The Dynamics of a Quantum Soft-Impact Oscillator

Ganesh, Jeware Pratik (2021) The Dynamics of a Quantum Soft-Impact Oscillator. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Jeware Pratik Ganesh (15MS090)) 15MS090_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (9MB)

Abstract

We have proposed di↵erent model systems consisting of a combination of microscopic particles as well as macroscopic bodies. We have used these model systems to test various aspects of the property of collapse of the wavefunction associated with quantum particles or their systems. The dynamics pertaining to the motion of these model systems was studied as well. We have used two systems primarily to showcase these aspects: 1. A quantum soft impact oscillator, which basically is the quantum analog of the classical soft-impact oscillator system which comprises of a harmonic oscillator that is constrained by a soft wall. 2. A system of two distinguishable quantum particles that can be regarded as spatially local. This is a classical analog of two harmonic oscillators in vicinity. In the first model system, the presence of the proposed soft wall, which being a macroscopic body, any impact with the quantum particle would lead to its collapse. We have further proposed four postulates with which we can numerically realize this process of collapse as we simulate the time evolution of the system in hand. We have also looked to obtain experimentally testable predictions from the results of the simulation. To study the dynamics of this system, use of the overlap integral was done to obtain the time series data. Since the classical soft-impact oscillator is known to to exhibit complex dynamics and chaos close to the grazing bifurcation. We explored if this was the case in the quantum domain as well. It was found out that it exhibited a non-chaotic behaviour. The second model system consisted of the soft-impact oscillator system but with the soft wall taken as a microscopic body. Being a only microscopic object system, we have proposed an algorithm by which a spontaneous collapse of the respective wavefunctions of the distinguishable particles gets incorporated as it evolves according to the Schrodinger equation. The postulation in this system regarding collapse is brought out by conserving energy of either the whole system or the individual particles. 9

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