Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is ``experimental'', I only provide a ``physicist's'' proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in the Appendix, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present article is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now treated as independent from their continuous version; new examples of discrete short-time approximations of order three and four are given; a new appendix containing a short review on Brownian motion has been added; also, some additional explanations are provided here and there; this is the last version; to appear in Phys. Rev.

Constitutive cytoplasmic localization of p21Waf1/Cip1 affects the apoptotic process in monocytic leukaemia

In the present study, we analysed the expression and localization of p21Waf1/Cip1 in normal and malignant haematopoietic cells. We demonstrate that in normal monocytic cells, protein kinase C (PKC)-induced p21 gene activation, which is nuclear factor-κB (NF-κB) independent, results in predominantly cytoplasmic localized p21 protein. In acute monocytic leukaemia (M4, M5), monocytic blasts (N=12) show constitutive cytoplasmic p21 expression in 75% of the cases, while in myeloid leukaemic blasts (N=10), low nuclear and cytoplasmic localization of p21 could be detected, which is also PKC dependent. Constitutive p21 expression in monocytic leukaemia might have important antiapoptotic functions. This is supported by the finding that in U937 cells overexpressing p21, VP16-induced apoptosis is significantly reduced (20.0±0.9 vs 55.8±3.8%, P<0.01, N=5), reflected by a reduced phosphorylation of p38 and JNK. Similarly, AML blasts with high cytoplasmic p21 were less sensitive to VP16-induced apoptosis as compared to AML cases with low or undetectable p21 expression (42.25 vs 12.3%, P<0.01). Moreover, complex formation between p21 and ASK1 could be demonstrated in AML cells, by means of coimmunoprecipitation. In summary, these results indicate that p21 has an antiapoptotic role in monocytic leukaemia, and that p21 expression is regulated in a PKC-dependent and NF-κB independent manner.

Polarised target for Drell-Yan experiment in COMPASS at CERN, part I

In the polarised Drell-Yan experiment at the COMPASS facility in CERN pion beam with momentum of 190 GeV/c and intensity about $10^8$ pions/s interacted with transversely polarised NH$_3$ target. Muon pairs produced in Drel-Yan process were detected. The measurement was done in 2015 as the 1st ever polarised Drell-Yan fixed target experiment. The hydrogen nuclei in the solid-state NH$_3$ were polarised by dynamic nuclear polarisation in 2.5 T field of large-acceptance superconducting magnet. Large helium dilution cryostat was used to cool the target down below 100 mK. Polarisation of hydrogen nuclei reached during the data taking was about 80 %. Two oppositely polarised target cells, each 55 cm long and 4 cm in diameter were used. Overview of COMPASS facility and the polarised target with emphasis on the dilution cryostat and magnet is given. Results of the polarisation measurement in the Drell-Yan run and overviews of the target material, cell and dynamic nuclear polarisation system are given in the part II.Comment: 4 pages, 2 figures, Proceedings of the 22nd International Spin Symposium, Urbana-Champaign, Illinois, USA, 25-30 September 201

Loop algorithms for quantum simulations of fermion models on lattices

Two cluster algorithms, based on constructing and flipping loops, are presented for worldline quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip and loop-exchange algorithms. For these two algorithms and the standard worldline algorithm, we calculated the autocorrelation times for various physical quantities and found that the ordinary worldline algorithm, which uses only local moves, suffers from very long correlation times that makes not only the estimate of the error difficult but also the estimate of the average values themselves difficult. These difficulties are especially severe in the low-temperature, large-$U$ regime. In contrast, we find that new algorithms, when used alone or in combinations with themselves and the standard algorithm, can have significantly smaller autocorrelation times, in some cases being smaller by three orders of magnitude. The new algorithms, which use non-local moves, are discussed from the point of view of a general prescription for developing cluster algorithms. The loop-flip algorithm is also shown to be ergodic and to belong to the grand canonical ensemble. Extensions to other models and higher dimensions is briefly discussed.Comment: 36 pages, RevTex ver.

