Global boundary conditions for a Dirac operator on the solid torus

We study a Dirac operator subject to Atiayh-Patodi-Singer like boundary conditions on the solid torus and show that the corresponding boundary value problem is elliptic, in the sense that the Dirac operator has a compact parametrix

Linear scaling computation of the Fock matrix VII. Periodic Density Functional Theory at the Γ\Gamma-point

Linear scaling quantum chemical methods for Density Functional Theory are extended to the condensed phase at the $\Gamma$-point. For the two-electron Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb summation [J. Chem. Phys. {\bf 106}, 5526 (1997)], together with multipole representation of the crystal field [J. Chem. Phys. {\bf 107}, 10131 (1997)]. A periodic version of the hierarchical cubature algorithm [J. Chem. Phys. {\bf 113}, 10037 (2000)], which builds a telescoping adaptive grid for numerical integration of the exchange-correlation matrix, is shown to be efficient when the problem is posed as integration over the unit cell. Commonalities between the Coulomb and exchange-correlation algorithms are discussed, with an emphasis on achieving linear scaling through the use of modern data structures. With these developments, convergence of the $\Gamma$-point supercell approximation to the ${\bf k}$-space integration limit is demonstrated for MgO and NaCl. Linear scaling construction of the Fockian and control of error is demonstrated for RBLYP/6-21G* diamond up to 512 atoms

Landau-Zener Problem for Trilinear Hamiltonians

We consider a nonlinear version of the Landau-Zener problem, focusing on photoassociation of a Bose-Einstein condensate as a specific example. Contrary to the exponential rate dependence obtained for the linear problem, a series expansion technique indicates that, when the resonance is crossed slowly, the probability for failure of adiabaticity is directly proportional to the rate at which the resonance is crossed.Comment: 4.5 pages, 1 figure, transferred to PRA; v2 adds discussion, clarification, and explicit numbers for Na and 87R

Analogue model of a FRW universe in Bose-Einstein condensates: Application of the classical field method

Analogue models of gravity have been motivated by the possibility of investigating phenomena not readily accessible in their cosmological counterparts. In this paper, we investigate the analogue of cosmological particle creation in a Friedmann-Robertson-Walker universe by numerically simulating a Bose-Einstein condensate with a time-dependent scattering length. In particular, we focus on a two-dimensional homogeneous condensate using the classical field method via the truncated Wigner approximation. We show that for various forms of the scaling function the particle production is consistent with the underlying theory in the long wavelength limit. In this context, we further discuss the implications of modified dispersion relations that arise from the microscopic theory of a weakly interacting Bose gas.Comment: 26 pages, 8 figure

Iron line profiles and self-shadowing from relativistic thick accretion discs

We present Fe Kalpha line profiles from and images of relativistic discs with finite thickness around a rotating black hole using a novel code. The line is thought to be produced by iron fluorescence of a relatively cold X-ray illuminated material in the innermost parts of the accretion disc and provides an excellent diagnostic of accretion flows in the vicinity of black holes. Previous studies have concentrated on the case of a thin, Keplerian accretion disc. This disc must become thicker and sub-Keplerian with increasing accretion rates. These can affect the line profiles and in turn can influence the estimation of the accretion disc and black hole parameters from the observed line profiles. We here embark on, for the first time, a fully relativistic computation which offers key insights into the effects of geometrical thickness and the sub-Keplerian orbital velocity on the line profiles. We include all relativistic effects such as frame-dragging, Doppler boost, time dilation, gravitational redshift and light bending. We find that the separation and the relative height between the blue and red peaks of the line profile diminish as the thickness of the disc increases. This code is also well-suited to produce accretion disc images. We calculate the redshift and flux images of the accretion disc and find that the observed image of the disc strongly depends on the inclination angle. The self-shadowing effect appears remarkable for a high inclination angle, and leads to the black hole shadow being completely hidden by the disc itself.Comment: 11 pages, 11 figures, some typographical errors are correcte

Assessment of Knowledge-Based Planning for Prostate Intensity Modulated Proton Therapy

Purpose: To assess the performance of a proton-specific knowledge based planning (KBPP) model in creation of robustly optimized intensity-modulated proton therapy (IMPT) plans for treatment of patients with prostate cancer. Materials and Methods: Forty-five patients with localized prostate cancer, who had previously been treated with volumetric modulated arc therapy, were selected and replanned with robustly optimized IMPT. A KBPP model was generated from the results of 30 of the patients, and the remaining 15 patient results were used for validation. The KBPP model quality and accuracy were evaluated with the model-provided organ-at-risk regression plots and metrics. The KBPP quality was also assessed through comparison of expert and KBPP-generated IMPT plans for target coverage and organ-at-risk sparing. Results: The resulting R (2) (mean ± SD, 0.87 ± 0.07) between dosimetric and geometric features, as well as the χ(2) test (1.17 ± 0.07) between the original and estimated data, showed the model had good quality. All the KBPP plans were clinically acceptable. Compared with the expert plans, the KBPP plans had marginally higher dose-volume indices for the rectum V65Gy (0.8% ± 2.94%), but delivered a lower dose to the bladder (-1.06% ± 2.9% for bladder V65Gy). In addition, KBPP plans achieved lower hotspot (-0.67Gy ± 2.17Gy) and lower integral dose (-0.09Gy ± 0.3Gy) than the expert plans did. Moreover, the KBPP generated better plans that demonstrated slightly greater clinical target volume V95 (0.1% ± 0.68%) and lower homogeneity index (-1.13 ± 2.34). Conclusions: The results demonstrated that robustly optimized IMPT plans created by the KBPP model are of high quality and are comparable to expert plans. Furthermore, the KBPP model can generate more-robust and more-homogenous plans compared with those of expert plans. More studies need to be done for the validation of the proton KBPP model at more-complicated treatment sites

