The Influence of the Symmetry of Identical Particles on Flight Times.

In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a 'screen' is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ-barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles.

Nonequilibrium molecular dynamics simulation of pressure-driven water transport through modified CNT membranes.

Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigate the effect of water-membrane interactions on the transport properties of pressure-driven water flow passing through carbon nanotube (CNT) membranes. The CNT membrane is modified with different physical properties to alter the van der Waals interactions or the electrostatic interactions between water molecules and the CNT membranes. The unmodified and modified CNT membranes are models of simplified nanofiltration (NF) membranes at operating conditions consistent with real NF systems. All NEMD simulations are run with constant pressure difference (8.0 MPa) temperature (300 K), constant pore size (0.643 nm radius for CNT (12, 12)), and membrane thickness (6.0 nm). The water flow rate, density, and velocity (in flow direction) distributions are obtained by analyzing the NEMD simulation results to compare transport through the modified and unmodified CNT membranes. The pressure-driven water flow through CNT membranes is from 11 to 21 times faster than predicted by the Navier-Stokes equations. For water passing through the modified membrane with stronger van der Waals or electrostatic interactions, the fast flow is reduced giving lower flow rates and velocities. These investigations show the effect of water-CNT membrane interactions on water transport under NF operating conditions. This work can help provide and improve the understanding of how these membrane characteristics affect membrane performance for real NF processes.

Nonequilibrium molecular dynamics simulation of water transport through carbon nanotube membranes at low pressure.

Nonequilibrium molecular dynamics (NEMD) simulations are used to investigate pressure-driven water flow passing through carbon nanotube (CNT) membranes at low pressures (5.0 MPa) typical of real nanofiltration (NF) systems. The CNT membrane is modeled as a simplified NF membrane with smooth surfaces, and uniform straight pores of typical NF pore sizes. A NEMD simulation system is constructed to study the effects of the membrane structure (pores size and membrane thickness) on the pure water transport properties. All simulations are run under operating conditions (temperature and pressure difference) similar to a real NF processes. Simulation results are analyzed to obtain water flux, density, and velocity distributions along both the flow and radial directions. Results show that water flow through a CNT membrane under a pressure difference has the unique transport properties of very fast flow and a non-parabolic radial distribution of velocities which cannot be represented by the Hagen-Poiseuille or Navier-Stokes equations. Density distributions along radial and flow directions show that water molecules in the CNT form layers with an oscillatory density profile, and have a lower average density than in the bulk flow. The NEMD simulations provide direct access to dynamic aspects of water flow through a CNT membrane and give a view of the pressure-driven transport phenomena on a molecular scale.

Two-channel conduction through polyacenes--extension of the source-sink potential method to multichannel coupling to leads.

The source and sink potential method of Goyer et al. [J. Chem. Phys. 126, 144104 (2007)] is extended to the case of multichannel coupling to leads. The formulation leads to a nonlinear equation for just one (the elastic) reflection coefficient. Solution of this equation, in general, requires repeated computation of an n × n determinant, where n is the number of supermolecule basis functions directly coupled to the source lead, as opposed to a determinant with order equal to the full size of supermolecule basis. The method is applied to a Hückel model of two-channel polyacene conduction. A simple model of resonance lineshapes is developed in case of weak coupling to leads. The model accurately relates peak characteristics to orbital probabilities associated with the eigenvectors of the isolated molecule Hamiltonian. The model shows how orbital probabilities that give rise to transmission resonances (i.e., 100% transmission), in the case of single-channel conduction, give rise to equal probabilities (of 1∕4) for the two reflections and two transmissions, in the case of two-channel conduction. The model also shows how splitting of degenerate eigenvalues of the isolated molecule Hamiltonian results in overlapping resonances characterized by a single complex lineshape.

Implicit restart Lanczos as an eigensolver.

This paper investigates the efficiency of the implicit restart Lanczos and simple (without reorthogonalization) Lanczos algorithms, as eigensolvers for large scale computations in molecular and chemical physics. Using the cardioid billiard and the hydrogen cyanide/hydrogen isocyanide (HCN/HNC) molecule as model systems we demonstrate superior efficiency of implicit restart Lanczos compared to the simple Lanczos algorithm. A modified implementation of implicit restart Lanczos is also presented which works with a smaller Krylov space-with associated savings in memory-and can handle larger basis sets than the usual implicit restart Lanczos. It also enables getting all eigenpairs of a matrix, or all eigenvalues below a threshold (where the number of such is not known before hand), which is more difficult with the usual implicit restart algorithm.

Non-normal Lanczos methods for quantum scattering.

This article presents a new complex absorbing potential (CAP) block Lanczos method for computing scattering eigenfunctions and reaction probabilities. The method reduces the problem of computing energy eigenfunctions to solving two energy dependent systems of equations. An energy independent block Lanczos factorization casts the system into a block tridiagonal form, which can be solved very efficiently for all energies. We show that CAP-Lanczos methods exhibit instability due to the non-normality of CAP Hamiltonians and may break down for some systems. The instability is not due to loss of orthogonality but to non-normality of the Hamiltonian matrix. While use of a Woods-Saxon exponential CAP-as opposed to a polynomial CAP-reduced non-normality, it did not always ensure convergence. Our results indicate that the Arnoldi algorithm is more robust for non-normal systems and less prone to break down. An Arnoldi version of our method is applied to a nonadiabatic tunneling Hamiltonian with excellent results, while the Lanczos algorithm breaks down for this system.

Long time wave packet dynamics from energy eigenfunctions: nonuniform energy resolution via adaptive bisection fast Fourier transformation.

This article presents a new approach to long time wave packet propagation. The methodology relies on energy domain calculations and an on-the-surface straightforward energy to time transformation to provide wave packet time evolution. The adaptive bisection fast Fourier transform method employs selective bisection to create a multiresolution energy grid, dense near resonances. To implement fast Fourier transforms on the nonuniform grid, the uniform grid corresponding to the finest resolution is reconstructed using an iterative interpolation process. By proper choice of the energy grid points, we are able to produce results equivalent to grids of the finest resolution, with far fewer grid points. We have seen savings 20-fold in the number of eigenfunction calculations. Since the method requires computation of energy eigenfunctions, it is best suited for situations where many wave packet propagations are of interest at a fixed small set of points--as in time dependent flux computations. The fast Fourier transform (FFT) algorithm used is an adaptation of the Danielson-Lanczos FFT algorithm to sparse input data. A specific advantage of the adaptive bisection FFT is the possibility of long time wave packet propagations showing slow resonant decay. A method is discussed for obtaining resonance parameters by least squares fitting of energy domain data. The key innovation presented is the means of separating out the smooth background from the sharp resonance structure.