arXiv subjects
Publications and source records attributed to D. Bauer.
We survey sufficient degree conditions, for a variety of graph properties, that are best possible in the same sense that Chvatal's well-known degree condition for hamiltonicity is best possible.
The influence of inner electrons on the ionization dynamics in strong laser fields is investigated in a wavelength regime where the inner electron dynamics is usually assumed to be negligible. The role of inner electrons is of particular interest for the application of frozen-core approximations and pseudopotentials in time-dependent density functional theory (TDDFT) and the single-active-electron (SAE) approximation in strong-field laser physics. Results of TDDFT and SAE calculations are compared with exact ones obtained by the numerical ab initio solution of the three-electron time-dependent Schrödinger equation for a lithium model atom. It is found that dynamical anti-screening, i.e., a particular form of dynamical core polarization, may substantially alter the ionization rate in the single-photon regime. Requirements for the validity of the approximations in the single and multiphoton ionization domain are identified.
The strong field approximation (SFA) formulated in terms of so-called "quantum orbits" led to much insight into intense-laser driven ionization dynamics. In plain SFA, the emitted electron is treated as a free electron in the laser field alone. However, with improving experimental techniques and more advanced numerical simulations it becomes more and more obvious that the plain SFA misses interesting effects even on a qualitative level. Examples are holographic side lobes, the low-energy structure, radial patterns in photoelectron spectra at low kinetic energies, and strongly rotated angular distributions. For this reason increasing effort has been recently devoted to Coulomb corrections of the SFA. In the current paper, we follow a similar line but consider ionization of metal clusters. It is known that photoelectrons from clusters can be much more energetic than those emitted from atoms or small molecules, especially if the Mie resonance of the expanding cluster is evoked. We develop a SFA that takes the collective field inside the cluster via the simple rigid-sphere model into account. Our approach is based on field-corrected quantum orbits so that the acceleration process (or any other spectral feature of interest) can be investigated in detail.
Favorably scaling numerical time-dependent many-electron techniques such as time-dependent density functional theory (TDDFT) with adiabatic exchange-correlation potentials typically fail in capturing highly correlated electron dynamics. We propose a method based on natural orbitals, i.e., the eigenfunctions of the one-body reduced density matrix, that is almost as inexpensive numerically as adiabatic TDDFT, but which is capable of describing correlated phenomena such as doubly excited states, autoionization, Fano profiles in the photoelectron spectra, and strong-field ionization in general. Equations of motion (EOM) for natural orbitals and their occupation numbers have been derived earlier. We show that by using renormalized natural orbitals (RNO) both can be combined into one equation governed by a hermitian effective Hamiltonian. We specialize on the two-electron spin-singlet system, known as being a "worst case" testing ground for TDDFT, and employ the widely used, numerically exactly solvable, one-dimensional helium model atom (in a laser field) to benchmark our approach. The solution of the full, nonlinear EOM for the RNO is plagued by instabilities, and resorting to linear response is not an option for the ultimate goal to study nonperturbative dynamics in intense laser fields. We therefore make two rather bold approximations: we employ the initial-state-"frozen" effective RNO Hamiltonian for the time-propagation and truncate the number of RNO to only two per spin. Surprisingly, it turns out that even with these strong approximations we obtain a highly accurate ground state, reproduce doubly-excited states, and autoionization.
As part of the Snowmass process, the Cosmic Frontier WIMP Direct Detection subgroup (CF1) has drawn on input from the Cosmic Frontier and the broader Particle Physics community to produce this document. The charge to CF1 was (a) to summarize the current status and projected sensitivity of WIMP direct detection experiments worldwide, (b) motivate WIMP dark matter searches over a broad parameter space by examining a spectrum of WIMP models, (c) establish a community consensus on the type of experimental program required to explore that parameter space, and (d) identify the common infrastructure required to practically meet those goals.
We study the ionization dynamics in intense laser-droplet interaction using three-dimensional, relativistic particle-in-cell simulations. Of particular interest is the laser intensity and frequency regime for which initially transparent, wavelength-sized targets are not homogeneously ionized. Instead, the charge distribution changes both in space and in time on a sub-cycle scale. One may call this the extreme nonlinear Mie-optics regime. We find that - despite the fact that the plasma created at the droplet surface is overdense - oscillating electric fields may penetrate into the droplet under a certain angle, ionize, and propagate in the just generated plasma. This effect can be attributed to the local field enhancements at the droplet surface predicted by standard Mie theory. The penetration of the fields into the droplet leads to the formation of a highly inhomogeneous charge density distribution in the droplet interior, concentrated mostly in the polarization plane. We present a self-similar, exponential fit of the fractional ionization degree which depends only on a dimensionless combination of electric field amplitude, droplet radius, and plasma frequency with only a weak dependence on the laser frequency in the overdense regime.
