Happy Thanksgiving! :-)
Roman V. Buniy and Stephen D.H. Hsu
For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics.It may come as a surprise to many physicists that Schrodinger evolution in large isolated quantum systems leads generically to macroscopic superposition states. For example, in the familiar Brownian motion setup of a ball interacting with a gas of particles, after sufficient time the system evolves into a superposition state with the ball in macroscopically different locations. We use von Neumann's 1929 Quantum Ergodic Theorem as a tool to deduce this dynamical result.
The natural state of a complex quantum system is a superposition ("Schrodinger cat state"!), absent mysterious wavefunction collapse, which has yet to be fully defined either in logical terms or explicit dynamics. Indeed wavefunction collapse may not be necessary to explain the phenomenology of quantum mechanics. This is the underappreciated meaning of work on decoherence dating back to Zeh and Everett. See talk slides linked here, or the introduction of this paper.
We also derive some new (sharper) concentration of measure bounds that can be applied to small systems (e.g., fewer than 10 qubits).
Fun fact: Professor Buniy was a postdoc in my group at Oregon. Before coming to the US for graduate school in theoretical physics he was among the last group of young men to serve in the Soviet Army (Strategic Missile Forces IIRC!)
I suppose he has a document like this one:
Here he is in 2011, working on the null energy condition and instabilities in quantum field theories: