Introduction to the Diffusion Monte Carlo Method

A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H2+ ion and of the H2 molecule. A computer program on which the sample calculations are based is available upon request.Comment: RevTeX 3.0, 14 pages, 8 EPS figures (included

Boundary Integral Method for Stationary States of Two-Dimensional Quantum Systems

The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method, wave functions inside the domain of the device or billiard are expressed in terms of line integrals of the wave function and its normal derivative along the domain's boundary; the respective energy eigenvalues are obtained as the roots of Fredholm determinants. Numerical implementations of the method are described and applied to determine the energy level statistics of billiards with circular and stadium shapes and demonstrate the quantum mechanical characteristics of chaotic motion. The treatment of other examples as well as the advantages and limitations of the boundary integral method are discussed.Comment: RevTeX3.0, 24 pages, 9 EPS figures (included); To be published in Int. J. of Mod. Phys.

Cellular aggregates under pressure

DOI: 10.1103/Physics.3.43Researchers develop a new approach to measuring the viscoelastic properties of multicellular aggregates by using a micropipette aspiration technique

Unusual thermodynamical and transport signatures of short coherence length superconductors: A BCS Bose-Einstein crossover approach

In this paper we present predictions for thermodynamic and transport properties of a BCS Bose-Einstein crossover theory, below Tc, which theory satisfies the reasonable constraints that it yield (i) the Leggett ground state and (ii) BCS theory at weak coupling and all temperatures. The nature of the strong coupling limit is inferred, along with the behavior of the Knight shift, superfluid density, and specific heat. Comparisons with existing data on short coherence length superconductors, such as organic and high Tc systems, are presented, which provide some support for the present picture.Comment: REVTeX 3.1, 4 pages, 3 EPS figures, significant revisions, to appear in PR

Short Coherence Length Superconductivity: A Generalization of BCS Theory for the Underdoped Cuprates

On the basis of the observed short coherence lengths in the cuprates we argue that a BCS-Bose-Einstein condensation (BEC) crossover approach is an appropriate starting point for correcting the mean field approach of BCS and, thereby, for addressing pseudogap phenomena in these materials. Our version of the BCS-BEC approach is based on a particular Greens' function decoupling scheme which should be differentiated from others in the literature, and which yields (i) the Leggett crossover ground state (for all coupling constants g, at T=0) and (ii) BCS theory (for all $T \leq T_c$ over a range of small g). In this paper we provide a simple physical picture of the pseudogap phase above and below $T_c$, and review the quantitative and qualitative implications of this theory, which, for the most part have been published in a series of recent papers.Comment: M2S-HTSC-VI conference paper, (4 pages, 1 figure), using Elsevier style espcrc2.st

Theoretical prediction of spectral and optical properties of bacteriochlorophylls in thermally disordered LH2 antenna complexes

doi:10.1063/1.2210481A general approach for calculating spectral and optical properties of pigment-protein complexes of known atomic structure is presented. The method, that combines molecular dynamics simulations, quantum chemistry calculations, and statistical mechanical modeling, is demonstrated by calculating the absorption and circular dichroism spectra of the B800-B850 bacteriochlorophylls of the LH2 antenna complex from Rs. molischianum at room temperature. The calculated spectra are found to be in good agreement with the available experimental results. The calculations reveal that the broadening of the B800 band is mainly caused by the interactions with the polar protein environment, while the broadening of the B850 band is due to the excitonic interactions. Since it contains no fitting parameters, in principle, the proposed method can be used to predict optical spectra of arbitrary pigment-protein complexes of known structure.This work was supported in part by grants from the University of Missouri Research Board, the Institute for Theoretical Sciences, a joint institute of Notre Dame University and Argonne National Laboratory, the U.S. Department of Energy, Office of Science through Contract No. W-31-109-ENG-38, and NSF through Grant No. FIBR-0526854. One of the authors (A.D.) acknowledges support from the Burroughs Welcome Fund. The authors also acknowledge computer time provided by NCSA Allocations Board grant MCB020036

Monte Carlo modeling of the formation of branched tube structures from cellular aggregates [abstract]

Abstract only availableFaculty Mentor: Gabor Forgacs, Physics and AstronomyMonte Carlo method has been used previously for modeling the fusion of cellular aggregates to produce capillary-like structures and hollow tubes from cell aggregates consisting of smooth muscle cells and endothelial cells.  Here we have extended these modeling efforts to branched tubular structures built of cellular aggregates in the presence of two types of biocompatible gels.  A MATLAB script was created to generate a construct of simulated cell aggregates resembling a branched tube.  All of the simulated cells and gel particles were placed on a uniform 3D lattice.  The main tube consisted of layers of spherical cell aggregates arranged in circles and stacked on top of each other in a close-packed arrangement.  All the aggregates were composed of 30% endothelial cells and 70% smooth muscle cells, randomly distributed, with the exception of a set of three cells adjacent to any branch.  These aggregates were filled to 83% of their radius with gel.  Branches were attached at a site of three gel-filled aggregates, and the aggregates comprising the branch had a radius between 165% and 185% of that of the aggregates in the main tube; these aggregates were gel-filled to approximately 80% of their radius, with the remaining cells distributed as described above.  The lumen of the main tube was filled with the same type of gel as in the centers of the aggregates, and the remainder of the environment was filled with a second type of gel.  The structure was then subjected to Monte Carlo simulation for fifty-thousand steps.  The final equilibrium structure (when simulated with the proper parameters) strongly resembles a branched blood vessel: the cell aggregates fused, and the smooth muscle cells migrated to the outside of the main tube and branch, while the endothelial cells migrated to the interior of the tube and branch.  In addition, the lumen of the branch and main tube were contiguous.  The results of these simulations are currently being used to guide the construction of such structures through in vitro experiments

Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski's equality

doi:10.1063/1.2166379In general, the direct application of the Jarzynski equality (JE) to reconstruct potentials of mean force (PMFs) from a small number of nonequilibrium unidirectional steered molecular-dynamics (SMD) paths is hindered by the lack of sampling of extremely rare paths with negative dissipative work. Such trajectories that transiently violate the second law of thermodynamics are crucial for the validity of JE. As a solution to this daunting problem, we propose a simple and efficient method, referred to as the FR method, for calculating simultaneously both the PMF U(z) and the corresponding diffusion coefficient D(z) along a reaction coordinate z for a classical many-particle system by employing a small number of fast SMD pullings in both forward (F) and time reverse (R) directions, without invoking JE. By employing Crooks [ Phys. Rev. E 61, 2361 (2000) ] transient fluctuation theorem (that is more general than JE) and the stiff-spring approximation, we show that (i) the mean dissipative work mathd in the F and R pullings is the same, (ii) both U(z) and mathd can be expressed in terms of the easily calculable mean work of the F and R processes, and (iii) D(z) can be expressed in terms of the slope of mathd. To test its viability, the FR method is applied to determine U(z) and D(z) of single-file water molecules in single-walled carbon nanotubes (SWNTs). The obtained U(z) is found to be in very good agreement with the results from other PMF calculation methods, e.g., umbrella sampling. Finally, U(z) and D(z) are used as input in a stochastic model, based on the Fokker-Planck equation, for describing water transport through SWNTs on a mesoscopic time scale that in general is inaccessible to MD simulations.This work was supported in part by grants from the University of Missouri Research Board, the Institute for Theoretical Sciences, a joint institute of Notre Dame University and Argonne National Laboratory, the U.S. Department of Energy, Office of Science through Contract No. W-31-109-ENG-38, and NSF through FIBR-0526854