The Floquet theorem allows to reformulate periodic time-dependent problems such as the interaction of a many-body system with a laser field in terms of time-independent, field-dressed states, also known as Floquet states. If this was possible for density functional theory as well, one could reduce in such cases time-dependent density functional theory to a time-independent Floquet density functional theory. We analyze under which conditions the Floquet theorem is applicable in a density-functional framework. By employing numerical {\em ab initio} solutions of the interacting time-dependent Schrödinger equation with time-periodic external potentials we show that the exact effective potential in the corresponding Kohn-Sham equation is {\em not} unconditionally periodic. Whenever several Floquet states in the interacting system are involved in a physical process the corresponding Hartree-exchange-correlation potential is not periodic with the external frequency only. Using an analytically solvable example we demonstrate that, in general, the periodicity of the time-dependent Kohn-Sham Hamiltonian cannot be restored by choosing a different initial state. Only if the external periodic potential is sufficiently weak such that the initial state of the interacting system evolves adiabatically to a single, field-dressed state, the resulting Kohn-Sham system admits the application of the Floquet theorem.
We use a quantum trajectory-based semi-classical method to account for Coulomb interaction between the photoelectron and the parent ion in the classically forbidden, sub-barrier region during strong-field tunneling ionization processes. We show that---besides the well-known modification of the tunneling ionization probability---there is also an influence on the interference pattern in the photoelectron spectra. In the long-wavelength limit, the shift of the intra-cycle interference fringes caused by sub-barrier Coulomb effects in the laser polarization direction can be derived analytically. We compare our results with \emph{ab initio} solutions of the time-dependent Schrödinger equation and find good agreement in the long-wavelength regime, whereas the standard strong field approximation fails. We show that the nodal structure along low-order above-threshold ionization rings is also affected by sub-barrier Coulomb effects.
The screening of a 2p core-hole in Na clusters is investigated using density functional theory applied to an extended jellium model with an all-electron atom in the center. The study is related to recent experiments at the free electron laser at DESY in which photoelectron spectra from mass-selected, core-shell ionized metal clusters have been recorded. Relaxed and unrelaxed binding energies as well as Kohn-Sham orbital energies are calculated in Perdew-Zunger self-interaction-corrected exchange-only local spin-density approximation for valence and 2p core electrons in Na clusters up to 58 atoms. The relaxed binding energies follow approximately the metal-sphere behavior. The same behavior is seen in the experiment for sufficiently big clusters, indicating perfect screening and that the relaxation energy due to screening goes to the photoelectron. Instead, calculating the kinetic energy of the photoelectrons using unrelaxed binding energies or Kohn-Sham orbital energies yields wrong results for core-shell electrons. The screening {\em dynamics} are investigated using time-dependent density functional theory. It is shown that screening occurs on two time scales, a core-shell-dependent inner-atomic and an inter-atomic valence electron time scale. In the case of Na 2p ionization the remaining electrons in the 2p shell screen within tens of attoseconds while the screening due to cluster valence electrons occurs within several hundreds of attoseconds. The screening time-scales may be compared to the photon energy and cluster size-dependent escape times of the photoelectron in order to estimate whether the photoelectron is capable of picking up the relaxation energy or whether the residual system is left in an excited state.
We propose a method to obtain Floquet states---also known as light-induced states---and their quasi-energies from real-time wavefunctions without solving the Floquet equation. This is useful for the analysis of various phenomena in time-dependent quantum dynamics if the Hamiltonian is not strictly periodic, as in short laser pulses, for instance. There, the population of the Floquet states depends on the pulse form and is automatically contained in the real-time wavefunction but not in the standard Floquet approach. Several examples in the area of intense laser-atom interaction are exemplarily discussed: (i) the observation of even harmonics for an inversion-symmetric potential with a single bound state; (ii) the dependence of the population of Floquet states on (gauge) transformations and the emergence of an invariant, observable photoelectron spectrum; (iii) the driving of resonant transitions between dressed states, i.e., the dressing of dressed states, and (iv) spectral enhancements at channel closings due to the ponderomotive shift of above-threshold ionization peaks.
We prove a generalization of the van Leeuwen theorem towards quantum electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham construction for coupled quantized matter and electromagnetic fields. Thereby we circumvent the symmetry-causality problems associated with the action-functional approach to Kohn-Sham systems. We show that the effective external four-potential and four-current of the Kohn-Sham system are uniquely defined and that the effective four-current takes a very simple form. Further we rederive the Runge-Gross theorem for quantum electrodynamics.
