Emergence of Classical Dynamics from a Random Matrix Schrödinger Model

Abstract

The Newtonian motion of a macroscopic particle is derived from the linear Schrödinger equation with a Hamiltonian consisting of the free-particle term and a random Hamiltonian drawn from the Gaussian Unitary Ensemble. The random term models interaction with the environment. We show that the parameters governing the resulting state-space random walk, together with the treatment of experimentally indistinguishable states as equivalence classes, explain the contrasting behavior of microscopic and macroscopic systems. The analysis extends previous work deriving the Born rule for microscopic particles when the free-particle term is negligible.

References in corpus (16)

• Decoherence, einselection, and the quantum origins of the classical
• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Dynamical Reduction Models
• A Straightforward Introduction to Continuous Quantum Measurement
• Sudden transition between classical and quantum decoherence
• Classical world arising out of quantum physics under the restriction of coarse-grained measurements
• Lower and Upper Bounds on CSL Parameters from Latent Image Formation and IGM Heating
• Experimental bounds on collapse models from gravitational wave detectors
• Quantum-to-Classical Transition in Cavity Quantum Electrodynamics
• Coarsening Measurement References and the Quantum-to-Classical Transition
• Novel CSL bounds from the noise-induced radiation emission from atoms
• Geometric derivation of quantum uncertainty
• Entanglement vs. the quantum-to-classical transition
• Mathematics of the classical and the quantum
• Improved bounds on collapse models from rotational noise of LISA Pathfinder
• Dynamics of a particle in the double-slit experiment with measurement