Conserving Approximations in Time-Dependent Density Functional Theory

In the present work we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid nineties. Due to this feature the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio

Global fixed point proof of time-dependent density-functional theory

We reformulate and generalize the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed point question for potentials on a given time-interval. We show that the unique fixed point, i.e. the unique potential generating a given density, is reached as the limiting point of an iterative procedure. The one-to-one correspondence between densities and potentials is a straightforward result provided that the response function of the divergence of the internal forces is bounded. The existence, i.e. the v-representability of a density, can be proven as well provided that the operator norms of the response functions of the members of the iterative sequence of potentials have an upper bound. The densities under consideration have second time-derivatives that are required to satisfy a condition slightly weaker than being square-integrable. This approach avoids the usual restrictions of Taylor-expandability in time of the uniqueness theorem by Runge and Gross [Phys.Rev.Lett.52, 997 (1984)] and of the existence theorem by van Leeuwen [Phys.Rev.Lett. 82, 3863 (1999)]. Owing to its generality, the proof not only answers basic questions in density-functional theory but also has potential implications in other fields of physics.Comment: 4 pages, 1 figur

Kadanoff-Baym approach to time-dependent quantum transport in AC and DC fields

We have developed a method based on the embedded Kadanoff-Baym equations to study the time evolution of open and inhomogeneous systems. The equation of motion for the Green's function on the Keldysh contour is solved using different conserving many-body approximations for the self-energy. Our formulation incorporates basic conservation laws, such as particle conservation, and includes both initial correlations and initial embedding effects, without restrictions on the time-dependence of the external driving field. We present results for the time-dependent density, current and dipole moment for a correlated tight binding chain connected to one-dimensional non-interacting leads exposed to DC and AC biases of various forms. We find that the self-consistent 2B and GW approximations are in extremely good agreement with each other at all times, for the long-range interactions that we consider. In the DC case we show that the oscillations in the transients can be understood from interchain and lead-chain transitions in the system and find that the dominant frequency corresponds to the HOMO-LUMO transition of the central wire. For AC biases with odd inversion symmetry odd harmonics to high harmonic order in the driving frequency are observed in the dipole moment, whereas for asymmetric applied bias also even harmonics have considerable intensity. In both cases we find that the HOMO-LUMO transition strongly mixes with the harmonics leading to harmonic peaks with enhanced intensity at the HOMO-LUMO transition energy.Comment: 16 pages, 9 figures. Submitted at "Progress in Nonequilibrium Green's Functions IV" conferenc

Correlation effects in bistability at the nanoscale: steady state and beyond

The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the non-equilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born (2B) and GW level. Assuming the existence of a steady-state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate if and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability.Comment: 13 pages, 12 figure

Optimising the multiplex factor of the frequency domain multiplexed readout of the TES-based microcalorimeter imaging array for the X-IFU instrument on the Athena Xray observatory

Athena is a space-based X-ray observatory intended for exploration of the hot and energetic universe. One of the science instruments on Athena will be the X-ray Integrated Field Unit (X-IFU), which is a cryogenic X-ray spectrometer, based on a large cryogenic imaging array of Transition Edge Sensors (TES) based microcalorimeters operating at a temperature of 100mK. The imaging array consists of 3800 pixels providing 2.5 eV spectral resolution, and covers a field of view with a diameter of of 5 arc minutes. Multiplexed readout of the cryogenic microcalorimeter array is essential to comply with the cooling power and complexity constraints on a space craft. Frequency domain multiplexing has been under development for the readout of TES-based detectors for this purpose, not only for the X-IFU detector arrays but also for TES-based bolometer arrays for the Safari instrument of the Japanese SPICA observatory. This paper discusses the design considerations which are applicable to optimise the multiplex factor within the boundary conditions as set by the space craft. More specifically, the interplay between the science requirements such as pixel dynamic range, pixel speed, and cross talk, and the space craft requirements such as the power dissipation budget, available bandwidth, and electromagnetic compatibility will be discussed

Rotation periods of late-type stars in the young open cluster IC 2602

We present the results of a monitoring campaign aimed at deriving rotation periods for a representative sample of stars in the young (30 Myr) open cluster IC 2602. Rotation periods were derived for 29 of 33 stars monitored. The periods derived range from 0.2d (one of the shortest known rotation periods of any single open cluster star) to about 10d (which is almost twice as long as the longest period previously known for a cluster of this age). We are able to confirm 8 previously known periods and derive 21 new ones, delineating the long period end of the distribution. Despite our sensitivity to longer periods, we do not detect any variables with periods longer than about 10d. The combination of these data with those for IC 2391, an almost identical cluster, leads to the following conclusions: 1) The fast rotators in a 30 Myr cluster are distributed across the entire 0.5 < B-V < 1.6 color range. 2) 6 stars in our sample are slow rotators, with periods longer than 6d. 3) The amplitude of variability depends on both the color and the period. The dependence on the latter might be important in understanding the selection effects in the currently available rotation period database and in planning future observations. 4) The interpretation of these data in terms of theoretical models of rotating stars suggests both that disk-interaction is the norm rather than the exception in young stars and that disk-locking times range from zero to a few Myr.Comment: 23 pages, 8 figures, accepted for publication in the Astrophysical Journa

Evidence for nonhadronic degrees of freedom in the transverse mass spectra of kaons from relativistic nucleus-nucleus collisions?