van Vleck determinants: traversable wormhole spacetimes

Calculating the van Vleck determinant in traversable wormhole spacetimes is an important ingredient in understanding the physical basis behind Hawking's chronology protection conjecture. This paper presents extensive computations of this object --- at least in the short--throat flat--space approximation. An important technical trick is to use an extension of the usual junction condition formalism to probe the full Riemann tensor associated with a thin shell of matter. Implications with regard to Hawking's chronology protection conjecture are discussed. Indeed, any attempt to transform a single isolated wormhole into a time machine results in large vacuum polarization effects sufficient to disrupt the internal structure of the wormhole before the onset of Planck scale physics, and before the onset of time travel. On the other hand, it is possible to set up a putative time machine built out of two or more wormholes, each of which taken in isolation is not itself a time machine. Such ``Roman configurations'' are much more subtle to analyse. For some particularly bizarre configurations (not traversable by humans) the vacuum polarization effects can be arranged to be arbitrarily small at the onset of Planck scale physics. This indicates that the disruption scale has been pushed down into the Planck slop. Ultimately, for these configurations, questions regarding the truth or falsity of Hawking's chronology protection can only be addressed by entering the uncharted wastelands of full fledged quantum gravity.Comment: 42 pages, ReV_TeX 3.

Assessment of IMPT versus VMAT plans using different uncertainty scenarios for prostate cancer

Background To assess the impact of systematic setup and range uncertainties for robustly optimized (RO) intensity modulated proton therapy (IMPT) and volumetric modulated arc therapy (VMAT) plans in patients with localized prostate cancer. Methods Twenty-six localized prostate patients previously treated with VMAT (CTV to PTV expansion of 3-5 mm) were re-planned with RO-IMPT with 3 mm and 5 mm geometrical uncertainties coupled with 3% range uncertainties. Robust evaluations (RE) accounting for the geometrical uncertainties of 3 and 5 mm were evaluated for the IMPT and VMAT plans. Clinical target volume (CTV), anorectum, and bladder dose metrics were analyzed between the nominal plans and their uncertainty perturbations. Results With geometric uncertainties of 5 mm and accounting for potential inter-fractional perturbations, RO-IMPT provided statistically significant (p < 0.05) sparing at intermediate doses (V-4000cGy) to the anorectum and bladder and high dose sparring (V-8000cGy) to the bladder compared to VMAT. Decreasing the RO and RE parameters to 3 mm improved IMPT sparing over VMAT at all OAR dose levels investigated while maintaining equivalent coverage to the CTV. Conclusions For localized prostate treatments, if geometric uncertainties can be maintained at or below 3 mm, RO-IMPT provides clear dosimetric advantages in anorectum and bladder sparing compared to VMAT. This advantage remains even under uncertainty scenarios. As geometric uncertainties increase to 5 mm, RO-IMPT still provides dosimetric advantages, but to a smaller magnitude

Assessment of daily dose accumulation for robustly optimized intensity modulated proton therapy treatment of prostate cancer

To implement a daily CBCT based dose accumulation technique in order to assess ideal robust optimization (RO) parameters for IMPT treatment of prostate cancer. Ten prostate cancer patients previously treated with VMAT and having daily CBCT were included. First, RO-IMPT plans were created with ± 3 mm and ± 5 mm patient setup and ± 3% proton range uncertainties, respectively. Second, the planning CT (pCT) was deformably registered to the CBCT to create a synthetic CT (sCT). Both daily and weekly sampling strategies were employed to determine optimal dose accumulation frequency. Doses were recalculated on sCTs for both ± 3 mm/±3% and ± 5 mm/±3% uncertainties and were accumulated back to the pCT. Accumulated doses generated from ± 3 mm/±3% and ± 5 mm/±3% RO-IMPT plans were evaluated using the clinical dose volume constraints for CTV, bladder, and rectum. Daily accumulated dose based on both ± 3mm/±3% and ±5 mm/±3% uncertainties for RO-IMPT plans resulted in satisfactory CTV coverage (RO-IMPT CTV  = 99.01 ± 0.87% vs. RO-IMPT CTV  = 99.81 ± 0.2%, P = 0.002). However, the accumulated dose based on ± 3 mm/3% RO-IMPT plans consistently provided greater OAR sparing than ±5 mm/±3% RO-IMPT plans (RO-IMPT rectum  = 2.93 ± 2.39% vs. RO-IMPT rectum  = 4.38 ± 3%, P < 0.01; RO-IMPT bladder  = 5.2 ± 7.12% vs. RO-IMPT bladder  = 7.12 ± 9.59%, P < 0.01). The gamma analysis showed high dosimetric agreement between weekly and daily accumulated dose distributions. This study demonstrated that for RO-IMPT optimization, ±3mm/±3% uncertainty is sufficient to create plans that meet desired CTV coverage while achieving superior sparing to OARs when compared with ± 5 mm/±3% uncertainty. Furthermore, weekly dose accumulation can accurately estimate the overall dose delivered to prostate cancer patients