Wigner Function Analysis of GRW and CSL Models: Mathematical Foundations and Simulations

Mech, Dibyajyoti (2025) Wigner Function Analysis of GRW and CSL Models: Mathematical Foundations and Simulations. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Dibyajyoti Mech (20MS021)) 20MS021_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (3MB)

Abstract

This thesis investigates the quantum measurement problem through the lens of dynamical reduction models, specifically the Ghirardi-Rimini-Weber (GRW) and Continuous Spontaneous Localization (CSL) frameworks. The analysis employs the Wigner function as a central tool for visualizing and comparing collapse dynamics in quantum phase space. By contrasting the discrete localization characteristic of GRW with the smooth localization of CSL, the Wigner function reveals distinct signatures of each model’s approach to wavefunction collapse. Visualization techniques—such as contour and 3D surface plots—highlight differences in localization behavior and illustrate the amplification mechanism in multi-particle systems. In particular, the narrowing of the center-of-mass Wigner function with increasing particle number demonstrates an emergent classicality, though simulations are bounded by computational feasibility. While quantitative precision remains limited by resolution and algorithmic order, the results offer qualitative insight into the nature of spontaneous localization. This work contributes to foundational studies by providing a unified analytical and visual framework for examining collapse dynamics, independent of observer-centric interpretations. It reinforces the role of phase-space techniques in bridging microscopic quantum behavior with macroscopic classical phenomena.

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