An exact representation of the fermion dynamics in terms of Poisson processes and its connection with Monte Carlo algorithms

We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer implementation of this formula leads to a family of algorithms parametrized by the values of the jump rates of the Poisson processes. From these an optimal algorithm can be chosen which coincides with the Green Function Monte Carlo method in the limit when the latter becomes exact.Comment: 4 pages, 1 PostScript figure, REVTe

Comment on "Why quantum mechanics cannot be formulated as a Markov process"

In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's "measurement probabilities" \it are \rm the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability measure of the process to follow the quantally implemented (via the Born statistical postulate) evolution, then we arrive at the jump process which \it can \rm be interpreted as a Markov process if restricted to a suitable duration time. However, there is no corresponding Markov process consistent with the $Z_2$ event space assumption, if we require its existence for all times $t\in R_+$.Comment: Latex file, resubm. to Phys. Rev.

Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths

Using a hydrodynamic approach we examine bulk- and surface-induced second and third harmonic generation from semiconductor nanowire gratings having a resonant nonlinearity in the absorption region. We demonstrate resonant, broadband and highly efficient optical frequency conversion: contrary to conventional wisdom, we show that harmonic generation can take full advantage of resonant nonlinearities in a spectral range where nonlinear optical coefficients are boosted well beyond what is achievable in the transparent, long-wavelength, non-resonant regime. Using femtosecond pulses with approximately 500 MW/cm2 peak power density, we predict third harmonic conversion efficiencies of approximately 1% in a silicon nanowire array, at nearly any desired UV or visible wavelength, including the range of negative dielectric constant. We also predict surface second harmonic conversion efficiencies of order 0.01%, depending on the electronic effective mass, bistable behavior of the signals as a result of a reshaped resonance, and the onset fifth order nonlinear effects. These remarkable findings, arising from the combined effects of nonlinear resonance dispersion, field localization, and phase-locking, could significantly extend the operational spectral bandwidth of silicon photonics, and strongly suggest that neither linear absorption nor skin depth should be motivating factors to exclude either semiconductors or metals from the list of useful or practical nonlinear materials in any spectral range.Comment: 12 pages, 4 figure

On the zig-zag pilot-wave approach for fermions

We consider a pilot-wave approach for the Dirac theory that was recently proposed by Colin and Wiseman. In this approach, the particles perform a zig-zag motion, due to stochastic jumps of their velocity. We respectively discuss the one-particle theory, the many-particle theory and possible extensions to quantum field theory. We also discuss the non-relativistic limit of the one-particle theory. For a single particle, the motion is always luminal, a feature that persists in the non-relativistic limit. For more than one particle the motion is in general subluminal.Comment: 23 pages, no figures, LaTe

Exact Monte Carlo time dynamics in many-body lattice quantum systems

On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We extend this algorithm to the exact simulation of time-dependent correlation functions. The techniques generally employed in Monte Carlo simulations to control fluctuations, namely reconfigurations and importance sampling, are adapted to the present algorithm and their validity is rigorously proved. We complete the analysis by several examples for the hard-core boson Hubbard model and for the Heisenberg model

Implant survival and success rates in patients with risk factors: results from a long-term retrospective study with a 10 to 18 years follow-up

OBJECTIVE: Risk factors for implant therapy are represented by all general and local conditions that through various mechanisms can increase either short-term and long-term failure risk. The aim of this study is to assess the implant survival and implant success rates with single and multiple risk factors. PATIENTS AND METHODS: To address the research purpose, a retrospective cohort study was designed and implemented, including a sample of 225 patients with a total of 871 implants placed. The following risk factors were considered: smoking, bruxism, bone augmentation procedures and the presence of load risk (implants with crown/implant relation > 0.8; angulation > 25°; presence of cantilever). Follow-up ranged from 10 years to 18 years (average follow-up 13.6 years). Failures were subdivided into short-term failures, before the prosthetic phase, and long-term failures, after definitive prosthesis. The success criteria published by Albrektsson and Zarb were adopted. A Cox proportional hazard regression model was used to calculate hazard ratio, with a statistically significant p-value <0.05. RESULTS: Out of the 871 implants placed, 138 did not meet the success criteria, (success rate 84.16%), sixty (43.47%) were classified as "early failure" and seventy-eight as "late failure" (56.53%). A total of 70 dental implants were removed, with a survival rate of 91.96%. CONCLUSIONS: The presence of a single risk factor does not imply a marked increase of failure risk. Among the analyzed factors, the one that proved to be the most dangerous was bruxism, even when presented as the only risk factor. Bruxism with load risk proved to be the most dangerous association (success rate 69.23%) and could be included among the absolute contraindications for implant treatment

Impossibility of spontaneously breaking local symmetries and the sign problem

Elitzur's theorem stating the impossibility of spontaneous breaking of local symmetries in a gauge theory is reexamined. The existing proofs of this theorem rely on gauge invariance as well as positivity of the weight in the Euclidean partition function. We examine the validity of Elitzur's theorem in gauge theories for which the Euclidean measure of the partition function is not positive definite. We find that Elitzur's theorem does not follow from gauge invariance alone. We formulate a general criterion under which spontaneous breaking of local symmetries in a gauge theory is excluded. Finally we illustrate the results in an exactly solvable two dimensional abelian gauge theory.Comment: Latex 6 page

Dynamic chirality in the interacting boson fermion-fermion model

The chiral interpretation of twin bands in odd-odd nuclei was investigated in the interacting boson fermion-fermion model. The analysis of the wave functions has shown that the possibility for angular momenta of the valence proton, neutron and core to find themselves in the favorable, almost orthogonal geometry is present, but not dominant. Such behavior is found to be similar in nuclei where both the level energies and the electromagnetic decay properties display the chiral pattern, as well as in those where only the level energies of the corresponding levels in the twin bands are close together. The difference in the structure of the two types of chiral candidates nuclei can be attributed to different β and γ fluctuations, induced by the exchange boson-fermion interaction of the interacting boson fermion-fermion model. In both cases the chirality is weak and dynamic