Screening of Nuclear Reactions in the Sun and Solar Neutrinos

We quantitatively determine the effect and the uncertainty on solar neutrino production arising from the screening process. We present predictions for the solar neutrino fluxes and signals obtained with different screening models available in the literature and by using our stellar evolution code. We explain these numerical results in terms of simple laws relating the screening factors with the neutrino fluxes. Futhermore we explore a wider range of models for screening, obtained from the Mitler model by introducing and varying two phenomenological parameters, taking into account effects not included in the Mitler prescription. Screening implies, with respect to a no-screening case, a central temperat reduction of 0.5%, a 2% (8%) increase of Beryllium (Boron)-neutrino flux and a 2% (12%) increase of the Gallium (Chlorine) signal. We also find that uncertainties due to the screening effect ar at the level of 1% for the predicted Beryllium-neutrino flux and Gallium signal, not exceeding 3% for the Boron-neutrino flux and the Chlorine signal.Comment: postscript file 11 pages + 4 figures compressed and uuencoded we have replaced the previous paper with a uuencoded file (the text is the same) for any problem please write to [email protected]

The role of winding numbers in quantum Monte Carlo simulations

We discuss the effects of fixing the winding number in quantum Monte Carlo simulations. We present a simple geometrical argument as well as strong numerical evidence that one can obtain exact ground state results for periodic boundary conditions without changing the winding number. However, for very small systems the temperature has to be considerably lower than in simulations with fluctuating winding numbers. The relative deviation of a calculated observable from the exact ground state result typically scales as $T^{\gamma}$, where the exponent $\gamma$ is model and observable dependent and the prefactor decreases with increasing system size. Analytic results for a quantum rotor model further support our claim.Comment: 5 pages, 5 figure

Sedimentation and subsidence history of the Lomonosov Ridge

During the first scientific ocean drilling expedition to the Arctic Ocean (Arctic Coring Expedition [ACEX]; Integrated Ocean Drilling Program Expedition 302), four sites were drilled and cored atop the central part of the Lomonosov Ridge in the Arctic Ocean at ~88°N, 140°E (see Fig. F18 in the "Sites M0001–M0004" chapter). The ridge was rifted from the Eurasian continental margin at ~57 Ma (Fig. F1) (Jokat et al., 1992, 1995). Since the rifting event and the concurrent tilting and erosion of this sliver of the outer continental margin, the Lomonosov Ridge subsided while hemipelagic and pelagic sediments were deposited above the angular rifting unconformity (see Fig. F7A in the "Sites M0001–M0004" chapter).The sections recovered from the four sites drilled during Expedition 302 can be correlated using their seismic signature, physical properties (porosity, magnetic susceptibility, resistivity, and P-wave velocity), chemostratigraphy (ammonia content of pore waters), lithostratigraphy, and biostratigraphy. The lithostratigraphy of the composite section combined with biostratigraphy provides an insight into the complex history of deposition, erosion, and preservation of the biogenic fraction. Eventually, the ridge subsided to its present water depth as it drifted from the Eurasian margin. In this chapter, we compare a simple model of subsidence history with the sedimentary record recovered from atop the ridge

Numerical Investigation of Cosmological Singularities

Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular symplectic numerical integration scheme fits naturally into the Einstein equations for a large class of cosmological models and thus allows study of their approach to the singularity. The numerical method also naturally singles out the asymptotically velocity term dominated (AVTD) behavior known to be characteristic of some of these models, conjectured to describe others, and probably characteristic of a subclass of the rest. The method is first applied to the unpolarized Gowdy T$^3$ cosmology. Exact pseudo-unpolarized solutions are used as a code test and demonstrate that a 4th order accurate implementation of the numerical method yields acceptable agreement. For generic initial data, support for the conjecture that the singularity is AVTD with geodesic velocity (in the harmonic map target space) < 1 is found. A new phenomenon of the development of small scale spatial structure is also observed. Finally, it is shown that the numerical method straightforwardly generalizes to an arbitrary cosmological spacetime on $T^3 \times R$ with one spacelike U(1) symmetry.Comment: 37 pp +14 figures (not included, available on request), plain Te

