. Using the lowest-order perturbation theory, we find that for B_hhh the best-fit parameters are in reasonable agreement with one another as the triangle scale is varied, but that the fits become poor as smaller scales are included. The same is true for Q_hhh. The best-fit parameters depend on the discreteness correction. This led us to consider halo-mass cross-bispectra. The results from these statistics support our earlier findings. We develop a test to explore the importance of missing higher-order terms in the models. We prove that low-order expansions are not able to correctly model the data, even on scales k_1~0.04 h/Mpc. If robust inferences are to be drawn from galaxy surveys, then accurate models for the full nonlinear matter bispectrum and trispectrum will be essential.

Investigation of heavy–heavy pseudoscalar mesons in thermal QCD sum rules

We investigate the mass and decay constant of the heavy–heavy pseudoscalar, Bc, ηc and ηb mesons in the framework of finite-temperature QCD sum rules. The annihilation and scattering parts of spectral density are calculated in the lowest order of perturbation theory. Taking into account the additional operators arising at finite temperature, the nonperturbative corrections are also evaluated. The masses and decay constants remain unchanged under T≅100 MeV, but after this point, they start to diminish with increasing temperature. At critical or deconfinement temperature, the decay constants reach approximately 35% of their values in vacuum, while the masses are decreased about 7%, 12% and 2% for Bc, ηc and ηb states, respectively. The results at zero temperature are in good consistency with the existing experimental values as well as predictions of the other nonperturbative approaches.

Effective field theory and tunneling currents in the fractional quantum Hall effect

We review the construction of a low-energy effective field theory and its state space for “abelian” quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern–Simons theory in 2+1 dimensions on a manifold with boundary. In such a field theory, gauge invariance implies the presence of anomalous chiral modes localized on the edge of the sample. We assume a simple boundary structure, i.e., the absence of a reconstructed edge. For the bulk, we consider a multiply connected planar geometry. We study tunneling processes between two boundary components of the fluid and calculate the tunneling current to lowest order in perturbation theory as a function of dc bias voltage. Particular attention is paid to the special cases when the edge modes propagate at the same speed, and when they exhibit two significantly distinct propagation speeds. We distinguish between two “geometries” of interference contours corresponding to the (electronic) Fabry–Perot and Mach–Zehnder interferometers, respectively. We find that the interference term in the current is absent when exactly one hole in the fluid corresponding to one of the two edge components involved in the tunneling processes lies inside the interference contour (i.e., in the case of a Mach–Zehnder interferometer). We analyze the dependence of the tunneling current on the state of the quantum Hall fluid and on the external magnetic flux through the sample.

Formula omitted] Meson at Finite Temperature

In the present work, we investigate properties of B c meson in the basis of thermal QCD sum rules. The annihilation and scattering parts of spectral density are calculated in the lowest order of perturbation theory. Taking into account the additional operators arising at finite temperature and perturbative two-loop order α s correction to the spectral density, thermal QCD sum rule is obtained. In particular, the temperature dependence of the mass and leptonic decay constant of B c mesons are discussed. The obtained results show that at critical or deconfinement temperature, the decay constant decreases approximately 54%. The results at zero temperature are in a good consistency with the existing experimental values as well as predictions of the other nonperturbative approaches.

Entrainment by a rotating magnetic field of a ferrofluid contained in a cylinder

Entrainment by a rotating magnetic field of a ferrofluid contained in a cylinder is studied on the basis of spin-diffusion theory. The equations for flow velocity and spin velocity, coupled to Maxwell's equations of magnetostatics, are solved in first-harmonic approximation under the assumption that the magnetic field is small compared to the saturation magnetization. The solution leads to a coupled set of nonlinear integral equations, which can be solved numerically by iteration in a recursive scheme by use of the analytic lowest order perturbation theory solution as the initial state. At a critical applied field, the recursive scheme shows bifurcation. At sufficiently high field, the solution with the lower rate of dissipation shows flow in the direction opposite to the rotating applied field.

Ionization of water molecules by fast charged projectiles

Single-ionization cross sections of water molecules colliding with fast protons are calculated from lowest-order perturbation theory by taking all electrons and molecular orientations consistently into account. Explicit analytical formulas based on the peaking approximation are obtained for differential ionization cross sections with the partial contribution from the various electron orbitals accounted for. The results, which are in very good agreement with total and partial cross sections at high electron and projectile energies, display a strong variation on molecular orientation and molecular orbitals.

Spin dynamics in nonsequential two-photon double ionization of helium in an intense laser field

Nonsequential two-photon double ionization of a two-electron system (He and He-like ions) in a circularly polarized intense laser field is developed in a relativistic field theoretic way. Antisymmetry is maintained in the correlated wave functions of He in the initial state after modification to include Dirac spinor, and in the Volkov wave functions of the two electrons in the final free state. The present theory endeavors to provide an estimate of the helicity-dependent angular asymmetry in spin-current generation in nonsequential two-photon double ionization. Angular dependence of circular dichroism obtained in this paper, in coplanar and orthogonal geometries, is compared with the only existing nonrelativistic result obtained using lowest-order perturbation theory. Present result for dichroism underestimates the nonrelativistic result. Entanglement in the spins of the ejected electrons is concluded.

Strong-coupling approach to the Mott-Hubbard insulator on a Bethe lattice in dynamical mean-field theory

We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe lattice with infinite coordination number up to and including third order in the inverse Hubbard interaction. We employ the Kato--Takahashi perturbation theory to solve the self-consistency equation of the Dynamical Mean-Field Theory analytically for the single-impurity Anderson model in multi-chain geometry. The weight of the secondary Hubbard sub-bands is of fourth order so that the two-chain geometry is sufficient for our study. Even close to the Mott--Hubbard transition, our results for the Mott--Hubbard gap agree very well with those from numerical Dynamical Density-Matrix Renormalization Group (DDMRG) calculations. The density of states of the lower Hubbard band also agrees very well with DDMRG data, apart from a resonance contribution at the upper band edge which cannot be reproduced in low-order perturbation theory.

Nonlinear effects of phonon fluctuations on transport through nanoscale junctions

We analyze the effect of electron-phonon coupling on the full counting statistics of a molecular junction beyond the lowest order perturbation theory. Our approach allows to take into account analytically the feedback between the nonequilibrium phonon and electronic distributions in the quantum regime. We show that for junctions with high transmission and relatively weak electron-phonon coupling this feedback gives rise to increasingly higher nonlinearities in the voltage dependence of the cumulants of the transmitted charges distribution.

Space-time properties of a boson-dressed fermion for the Yukawa model

We analyze the interaction of fermions and bosons through a one-dimensional Yukawa model. We numerically compute the energy eigenstates that represent a physical fermion, which is a superposition of bare fermionic and bosonic eigenstates of the uncoupled Hamiltonian. It turns out that even fast bare fermions require only low-momentum dressing bosons, which attach themselves to the fast fermion through quantum correlations. We compare the space-time evolution of a physical fermion with that of its bare counterpart and show the importance of using dressed observables. The time evolution of the center of mass as well as the wave packet's spatial width suggests that the physical particle has a lower mass than the sum of the masses of its bare constituents. The numerically predicted dressed mass agrees with that from lowest-order perturbation theory as well as with the renormalized mass obtained from the corresponding Feynman graphs. For a given momentum, this lower mass leads to a faster physical particle and a different relativistic spreading behavior of the wave packet.