The fundamental of quantum zeno effect with mathematical approach in undergraduate study

Mohamad Nazri, Abu Zhar (2022) The fundamental of quantum zeno effect with mathematical approach in undergraduate study. [Project Paper] (Submitted)

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Abstract

If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. In contrast, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. We explore this said evolution in with non-Hermitian Hamiltonian and Hermitian Hamiltonian later the interaction between these two states. By following the calculation made, we can get the equation that can be define as “Zeno time”. With this information in hand, we can continue with quantum Zeno effect. The most familiar formulation of the quantum Zeno effect makes use of Von Neumann’s measurements, represented by one-dimensional projectors. We first undergo the two-level system first since it’s the simplest compared to the Von Neumann’s, in which the projection onto the initial state “slowly” evolves away from unity. Later, we show that the action of a measuring apparatus (performing. the von Neumann measurement) can be mimicked by a non-Hermitian Hamiltonian. Followed by showing that the non-Hermitian Hamiltonian can be obtained by considering the evolution engendered by a Hermitian Hamiltonian acting on a larger Hilbert space.

Item Type:	Project Paper
Faculty:	Fakulti Sains
Depositing User:	Ms. ROHANA ALIAS
Date Deposited:	19 Jun 2024 03:30
Last Modified:	19 Jun 2024 03:30
URI:	http://psaspb.upm.edu.my/id/eprint/1969

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