29,887 research outputs found
Exact and Fast Numerical Algorithms for the Stochastic Wave Equation
On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions. The algorithms are exact in a probabilistic sense
Heisenberg picture operators in the stochastic wave function approach to open quantum systems
A fast simulation algorithm for the calculation of multitime correlation
functions of open quantum systems is presented. It is demonstrated that any
stochastic process which ``unravels'' the quantum Master equation can be used
for the calculation of matrix elements of reduced Heisenberg picture operators,
and thus for the calculation of multitime correlation functions, by extending
the stochastic process to a doubled Hilbert space. The numerical performance of
the stochastic simulation algorithm is investigated by means of a standard
example.Comment: RevTex, 5 pages, 2 figures, uses multico
Stochastic Methods for Zero Energy Quantum Scattering
We investigate the use of stochastic methods for zero energy quantum
scattering based on a path integral approach. With the application to the
scattering of a projectile from a nuclear many body target in mind, we use the
potential scattering of a particle as a test for the accuracy and efficiency of
several methods. To be able to deal with complex potentials, we introduce a
path sampling action and a modified scattering observable. The approaches
considered are the random walk, where the points of a path are sequentially
generated, and the Langevin algorithm, which updates an entire path. Several
improvements are investigated. A cluster algorithm for dealing with scattering
problems is finally proposed, which shows the best accuracy and stability.Comment: 40 pages LaTeX, 1 Postscript file containig 20 figures; execute
main.tex file, which automatically will include other file
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
A variational approach to the stochastic aspects of cellular signal transduction
Cellular signaling networks have evolved to cope with intrinsic fluctuations,
coming from the small numbers of constituents, and the environmental noise.
Stochastic chemical kinetics equations govern the way biochemical networks
process noisy signals. The essential difficulty associated with the master
equation approach to solving the stochastic chemical kinetics problem is the
enormous number of ordinary differential equations involved. In this work, we
show how to achieve tremendous reduction in the dimensionality of specific
reaction cascade dynamics by solving variationally an equivalent quantum field
theoretic formulation of stochastic chemical kinetics. The present formulation
avoids cumbersome commutator computations in the derivation of evolution
equations, making more transparent the physical significance of the variational
method. We propose novel time-dependent basis functions which work well over a
wide range of rate parameters. We apply the new basis functions to describe
stochastic signaling in several enzymatic cascades and compare the results so
obtained with those from alternative solution techniques. The variational
ansatz gives probability distributions that agree well with the exact ones,
even when fluctuations are large and discreteness and nonlinearity are
important. A numerical implementation of our technique is many orders of
magnitude more efficient computationally compared with the traditional Monte
Carlo simulation algorithms or the Langevin simulations.Comment: 15 pages, 11 figure
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