Expedition 302 geophysics: integrating past data with new results

In preparation for IODP Expedition 302, Arctic Coring Expedition (ACEX), a site survey database comprising geophysical and geological data from the Lomonosov Ridge was compiled. The accumulated database includes data collected from ice islands, icebreakers, and submarines from 1961 to 2001. In addition, seismic reflection profiles were collected during Expedition 302 that complement the existing seismic reflection data and facilitate integration between the acoustic stratigraphy and the Expedition 302 drill cores. An overview of these data is presented in this chapter.It is well recognized that collecting geophysical data in ice-covered seas, in particular the Arctic Ocean, is a challenging endeavor. This is because much of the Arctic Ocean is continuously covered with ice thicknesses that vary from 1 to 6 m. Over the continental shelves, sea ice can be absent during summer months, but it is present year-round in the central basins. This ice cover is the most dominant feature of the Arctic Ocean environment. It circulates in the ocean basin in two main circulation patterns: the Transpolar Drift and the Beaufort Gyre (see the "Expedition 302 summary" chapter; Rudels et al., 1996).Expedition 302 sites are located within the less severe of these two ice circulation systems, the Transpolar Drift, which primarily moves sea ice from the shelves where it is formed (the Laptev and East Siberian Seas) across the basin and exits through the Fram Strait. During late summer, concentrations of Arctic sea ice can be &lt;100% (10/10 ice cover), making it possible for icebreakers to operate. Average ice concentrations in the central Arctic Ocean during summer months can locally vary from partially open water (6/10) to completely ice covered (10/10). This sea-ice cover can move at speeds up to 0.5 kt.Early Arctic Ocean geophysical exploration was performed from ice-drift stations (Weber and Roots, 1990). However, the tracks from these drifting ice stations were controlled "by the whims of nature" (Jackson et al., 1990), preventing detailed, systematic surveys of predetermined target areas. These ice-drift stations were set up on stable icebergs that were trapped in sea ice and moved generally with the large drift patterns, but locally they were erratic, so preselected locations could not be surveyed. In the late 1980s, single icebreakers began to be used for oceanographic survey work in the Arctic Ocean. Between 1991 and 2001, four scientific icebreaker expeditions to the Lomonosov Ridge took place. These cruises all experienced local sea-ice conditions varying between 8/10 and 10/10. During these expeditions, towed geophysical equipment was occasionally damaged or lost, either because of a rapidly closing wake caused by local ice pressure or because ice had cut the air gun array.Conventionally powered icebreakers reached as far as the North Pole for the first time during the 1991 Expedition (Andersen and Carlsonn, 1992; Fütterer, 1992). Geophysical results from this expedition collected two important reflection profiles, AWI-91090 and AWI-91091, that crossed the Lomonosov Ridge between 87° and 88°N. These profiles imaged a ~450 m thick, well-stratified and apparently undisturbed drape of sediments overlying a prominent acoustic unconformity (Jokat et al., 1992) that spawned the idea to conduct a paleoceanographic drilling expedition to this Ridge.The use of US Navy nuclear submarines for geophysical mapping was implemented through the Science Ice Exercise program (SCICEX) (Newton, 2000). The development of the Seafloor Characterization and Mapping Pods (SCAMP), which hold a Chirp subbottom profiler, swath bathymetric profiler, and side scan sonar, was an essential part of the SCICEX program (Chayes et al., 1996). In 1999, the Lomonosov Ridge geophysical database was augmented with acoustic data acquired during the SCICEX program using the SCAMP system mounted on the US nuclear submarine USS Hawkbill (Edwards and Coakley, 2003)

On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring

We perform a detailed study of the type IIA superstring in AdS(4) x CP(3). After introducing suitable bosonic light-cone and fermionic kappa worldsheet gauges we derive the pure boson and fermion SU(2|2) x U(1) covariant light-cone Hamiltonian up to quartic order in fields. As a first application of our derivation we calculate energy shifts for string configurations in a closed fermionic subsector and successfully match these with a set of light-cone Bethe equations. We then turn to investigate the mismatch between the degrees of freedom of scattering states and oscillatory string modes. Since only light string modes appear as fundamental Bethe roots in the scattering theory, the physical role of the remaining $4_F+4_B$ massive oscillators is rather unclear. By continuing a line of research initiated by Zarembo, we shed light on this question by calculating quantum corrections for the propagators of the bosonic massive fields. We show that, once loop corrections are incorporated, the massive coordinates dissolve in a continuum state of two light particles.Comment: 40 pages, 2 figures. v3: Minor clarifications made and reference list updated. Published version