scholarly journals A Generalized Monte Carlo Approach for the Analysis of Quantum-Transport Phenomena in Mesoscopic Systems: Interplay Between Coherence and Relaxation

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 197-202
Author(s):  
Fausto Rossi ◽  
Stefano Ragazzi ◽  
Aldo Di Carlo ◽  
Paolo Lugli
Keyword(s):  
Monte Carlo ◽  
Quantum Transport ◽  
Open Systems ◽  
Transport Phenomena ◽  
Kinetic Equations ◽  
Numerical Approach ◽  
Mesoscopic Systems ◽  
Bloch Oscillations ◽  
Self Energy ◽  
Spatial Boundary

A theoretical investigation of quantum-transport phenomena in mesoscopic systems is presented. In particular, a generalization to “open systems” of the well-known Semiconductor Bloch equations is proposed. Compared to the conventional Bloch theory, the presence of spatial boundary conditions manifest itself through self-energy corrections and additional source terms in the kinetic equations, which are solved by means of a generalized Monte Carlo simulation.The proposed numerical approach is applied to the study of the scattering-induced suppression of Bloch oscillations in semiconductor superlattices as well as to the analysis of quantum-transport phenomena in double-barrier structures.

scholarly journals Generating Empirical Core Size Distributions of Hedonic Games Using a Monte Carlo Method

2021 ◽  
pp. 2250001
Author(s):  
Andrew J. Collins ◽  
Sheida Etemadidavan ◽  
Wael Khallouli
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Numerical Approach ◽  
Core Stability ◽  
Size Distributions ◽  
Core Size ◽  
Empirical Distributions ◽  
Research Findings ◽  
Hedonic Games ◽  
Partition Size

Hedonic games have gained popularity over the last two decades, leading to several research articles that have used analytical methods to understand their properties better. In this paper, a Monte Carlo method, a numerical approach, is used instead. Our method includes a technique for representing, and generating, random hedonic games. We were able to create and solve, using core stability, millions of hedonic games with up to 16 players. Empirical distributions of the hedonic games’ core sizes were generated, using our results, and analyzed for games of up to 13 players. Results from games of 14–16 players were used to validate our research findings. Our results indicate that core partition size might follow the gamma distribution for games with a large number of players.

scholarly journals Neutrino Transport with the Monte Carlo Method. II. Quantum Kinetic Equations

2021 ◽  
Vol 257 (2) ◽  
pp. 55
Author(s):  
Chinami Kato ◽  
Hiroki Nagakura ◽  
Taiki Morinaga
Keyword(s):  
Monte Carlo ◽  
Technical Problem ◽  
Sudden Change ◽  
Kinetic Equations ◽  
Mean Free Path ◽  
High Energy ◽  
The Monte Carlo Method ◽  
Numerical Treatments ◽  
Quantum Feature ◽  
Statistical Noise

Abstract Neutrinos have a unique quantum feature as flavor conversions. Recent studies suggested that collective neutrino oscillations play important roles in high-energy astrophysical phenomena. The quantum kinetic equation (QKE) is capable of describing the neutrino flavor conversion, transport, and matter collision self-consistently. However, we have experienced many technical difficulties in their numerical implementation. In this paper, we present a new QKE solver based on a Monte Carlo (MC) approach. This is an upgraded version of our classical MC neutrino transport solver; in essence, a flavor degree of freedom including mixing state is added into each MC particle. This extension requires updating numerical treatments of collision terms, in particular for scattering processes. We deal with the technical problem by generating a new MC particle at each scattering event. To reduce statistical noise inherent in MC methods, we develop the effective mean free path method. This suppresses a sudden change of flavor state due to collisions without increasing the number of MC particles. We present a suite of code tests to validate these new modules with comparison to the results reported in previous studies. Our QKE-MC solver is developed with fundamentally different philosophy and design from other deterministic and mesh methods, suggesting that it will be complementary to others and potentially provide new insights into physical processes of neutrino dynamics.

PERFECT STOCHASTIC SUMMATION IN HIGH ORDER FEYNMAN GRAPH EXPANSIONS

2006 ◽  
Vol 17 (11) ◽  
pp. 1527-1549 ◽  
Author(s):  
J. N. CORCORAN ◽  
U. SCHNEIDER ◽  
H.-B. SCHÜTTLER
Keyword(s):  
Monte Carlo ◽  
Feynman Graph ◽  
Sampling Technique ◽  
Small Samples ◽  
Brute Force ◽  
Perfect Sampling ◽  
Self Energy ◽  
Graph Expansions ◽  
Low Dimensional ◽  
True Values

We describe a new application of an existing perfect sampling technique of Corcoran and Tweedie to estimate the self energy of an interacting Fermion model via Monte Carlo summation. Simulations suggest that the algorithm in this context converges extremely rapidly and results compare favorably to true values obtained by brute force computations for low dimensional toy problems. A variant of the perfect sampling scheme which improves the accuracy of the Monte Carlo sum for small samples is also given.

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