2025/11/18 by Myszkowski, Mikołaj, Paciarini, Mattia Damia, Sannino, Francesco
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Quantum Electrodynamics and Casimir Effect
paper · doi:10.48550/arxiv.2511.14547
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries compared to their fixed-dimensional counterparts. As an explicit example, we analyze a two-state system for which the number of spatial dimensions is represented by a quantum operator. By evaluating the corresponding partition function, we uncover a temperature-dependent effective dimension. Our framework opens a new avenue for constructing physical systems, from gravity to condensed matter, where the very notion of dimensionality becomes quantum.