Search results for "integral"
showing 10 items of 902 documents
Orthorhombic Phase of Crystalline Polyethylene: A Constant Pressure Path Integral Monte Carlo Study
1998
In this paper we present a Path Integral Monte Carlo (PIMC) simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles. This work represents a quantum extension of our recent classical simulation (J. Chem. Phys. 106, 8918 (1997)). It is aimed both at exploring the applicability of the PIMC method on such polymer crystal systems, as well as on a detailed assessment of the importance of quantum effects on different quantities. We used the $NpT$ ensemble and simulated the system at zero pressure in the temperature range 25 - 300 K, using Trotter numbers between 12 and 144. In order to investigate finite-size e…
Elastic Constants of Quantum Solids by Path Integral Simulations
2000
Two methods are proposed to evaluate the second-order elastic constants of quantum mechanically treated solids. One method is based on path-integral simulations in the (NVT) ensemble using an estimator for elastic constants. The other method is based on simulations in the (NpT) ensemble exploiting the relationship between strain fluctuations and elastic constants. The strengths and weaknesses of the methods are discussed thoroughly. We show how one can reduce statistical and systematic errors associated with so-called primitive estimators. The methods are then applied to solid argon at atmospheric pressures and solid helium 3 (hcp, fcc, and bcc) under varying pressures. Good agreement with …
Quantum effects on the herringbone ordering ofN2on graphite
1993
The effects of quantum fluctuations on the ``2-in'' herringbone ordering in a realistic model of 900 ${\mathrm{N}}_{2}$ molecules adsorbed in the (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} structure on graphite are studied via path-integral Monte Carlo (PIMC) simulations. Quasiclassical and quasiharmonic calculations agree for high and low temperatures, respectively, but only PIMC gives satisfactory results over the entire temperature range. We can quantify the lowering of the transition temperature and the depression of the ground state order to 10% as compared to classical modeling.
A numerical method to calculate the muon relaxation function in the presence of diffusion
2014
We present an accurate and efficient method to calculate the effect of random fluctuations of the local field at the muon, for instance in the case muon diffusion, within the framework of the strong collision approximation. The method is based on a reformulation of the Markovian process over a discretized time base, leading to a summation equation for the muon polarization function which is solved by discrete Fourier transform. The latter is formally analogous, though not identical, to the integral equation of the original continuous-time model, solved by Laplace transform. With real-case parameter values, the solution of the discrete-time strong collision model is found to approximate the …
Gradual freezing of orientational degrees of freedom in cubicAr1−x(N2)xmixtures
1995
The mixed crystal ${\mathrm{Ar}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{N}}_{2}$${)}_{\mathit{x}}$ is studied by Monte Carlo (MC) methods for x=0.33, 0.67, and 1.0 over a wide range of temperatures. For x=1 we find first-order transition from ordered cubic to disordered cubic, while for x=0.33 and x=0.67 we find broad nonuniform distribution functions of the local quadrupole Edwards-Anderson order parameter at low temperature. The short-range order of the quadrupolar mass distribution of the ${\mathrm{N}}_{2}$ molecules in the mixed systems is different from that observed in the pure ${\mathrm{N}}_{2}$ crystal, although the fcc symmetry has been chosen for the translational degrees…
The response field and the saddle points of quantum mechanical path integrals
2021
In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given by Marinov's path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov's integral, plays for pure states even. The discussion focuses on how the integral's semiclassical approximation relates to…
Spectral anomalies in focused waves of different Fresnel numbers
2004
Light propagation induces remarkable changes in the spectrum of focused diffracted beams. We show that spectral changes take place in the vicinity of phase singularities in the focal region of spatially coherent, polychromatic spherical waves of different Fresnel numbers. Instead of the Debye formulation, we use the Kirchhoff integral to evaluate the focal field accurately. We find that as a result of a decrease in the Fresnel number, some cylindrical spectral switches are geometrically transformed into conical spectral switches.
Enhanced depth of field integral imaging with sensor resolution constraints.
2009
One of the main challenges in integral imaging is to overcome the limited depth of field. Although it is widely assumed that such limitation is mainly imposed by diffraction due to lenslet imaging, we show that the most restricting factor is the pixelated structure of the sensor (CCD). In this context, we demonstrate that by proper reduction of the fill factor of pickup microlenses, the depth of field can be substantially improved with no deterioration of lateral resolution.
Phase Transitions in Classical Fluids and Fluids with Internal Quantum States in Two Dimensions: Computer Simulations and Theory
1993
1)We investigate the properties of a model fluid whose molecules have classical degrees of freedom in two dimensions and two internal quantum states. The attractive interactions are “turned on” when the internal states are hybridized, corresponding to the molecules acquiring a “dipole” moment. The phase diagram of this system in the temperature- density plane is investigated by a combination of path integral Monte Carlo and block size analysis techniques. The results are compared with mean- field—theory predictions. 2) We present molecular dynamics simulation results of quenches into the unstable region of a two-dimensional Lennard-Jones system. The evolution of the system from the non-equi…
The elastic scattering of 25MeV α-particles and neutron shell effects in the A = 50 TO A = 93 mass region
1982
Abstract Experimental elastic scattering angular distributions of 25 MeV α-particles scattered from 28 nuclei ranging from 50Cr to 93Nb have been measured and then analysed in terms of a regular optical model with standard Woods-Saxon geometries for both the real and imaginary potentials. The experimental distributions are well fitted over the whole angular range from 5° to 175° c.m. by the predictions, provided that a smaller than normal diffuseness is used for the imaginary potentials. The usual families of potentials with volume integrals differing by approximately 100 MeV · fm3 are found. The family with volume integral ranging from 540 to 420 MeV· fm3 over the nuclei studied has been c…