It is widely known that there is no sign problem in path integral Monte Carlo (PIMC) simulations of fermions in one dimension. As far as the author is aware, there is no direct proof of this in the literature. This work shows that the sign of the N-fermion antisymmetric free propagator is given by the product of all possible pairs of particle separations, or relative displacements.
View Article and Find Full Text PDFBy using the recently derived universal discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically and evaluated numerically at each imaginary time step for any short-time propagator. This work shows that, using only currently known short-time propagators, the Hamiltonian energy can be optimized to the twelfth-order, converging to the ground state energy of the harmonic oscillator in as few as three beads. This study makes it absolutely clear that the widely used second-order primitive approximation propagator, when used in computing thermodynamic energy, converges extremely slowly with an increasing number of beads.
View Article and Find Full Text PDFThe direct integration of the harmonic oscillator path integral obscures the fundamental structure of its discrete, imaginary time propagator (density matrix). This work, by first proving an operator identity for contracting two free propagators into one in the presence of interaction, derives the discrete propagator by simple algebra without doing any integration. This discrete propagator is universal, having the same two hyperbolic coefficient functions for all short-time propagators.
View Article and Find Full Text PDFThis paper shows that, in one dimension, due to its topology, a closed-loop product of short-time propagators is always positive, despite the fact that each antisymmetric free fermion propagator can be of either sign.
View Article and Find Full Text PDFInt J Environ Res Public Health
February 2023
The interplay of physical, social, and economic factors during the pandemic adversely affected the mental health of healthy people and exacerbated pre-existing mental disorders. This study aimed to determine the impact of the COVID-19 pandemic on the mental health of the general population in Malaysia. A cross-sectional study involving 1246 participants was conducted.
View Article and Find Full Text PDFBackground: The chlamydial major outer membrane protein, encoded by the ompA gene, is a primary target for chlamydial vaccine research. However, human studies of ompA-specific immunity are limited, and prior studies have been limited in differentiating re-infection from persistent infection. The purpose of this study was to assess whether children living in trachoma-endemic communities with re-infections of ocular chlamydia were more likely to be infected with a different or similar genovar.
View Article and Find Full Text PDFIt has been known for some time that when one uses the Lorentz force law, rather than Hamilton's equation, one can derive two basic algorithms for solving trajectories in a magnetic field formally similar to the velocity-Verlet (VV) and position-Verlet (PV) symplectic integrators independent of any finite-difference approximation. Because the Lorentz force law uses the mechanical rather than the canonical momentum, the resulting magnetic field algorithms are exact energy conserving, rather than symplectic. In general, both types of algorithms can only yield the exact trajectory in the limit of vanishing small time steps.
View Article and Find Full Text PDFGlucocorticoids (GCs) are hormones that aid the body under stress by regulating glucose and free fatty acids. GCs maintain energy homeostasis in multiple tissues, including those in the liver and skeletal muscle, white adipose tissue (WAT), and brown adipose tissue (BAT). WAT stores energy as triglycerides, while BAT uses fatty acids for heat generation.
View Article and Find Full Text PDFIt is well known that the use of the primitive second-order propagator in path-integral Monte Carlo calculations of many-fermion systems leads to the sign problem. This work will show that by using the similarity-transformed Fokker-Planck propagator, it is possible to solve for the ground state of a large quantum dot, with up to 100 polarized electrons, without solving the sign problem. These similarity-transformed propagators naturally produce rotational symmetry-breaking ground-state wave functions previously used in the study of quantum dots and quantum Hall effects.
View Article and Find Full Text PDFPurpose: To determine whether combinations of commonly used antiamoebic agents display synergy in their ability to kill Acanthamoeba cysts in vitro.
Methods: Synergy testing was performed with a microdilution checkerboard assay on 10 clinical Acanthamoeba keratitis isolates collected at the Proctor Foundation from 2008 to 2012. Each isolate was exposed to pairwise combinations of chlorhexidine, propamidine, and voriconazole.
Background: Frequent use of antibiotics is thought to create selection pressure by clearing susceptible bacteria and allowing resistant bacteria to spread in a community. A cluster-randomized trial comparing 2 different frequencies of mass azithromycin distributions for trachoma provided a convenient experiment for determining the causal relationship between antibiotic consumption and antibiotic resistance.
Methods: Twenty-four communities were randomized to either annual or biannual mass azithromycin distributions for trachoma.
