MONTE CARLO EVALUATION OF THE AHARONOV-BOHM EFFECT

1995 ◽  
Vol 06 (01) ◽  
pp. 67-76 ◽  
Author(s):  
GEORGE C. JOHN ◽  
VIJAY A. SINGH
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Integral Formalism ◽  
Feynman Path ◽  
Metropolis Monte Carlo ◽  
Monte Carlo Evaluation ◽  
Bohm Effect ◽  
Exact Calculations ◽  
Aharonov Bohm ◽  
The Magnetic Field

The electron propagator in the Aharonov-Bohm effect is investigated using the Feynman path integral formalism. The calculation of the propagator is effected using a variation of the Metropolis Monte Carlo algorithm. Unlike “exact” calculations, our approach permits us to include a nonvanishing solenoid radius. We investigate the dependence of the resulting interference pattern on the magnetic field as well as the solenoid radius. Our results agree with the exact case in the limit of an infinitesimally small solenoid radius.

scholarly journals A general method for deriving vector potentials produced by knotted solenoids

2014 ◽  
Vol 29 (35) ◽  
pp. 1450189
Author(s):  
V. V. Sreedhar
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Vector Potentials ◽  
Bohm Effect ◽  
Figure Eight Knot ◽  
Aharonov Bohm ◽  
The Magnetic Field ◽  
General Method

A general method for deriving exact expressions for vector potentials produced by arbitrarily knotted solenoids is presented. It consists of using simple physics ideas from magnetostatics to evaluate the magnetic field in a surrogate problem. The latter is obtained by modeling the knot with wire segments carrying steady currents on a cubical lattice. The expressions for a 31 (trefoil) and a 41 (figure-eight) knot are explicitly worked out. The results are of some importance in the study of the Aharonov–Bohm effect generalized to a situation in which charged particles moving through force-free regions are scattered by fluxes confined to the interior of knotted impenetrable tubes.

Uncertainty analysis of calibrated parameter values of an urban storm water quality model using metropolis monte carlo algorithm

1997 ◽  
Vol 36 (5) ◽  
pp. 141-148 ◽  
Author(s):  
A. Mailhot ◽  
É. Gaume ◽  
J.-P. Villeneuve
Keyword(s):  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Model Calibration ◽  
Monte Carlo Algorithm ◽  
Storm Water ◽  
Model Parameters ◽  
Calibration Data ◽  
Parameter Uncertainties ◽  
Metropolis Monte Carlo ◽  
Parameter Values

The Storm Water Management Model's quality module is calibrated for a section of Québec City's sewer system using data collected during five rain events. It is shown that even for this simple model, calibration can fail: similarly a good fit between recorded data and simulation results can be obtained with quite different sets of model parameters, leading to great uncertainty on calibrated parameter values. In order to further investigate the lack of data and data uncertainty impacts on calibration, we used a new methodology based on the Metropolis Monte Carlo algorithm. This analysis shows that for a large amount of calibration data generated by the model itself, small data uncertainties are necessary to significantly decrease calibrated parameter uncertainties. This also confirms the usefulness of the Metropolis algorithm as a tool for uncertainty analysis in the context of model calibration.

Order/Disorder and Phase Diagram of H on Pd(100)

1990 ◽  
Vol 193 ◽  
Author(s):  
P. Tibbits ◽  
M. Karimi ◽  
D. Ila ◽  
I. Dalins ◽  
G. Vidali
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Critical Temperature ◽  
Structure Factor ◽  
Energy Difference ◽  
Monte Carlo Algorithm ◽  
Temperature Phase ◽  
Embedded Atom ◽  
Large Numbers ◽  
Metropolis Monte Carlo

ABSTRACTAn atomistic simulation of H-Pd(100) provided a phase diagram for the c2×2 H overlayer phase. The Embedded Atom Method (EAM) calculated energy of each configuration of atoms and the Metropolis Monte Carlo algorithm equilibrated the structure and generated configurations from which to sample the structure factor for the H overlayer. The procedure provided the expectation of the square of the structure factor modulus, < |S2| >, as a function of temperature at three coverages. The inflection point of the < |S2| > versus T curve estimated the critical temperature for disordering, Tc,, for one value of coverage, θ. The plot of Tc versus θ, the phase boundary for the c2×2 phase, lay about 125 K below the experimentally determined boundary. A comparison of the energies of ordered and disordered phases showed ΔE = 0.016 eV per hydrogen atom. Equating this unrealistically small energy difference to thermal kinetic energy (3/2)kBTc at the critical temperature implies Tc ≈ 100 K. Obtaining – |S2| > values relatively free of noise at such low temperatures required large numbers of Monte Carlo steps. The c2×2 phase is the experimentally determined stable low temperature phase, and was assumed to be the lowest-energy phase possible in this simulation. The very small ΔE indicates that some other ordered phase may be more stable than c2×2 in the EAM model.

scholarly journals Is the Magnetic Field Necessary for the Aharonov-Bohm Effect in Mesoscopics?

1998 ◽  
Vol 80 (11) ◽  
pp. 2417-2420 ◽  
Author(s):  
I. D. Vagner ◽  
A. S. Rozhavsky ◽  
P. Wyder ◽  
A. Yu. Zyuzin
Keyword(s):  
Magnetic Field ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
The Magnetic Field
Sign in / Sign up

Export Citation Format

Share Document