Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What is Missing in, and Corrections to, the TD-DFT Adiabatic Approximation

In their famous paper Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of $N$ interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays however the realization that Nature is not always so nearsighted has driven us up Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very much like what the local density approximation (LDA) is to conventional ground-state DFT. While some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this article will focus on many-body corrections to LR-TD-DFT as one way to building hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.Comment: 56 pages, 17 figure

Nonlinear dynamics of flexural wave turbulence

The Kolmogorov-Zakharov spectrum predicted by the Weak Turbulence Theory remains elusive for wave turbulence of flexural waves at the surface of an thin elastic plate. We report a direct measurement of the nonlinear timescale $T_{NL}$ related to energy transfer between waves. This time scale is extracted from the space-time measurement of the deformation of the plate by studying the temporal dynamics of wavelet coefficients of the turbulent field. The central hypothesis of the theory is the time scale separation between dissipative time scale, nonlinear time scale and the period of the wave ($T_d>>T_{NL}>>T$). We observe that this scale separation is valid in our system. The discrete modes due to the finite size effects are responsible for the disagreement between observations and theory. A crossover from continuous weak turbulence and discrete turbulence is observed when the nonlinear time scale is of the same order of magnitude as the frequency separation of the discrete modes. The Kolmogorov-Zakharov energy cascade is then strongly altered and is frozen before reaching the dissipative regime expected in the theory.Comment: accepted for publication in Physical Review

Exit times in non-Markovian drifting continuous-time random walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.Comment: 9 pages, 3 color plots, two-column revtex 4; new Appendix and references adde

Parrondo-like behavior in continuous-time random walks with memory

The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this article we will show how the random combination of two different unbiased CTRWs can give raise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same of the Parrondo's paradox in game theoryComment: 8 pages, 3 figures, revtex; enlarged and revised versio

Un nuevo yacimiento de Vertebrados en el Burdigaliense de Martorell (Provincia de Barcelona)

Se describe en la nota presente un nuevo yacimiento inédito del Burdigaliense del Vallés-Penedés, cerca de Martorell y de la falla con la cadena litoral. Se da un resumen de la fauna encontrada y un corte estratigráfico detallado de la nueva localidadPeer reviewe

A quantum gate array can be programmed to evaluate the expectation value of any operator

A programmable gate array is a circuit whose action is controlled by input data. In this letter we describe a special--purpose quantum circuit that can be programmed to evaluate the expectation value of any operator $O$ acting on a space of states of $N$ dimensions. The circuit has a program register whose state $|\Psi(O)>_P$ encodes the operator $O$ whose expectation value is to be evaluated. The method requires knowledge of the expansion of $O$ in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.Comment: 4 pages, 3 figures include

Is Dark Energy Dynamical? Prospects for an Answer

Recent data advances offer the exciting prospect of a first look at whether dark energy has a dynamical equation of state or not. While formally theories exist with a constant equation of state, they are nongeneric -- Einstein's cosmological constant is a notable exception. So limits on the time variation, w', directly tell us crucial physics. Two recent improvements in supernova data from the Hubble Space Telescope allow important steps forward in constraining the dynamics of dark energy, possessing the ability to exclude models with w'\ga 1, if the universe truly has a cosmological constant. These data bring us much closer to the ``systematics'' era, where further improvements will come predominantly from more accurate, not merely more, observations. We examine the possible gains and point out the complementary roles of space and ground based observations in the near future. To achieve the leap to precision understanding of dark energy in the next generation will require specially designed space based measurements; we estimate the confidence level of detection of dynamics (e.g. distinguishing between $w'=0$ and $w'=1$) will be ~1.8\sigma after the ongoing generation, improving to more than 6.5\sigma in the dedicated space generation.Comment: 6 pages, 2 figures; version accepted to Phys. Rev.

Sarcoma sinovial sobre grave traumatismo de pie

El sarcoma sinovial es una neoplasia mesenquimal maligna poco frecuente, apareciendo como una tumoración profunda de crecimiento lento, con nulo o escaso dolor y poca alteración funcional por lo que el diagnóstico suele ser tardío. El antecedente traumático de ha registrado en algún caso sin probar relación etiológica. Se presenta el caso clínico de un varón de 56 años de edad, que sufrió un grave traumatismo en los pies con fractura de ambos calcáneos y II, III y IV MTT pie derecho más luxación articulación metatarso falángica del primer dedo. Tras la intervención mediante enclavijado sin exposición de los focos de lesión, la evolución de las fracturas fue buena, observando a los diez meses una tumoración en el dorso del pie derecho diagnosticada como sarcoma sinovial por biopsia. Tras el estudio de extensión de la neoplasia de objetivó afectación multisitémica y a pesar de los tratamientos instaurados al paciente falleció tres meses después. Se discute la dificultad del diagnóstico diferencialSynovial sarcoma is an inusual mesenchymal neoplasm, appearing as a deep tumour of show growth, with none or rare pain and few functional disturbances. These features usually lead to a late diagnosis. Previous injury is present in some cases but there in no proven ethilogical relation. We present a male, age 56, who suffered a serious feet injury leading to fracture of both calcaneus and II, III and IV MTT right foot with dislocation MTT-falangic of first finger. After surgery with with closed Kirschner wires, the evolution was good. Ten months later a tumour appeared on the right foot, diagnosed as a synovial sarcoma after biopsy. The stating study showed multisystemic damage and the patient died three months in spite of treatment. We address the difficulty of the differential diagnose