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arXiv:2511.14547

Systems with Quantum Dimensions

Mikołaj Myszkowski, Mattia Damia Paciarini, Francesco Sannino

quant-phcond-mat.otherhep-phhep-thSubmitted Nov 18, 2025• Announced Nov 19, 2025• 0 citations
v1 · Nov 18, 2025v2 · Jan 14, 2026
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Abstract

We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable. As a consequence, the effective dimension depends on the physical state of the system. Interestingly, systems of this form exhibit enhanced symmetries compared to their fixed-dimensional counterparts. As an explicit example, we analyze a harmonic oscillator for which the spatial dimension 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.

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5 pages, 2 figures

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