Dynamics and the global approach to quantization

William He

Discrete measurement outcomes are a defining feature of quantum mechanics, yet the origin of quantization itself remains conceptually unresolved. This work presents an interpretive and structural framework in which quantization arises from global constraint enforcement—due to symmetry, topology, and conservation laws—on continuous state manifolds. Standard quantized observables are reinterpreted as admissible resolutions under these constraints. A formal analogy with elliptic divisibility sequences illustrates rigid integer enforcement arising from global structure alone. The framework does not modify quantum dynamics, introduce collapse mechanisms, or posit hidden variables. The manuscript is currently under consideration at Foundations of Physics.

T. D. Palev

Jinwuk Seok, Changsik Cho

This work presents a quantum mechanical framework for analyzing quantization-based optimization algorithms. The sampling process of the quantization-based search is modeled as a gradient-flow dissipative system, leading to a Hamilton-Jacobi-Bellman (HJB) representation. Through a suitable transformation of the objective function, this formulation yields the Schroedinger equation, which reveals that quantum tunneling enables escape from local minima and guarantees access to the global optimum. By establishing the connection to the Fokker-Planck equation, the framework provides a thermodynamic interpretation of global convergence. Such an analysis between the thermodynamic and the quantum dynamic methodology unifies combinatorial and continuous optimization, and extends naturally to machine learning tasks such as image classification. Numerical experiments demonstrate that quantization-based optimization consistently outperforms conventional algorithms across both combinatorial problems and nonconvex continuous functions.

Georges Lochak

Irving E. Segal

Sanjib Ghosh

Microcavity exciton-polaritons have emerged as an excellent platform for realizing quantum phases of matter, owing to their ability to undergo non-equilibrium Bose-Einstein condensation. Here, we show that the interplay between multiple quantized levels in microcavities and polariton nonlinearity drives the emergence of unconventional phases. Specifically, we demonstrate that intra-site quantization in microcavity polariton lattices—manifested as multiple energy levels in strongly confined sites—provides a route to manipulating these phases. We show that nonlinear interactions transfer population into excited onsite energy levels, acting as an intrinsic dynamical channel that controls coherence across the lattice. While weak nonlinearity confines polaritons to the lowest mode, yielding a robust superfluid phase with broken U(1) symmetry, strong nonlinearity induces phase diffusion through inter-level mixing. This dynamically generated fluctuation suppresses global phase coherence and drives the system into a dynamical Bose-insulating phase. Transitions between these phases occur either as a non-equilibrium phase transition or a sharp crossover. This study investigates the destruction of global order in a non-equilibrium condensate within a lattice featuring onsite quantized energy levels. Long-range fluctuations suppress superfluid stiffness and the condensate fraction, while persistent local order reveals a dynamical Bose-insulating state.