Following a "Collapsing" Wavefunction

TL;DR

This paper investigates how a spin interacting with an apparatus exhibits wavefunction collapse through unitary evolution, analyzing the process via density matrices and consistent histories to understand quantum measurement dynamics.

Contribution

It provides a detailed analysis of wavefunction collapse in a spin-apparatus system using density matrices and consistent histories, highlighting the role of Hamiltonian structure.

Findings

Demonstrates loss of quantum coherence in the spin system

Contrasts density matrix and consistent histories approaches

Links collapse behavior to Hamiltonian form

Abstract

I study the quantum mechanics of a spin interacting with an ``apparatus''. Although the evolution of the whole system is unitary, the spin evolution is not. The system is chosen so that the spin exhibits loss of quantum coherence, or ``wavefunction collapse'', of the sort usually associated with a quantum measurement. The system is analyzed from the point of view of the spin density matrix (or ``Schmidt paths''), and also using the consistent histories approach. These two points of view are contrasted with each other. Connections between the results and the form of the Hamiltonian are discussed in detail.