Entanglement-Inducing Quantum Markov Processes

arXiv:2609.21438 · math-ph, math.MP, quant-ph · Submitted 2026-09-18 · Read on arXiv

math-ph, math.MP, quant-ph

Submitted: 2026-09-18

Updated: 2026-09-18

Comments: 27 pages, 1 figure; submitted

License: http://creativecommons.org/licenses/by/4.0/

The gist: We introduce a new model for a system of interacting bosons placed in an array of sites.

Terminology

Entanglement — 8× in this paper · explained in 3 episodes
Hilbert Space — 4× in this paper · explained in 2 episodes
Core — 2× in this paper · explained in 2 episodes
Generalization — 2× in this paper · explained in 13 episodes
Hubbard Model — 2× in this paper · explained in 3 episodes
Trace — 2× in this paper · explained in 2 episodes
Bose-Hubbard Hamiltonian — 1× in this paper
Geometric Distribution — 1× in this paper · explained in 2 episodes
Phase Transitions — 1× in this paper · explained in 2 episodes
Quantum Physics — 1× in this paper · explained in 10 episodes
Symmetry Breaking — 1× in this paper · explained in 3 episodes

Abstract

We introduce a new model for a system of interacting bosons placed in an array of sites. At its core is a nonlinear, nonlocal evolution equation, which we have dubbed the Schrödinger-Dirichlet equation. The construction is closely related to the Bose-Hubbard model and to a specific type of generalized bosons. In contrast to conventional mean-field closures, the resulting nonlinear dynamics need not preserve product structure and can generate entanglement from initially separable states. The relevant methods of analysis are based on harmonic analysis for the multiplicative group of positive rationals.

Terminology

Abstract

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