Can the Schrodinger dynamics explain measurement?
- URL: http://arxiv.org/abs/2301.01858v2
- Date: Mon, 12 Feb 2024 21:24:37 GMT
- Title: Can the Schrodinger dynamics explain measurement?
- Authors: Alexey A. Kryukov
- Abstract summary: We use the Hamiltonian represented by a random matrix in the Gaussian unitary ensemble to study the Schr"odinger evolution of non-stationary states.
It is shown that the Schr"odinger evolution with such a Hamiltonian models measurement on macroscopic and microscopic systems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The motion of a ball through an appropriate lattice of round obstacles models
the behavior of a Brownian particle and can be used to describe measurement on
a macro system. On another hand, such motion is chaotic and a known conjecture
asserts that the Hamiltonian of the corresponding quantum system must follow
the random matrix statistics of an appropriate ensemble. We use the Hamiltonian
represented by a random matrix in the Gaussian unitary ensemble to study the
Schr\"odinger evolution of non-stationary states. For Gaussian states
representing a classical system, the Brownian motion that describes the
behavior of the system under measurement is obtained. For general quantum
states, the Born rule for the probability of transition between states is
derived. It is then shown that the Schr\"odinger evolution with such a
Hamiltonian models measurement on macroscopic and microscopic systems, provides
an explanation for the classical behavior of macroscopic bodies and for
irreversibility of a measurement, and identifies the boundary between micro and
macro worlds.
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