On the problem of mass-dependence of the two-point function of the real scalar free massive field on the light cone

We investigate the generally assumed inconsistency in light cone quantum field theory that the restriction of a massive, real, scalar, free field to the nullplane $\Sigma=\{x^0+x^3=0\}$ is independent of mass \cite{LKS}, but the restriction of the two-point function depends on it (see, e.g., \cite{NakYam77, Yam97}). We resolve this inconsistency by showing that the two-point function has no canonical restriction to $\Sigma$ in the sense of distribution theory. Only the so-called tame restriction of the two-point function exists which we have introduced in \cite{Ull04sub}. Furthermore, we show that this tame restriction is indeed independent of mass. Hence the inconsistency appears only by the erroneous assumption that the two-point function would have a (canonical) restriction to $\Sigma$.Comment: 10 pages, 2 figure

Nonuniqueness in spin-density-functional theory on lattices

In electronic many-particle systems, the mapping between densities and spin magnetizations, {n(r), m(r)}, and potentials and magnetic fields, {v(r), B(r)}, is known to be nonunique, which has fundamental and practical implications for spin-density-functional theory (SDFT). This paper studies the nonuniqueness (NU) in SDFT on arbitrary lattices. Two new, non-trivial cases are discovered, here called local saturation and global noncollinear NU, and their properties are discussed and illustrated. In the continuum limit, only some well-known special cases of NU survive.Comment: 4 pages, 1 figur

Ionization of hydrogen by ion impact in the presence of a laser field resonant to bound–bound atomic transitions

We study the impact ionization of atomic hydrogen in collisions with fast ions assisted by the pulse of a weak laser field with a sub-nanosecond duration (T ~ 10−10 s). The field is linearly polarized and its frequency is resonant to the 1s–2p hydrogen transitions. We consider the field-assisted impact ionization by using a simple model in which the interaction between the atom and the resonant field is described in the rotating-wave approximation and the interaction of the field-dressed atom with the ion is treated using the continuum-distorted-wave-eikonal-initial-state approach. Our consideration for 1 MeV u−1 C6+–hydrogen collisions shows that the presence of the laser field can have a profound effect on all aspects of the impact ionization, including the angular and energy distributions of the emitted electrons, the total ionization cross section and the projectile scattering

Cluster ionization via two-plasmon excitation

We calculate the two-photon ionization of clusters for photon energies near the surface plasmon resonance. The results are expressed in terms of the ionization rate of a double plasmon excitation, which is calculated perturbatively. For the conditions of the experiment by Schlipper et al., we find an ionization rate of the order of 0.05-0.10 fs^(-1). This rate is used to determine the ionization probability in an external field in terms of the number of photons absorbed and the duration of the field. The probability also depends on the damping rate of the surface plasmon. Agreement with experiment can only be achieved if the plasmon damping is considerably smaller than its observed width in the room-temperature single-photon absorption spectrum.Comment: 17 pages and 6 PostScript figure

Time-dependent density-matrix functional theory for biexcitonic phenomena

We formulate a time-dependent density-matrix functional theory (TDDMFT) approach for higher-order correlation effects like biexcitons in optical processes in solids based on the reduced two-particle density-matrix formalism within the normal orbital representation. A TDDMFT version of the Schr\"odinger equation for biexcitons in terms of one- and two-body reduced density matrices is derived, which leads to finite biexcitonic binding energies already with an adiabatic approximation. Biexcitonic binding energies for several bulk semiconductors are calculated using a contact biexciton model

Time-Dependent Density Functional Theory of Open Quantum Systems in the Linear-Response Regime

Time-Dependent Density Functional Theory (TDDFT) has recently been extended to describe many-body open quantum systems (OQS) evolving under non-unitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a non-interacting open Kohn-Sham system yielding the correct non-equilibrium density evolution. A pseudo-eigenvalue equation analogous to the Casida equations of usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C$^{2+}$ atom in an optical resonator interacting with a bath of photons. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on Gorling-Levy perturbation theory is calculated.Comment: 18 pages, 4 figure

Co-regularised support vector regression

We consider a semi-supervised learning scenario for regression, where only few labelled examples, many unlabelled instances and different data representations (multiple views) are available. For this setting, we extend support vector regression with a co-regularisation term and obtain co-regularised support vector regression (CoSVR). In addition to labelled data, co-regularisation includes information from unlabelled examples by ensuring that models trained on different views make similar predictions. Ligand affinity prediction is an important real-world problem that fits into this scenario. The characterisation of the strength of protein-ligand bonds is a crucial step in the process of drug discovery and design. We introduce variants of the base CoSVR algorithm and discuss their theoretical and computational properties. For the CoSVR function class we provide a theoretical bound on the Rademacher complexity. Finally, we demonstrate the usefulness of CoSVR for the affinity prediction task and evaluate its performance empirically on different protein-ligand datasets. We show that CoSVR outperforms co-regularised least squares regression as well as existing state-of-the-art approaches for affinity prediction

Time-dependent electron transport through a strongly correlated quantum dot: multiple-probe open boundary conditions approach

We present a time-dependent study of electron transport through a strongly correlated quantum dot. The time-dependent current is obtained with the multiple-probe battery method, while adiabatic lattice density functional theory in the Bethe ansatz local-density approximation to the Hubbard model describes the dot electronic structure. We show that for a certain range of voltages the quantum dot can be driven into a dynamical state characterized by regular current oscillations. This is a manifestation of a recently proposed dynamical picture of Coulomb blockade. Furthermore, we investigate how the various approximations to the electron-electron interaction affect the line-shapes of the Coulomb peaks and the I-V characteristics. We show that the presence of the derivative discontinuity in the approximate exchange-correlation potential leads to significantly different results compared to those obtained at the simpler Hartree level of description. In particular, a negative differential conductance (NDC) in the I-V characteristics is observed at large bias voltages and large Coulomb interaction strengths. We demonstrate that such NDC originates from the combined effect of electron-electron interaction in the dot and the finite bandwidth of the electrodes.Comment: 10 pages, 7 figure