Prior studies have theorized that low chlamydial genetic diversity following mass azithromycin treatments for trachoma may create a population bottleneck that prevents the return of infection, but little empirical evidence exists to support this hypothesis. In this study, a single mass azithromycin distribution was administered to 21 communities in the Gurage Zone of Ethiopia in 2003. All children aged 1-5 years had conjunctival swabs performed before treatment and 2 and 6 months after treatment.
View Article and Find Full Text PDFGiven any background (or seed) solution of the nonlinear Schrödinger equation, the Darboux transformation can be used to generate higher-order breathers with much greater peak intensities. In this work, we use the Darboux transformation to prove, in a unified manner and without knowing the analytical form of the background solution, that the peak height of a high-order breather is just a sum of peak heights of first-order breathers plus that of the background, irrespective of the specific choice of the background. Detailed results are verified for breathers on a cnoidal background.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
December 2015
By invoking Bogoliubov's spectrum, we show that for the nonlinear Schrödinger equation, the modulation instability (MI) of its n=1 Fourier mode on a finite background automatically triggers a further cascading instability, forcing all the higher modes to grow exponentially in locked step with the n=1 mode. This fundamental insight, the enslavement of all higher modes to the n=1 mode, explains the formation of a triangular-shaped spectrum that generates the Akhmediev breather, predicts its formation time analytically from the initial modulation amplitude, and shows that the Fermi-Pasta-Ulam (FPU) recurrence is just a matter of energy conservation with a period twice the breather's formation time. For higher-order MI with more than one initial unstable mode, while most evolutions are expected to be chaotic, we show that it is possible to have isolated cases of "super-recurrence," where the FPU period is much longer than that of a single unstable mode.
View Article and Find Full Text PDFAs seen in this CME online activity (available at http://journal.cme.chestnet.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
March 2015
The conventional second-order path-integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of antisymmetric free-fermion propagators that are needed to extract the ground state wave function at large imaginary time. In this work we show that optimized fourth-order path-integral Monte Carlo methods, which use no more than five free-fermion propagators, can yield accurate quantum dot energies for up to 20 polarized electrons with the use of the Hamiltonian energy estimator.
View Article and Find Full Text PDFWe assessed the effect of mass azithromycin treatment on malaria parasitemia in a trachoma trial in Niger. Twenty-four study communities received treatment during the wet, high-transmission season. Twelve of the 24 communities were randomized to receive an additional treatment during the dry, low-transmission season.
View Article and Find Full Text PDFThe Ministry of Health (MOH) have updated the clinical practice guidelines on Depression to provide doctors and patients in Singapore with evidence-based treatment for depression. This article reproduces the introduction and executive summary (with recommendations from the guidelines) from the MOH clinical practice guidelines on Depression, for the information of readers of the Singapore Medical Journal. Chapters and page numbers mentioned in the reproduced extract refer to the full text of the guidelines, which are available from the Ministry of Health website: http://www.
View Article and Find Full Text PDFThe Ministry of Health (MOH) has updated the clinical practice guidelines on Schizophrenia to provide doctors and patients in Singapore with evidence-based treatment for schizophrenia. This article reproduces the introduction and executive summary (with recommendations from the guidelines) from the MOH clinical practice guidelines on Schizophrenia, for the information of readers of the Singapore Medical Journal. Chapters and page numbers mentioned in the reproduced extract refer to the full text of the guidelines, which are available from the Ministry of Health website: http://www.
View Article and Find Full Text PDFWe present a new class of high-order imaginary time propagators for path integral Monte Carlo simulations that require no higher order derivatives of the potential nor explicit quadratures of Gaussian trajectories. Higher orders are achieved by an extrapolation of the primitive second-order propagator involving subtractions. By requiring all terms of the extrapolated propagator to have the same Gaussian trajectory, the subtraction only affects the potential part of the path integral.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
September 2009
By exploiting the error functions of explicit symplectic integrators for solving separable Hamiltonians, I show that it is possible to develop explicit time-reversible symplectic integrators for solving nonseparable Hamiltonians of the product form. The algorithms are unusual in that they are of fractional orders.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
June 2008
The exponential splitting of the classical evolution operator yields symplectic integrators if the canonical Hamiltonian is separable. Similar splitting of the noncanonical evolution operator for a charged particle in a magnetic field produces exact energy-conserving algorithms. The latter algorithms evaluate the magnetic field directly with no need of a vector potential and are more stable with far less phase errors than symplectic integrators.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
November 2007
Since the kinetic and potential energy terms of the real-time nonlinear Schrödinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well-known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
March 2007
Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians. The error of the algorithm is the sum of each error Hamiltonian's perturbation on the exact solution. When symplectic integrators are applied to the Kepler problem, these error terms cause the orbit to precess.
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