We investigate transverse hadron spectra from relativistic nucleus-nucleus collisions which reflect important aspects of the dynamics - such as the generation of pressure - in the hot and dense zone formed in the early phase of the reaction. Our analysis is performed within two independent transport approaches (HSD and UrQMD) that are based on quark, diquark, string and hadronic degrees of freedom. Both transport models show their reliability for elementary $pp$ as well as light-ion (C+C, Si+Si) reactions. However, for central Au+Au (Pb+Pb) collisions at bombarding energies above $\sim$ 5 A$\cdot$GeV the measured $K^{\pm}$ transverse mass spectra have a larger inverse slope parameter than expected from the calculation. Thus the pressure generated by hadronic interactions in the transport models above $\sim$ 5 A$\cdot$GeV is lower than observed in the experimental data. This finding shows that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential and temperature - is generated by strong partonic interactions in the early phase of central Au+Au (Pb+Pb) collisions.Comment: 4 pages, 3 figures,discussions extended, references added, to be published in Phys. Rev. Let

A deconvolution map-making method for experiments with circular scanning strategies

Aims. To investigate the performance of a deconvolution map-making algorithm for an experiment with a circular scanning strategy, specifically in this case for the analysis of Planck data, and to quantify the effects of making maps using simplified approximations to the true beams. Methods. We present an implementation of a map-making algorithm which allows the combined treatment of temperature and polarisation data, and removal of instrumental effects, such as detector time constants and finite sampling intervals, as well as the deconvolution of arbitrarily complex beams from the maps. This method may be applied to any experiment with a circular scanning-strategy. Results. Low-resolution experiments were used to demonstrate the ability of this method to remove the effects of arbitrary beams from the maps and to demonstrate the effects on the maps of ignoring beam asymmetries. Additionally, results are presented of an analysis of a realistic full-scale simulated data-set for the Planck LFI 30 GHz channel. Conclusions. Our method successfully removes the effects of the beams from the maps, and although it is computationally expensive, the analysis of the Planck LFI data should be feasible with this approach.Comment: 14 pages, 14 figures, accepte

Total energies from variational functionals of the Green function and the renormalized four-point vertex

We derive variational expressions for the grand potential or action in terms of the many-body Green function $G$ which describes the propagation of particles and the renormalized four-point vertex $\Gamma$ which describes the scattering of two particles in many-body systems. The main ingredient of the variational functionals is a term we denote as the $\Xi$-functional which plays a role analogously to the usual $\Phi$-functional studied by Baym (G.Baym, Phys.Rev. 127, 1391 (1962)) in connection with the conservation laws in many-body systems. We show that any $\Xi$-derivable theory is also $\Phi$-derivable and therefore respects the conservation laws. We further set up a computational scheme to obtain accurate total energies from our variational functionals without having to solve computationally expensive sets of self-consistent equations. The input of the functional is an approximate Green function $\tilde{G}$ and an approximate four-point vertex $\tilde{\Gamma}$ obtained at a relatively low computational cost. The variational property of the functional guarantees that the error in the total energy is only of second order in deviations of the input Green function and vertex from the self-consistent ones that make the functional stationary. The functionals that we will consider for practical applications correspond to infinite order summations of ladder and exchange diagrams and are therefore particularly suited for applications to highly correlated systems. Their practical evaluation is discussed in detail.Comment: 21 pages, 10 figures. Physical Review B (accepted

On the Kirzhnits gradient expansion in two dimensions

We derive the semiclassical Kirzhnits expansion of the D-dimensional one-particle density matrix up to the second order in $\hbar$. We focus on the two-dimensional (2D) case and show that all the gradient corrections both to the 2D one-particle density and to the kinetic energy density vanish. However, the 2D Kirzhnits expansion satisfies the consistency criterion of Gross and Proetto [J. Chem. Theory Comput. 5, 844 (2009)] for the functional derivatives of the density and the noninteracting kinetic energy with respect to the Kohn-Sham potential. Finally we show that the gradient correction to the exchange energy diverges in agreement with the previous linear-response study