The effects of intense electromagnetic fields on the decay of quasistationary states are investigated theoretically. We focus on the parameter regime of strong laser fields and nonlinear effects where an essentially nonperturbative description is required. Our approach is based on the imaginary time method previously introduced in the theory of strong-field ionization. Spectra and total decay rates are presented for a test case and the results are compared with exact numerical calculations. The potential of this method is confirmed by good quantitative agreement with the numerical results.
We study theorems giving sufficient conditions on the vertex degrees of a graph $G$ to guarantee $G$ is $t$-tough. We first give a best monotone theorem when $t\ge1$, but then show that for any integer $k\ge1$, a best monotone theorem for $t=\frac1k\le 1$ requires at least $f(k)\cdot|V(G)|$ nonredundant conditions, where $f(k)$ grows superpolynomially as $k\rightarrow\infty$. When $t<1$, we give an additional, simple theorem for $G$ to be $t$-tough, in terms of its vertex degrees.
We consider sufficient conditions for a degree sequence $π$ to be forcibly $k$-factor graphical. We note that previous work on degrees and factors has focused primarily on finding conditions for a degree sequence to be potentially $k$-factor graphical. We first give a theorem for $π$ to be forcibly 1-factor graphical and, more generally, forcibly graphical with deficiency at most $β\ge0$. These theorems are equal in strength to Chvátal's well-known hamiltonian theorem, i.e., the best monotone degree condition for hamiltonicity. We then give an equally strong theorem for $π$ to be forcibly 2-factor graphical. Unfortunately, the number of nonredundant conditions that must be checked increases significantly in moving from $k=1$ to $k=2$, and we conjecture that the number of nonredundant conditions in a best monotone theorem for a $k$-factor will increase superpolynomially in $k$. This suggests the desirability of finding a theorem for $π$ to be forcibly $k$-factor graphical whose algorithmic complexity grows more slowly. In the final section, we present such a theorem for any $k\ge2$, based on Tutte's well-known factor theorem. While this theorem is not best monotone, we show that it is nevertheless tight in a precise way, and give examples illustrating this tightness.
Experiments on atoms in intense laser pulses and the corresponding exact ab initio solutions of the time-dependent Schrödinger equation (TDSE) yield photoelectron spectra with low-energy features that are not reproduced by the otherwise successful work horse of strong field laser physics: the "strong field approximation" (SFA). In the semi-classical limit, the SFA possesses an appealing interpretation in terms of interfering quantum trajectories. It is shown that a conceptually simple extension towards the inclusion of Coulomb effects yields very good agreement with exact TDSE results. Moreover, the Coulomb quantum orbits allow for a physically intuitive interpretation and detailed analysis of all low-energy features in the semi-classical regime, in particular the recently discovered "low-energy structure" [C.I. Blaga et al., Nature Physics 5, 335 (2009) and W. Quan et al., Phys. Rev. Lett. 103, 093001 (2009)].
One of the major challenges of particle physics has been to gain an in-depth understanding of the role of quark flavor and measurements and theoretical interpretations of their results have advanced tremendously: apart from masses and quantum numbers of flavor particles, there now exist detailed measurements of the characteristics of their interactions allowing stringent tests of Standard Model predictions. Among the most interesting phenomena of flavor physics is the violation of the CP symmetry that has been subtle and difficult to explore. Till early 1990s observations of CP violation were confined to neutral $K$ mesons, but since then a large number of CP-violating processes have been studied in detail in neutral $B$ mesons. In parallel, measurements of the couplings of the heavy quarks and the dynamics for their decays in large samples of $K, D$, and $B$ mesons have been greatly improved in accuracy and the results are being used as probes in the search for deviations from the Standard Model. In the near future, there will be a transition from the current to a new generation of experiments, thus a review of the status of quark flavor physics is timely. This report summarizes the results of the current generation of experiments that is about to be completed and it confronts these results with the theoretical understanding of the field.
We investigate the existence and properties of effective potentials in time-dependent density functional theory. We outline conditions for a general solution of the corresponding Sturm-Liouville boundary value problems. We define the set of potentials and v-representable densities, give a proof of existence of the effective potentials under certain restrictions, and show the set of v-representable densities to be independent of the interaction.
The resonant interaction of laser light with atoms is analyzed from the time-dependent density functional theory perspective using a model Helium atom which can be solved exactly. It is found that in exact-exchange approximation the time-dependent dipole shows Rabi-type oscillations of its amplitude. However, the time-dependent density itself is not well described. These seemingly contradictory findings are analyzed. The Rabi-type oscillations are found to be essentially of classical origin. The incompatibility of time-dependent density functional theory with few-level approximations for the description of resonant dynamics is discussed.