Mathematical Engine
Morphological Physics (MP) is, at root, a contribution to fundamental mathematics whose consequences run through derivable physics and into engineered observables. The four research themes of the FSU Quantum Initiative are not parallel claims that MP touches at the edges; they are downstream outputs of one mathematical engine working under different boundary conditions and observable extractions. This document maps MP’s contribution onto each theme, separating what is already a validated result from what follows directly from the framework’s existing structure and from what the framework structurally predicts.
Figure 1. One mathematical engine. Each FSU Quantum Initiative theme sits in the column where MP’s contribution to that theme originates: QTA in Mathematics, QTM in Physics, QDM and QON in Engineering.
Quantum Theory and Algorithms (QTA)
FSU Today
FSU’s QTA activity is the theoretical and computational backbone of the Quantum Initiative: tools to understand quantum systems, methods for strong electronic and light-matter correlations, quantum phase transitions, error correction and mitigation, algorithm design, and applications across chemistry, materials science, biology, and engineering. DePrince leads electronic-structure theory; Changlani, Bonesteel, Chen, Volya, and Fossez contribute across correlated systems, error correction, and computational quantum methods. This theme is MP’s institutional home — the framework is, formally, a theoretical and computational tool for quantum systems with applications spanning chemistry, materials, and engineering.
Morphological Physics
Existing Results. Analytic electronic-structure computation from molecular geometry alone — no density functional theory, no self-consistent field iteration, no finite-element method, no fitted parameters beyond element-level scalars. Validated on benzene HOMO–LUMO at 2.9% of literature, on the e\(_{2u}\) LUMO degeneracy and lobe pattern recovered from boundary symmetry alone, and on the four DNA bases at \(\pm 3\%\) across the bases with HOMO–LUMO ordering matching the oxidation sequence at chance probability below \(10^{-6}\).
Direct extensions. The same operator extends to larger conjugated systems — the OSC molecular catalog (Y6, ITIC, PM6, and related non-fullerene acceptors), polycyclic aromatic systems, fused-ring acceptors — by changing the domain rather than the machinery. Excited-state spectra beyond HOMO–LUMO are higher eigenvalues of the same operator. Dipole couplings, between-set couplings between donor and acceptor manifolds, and oscillator strengths are integrated outputs of the eigenvalue solve, not separate calculations layered on top.
Structural predictions. The eigenvalue computation is differentiable end-to-end from molecular geometry to observable, supplying the analytic gradient pathway that complements the physics-guided machine learning pipelines emerging for organic semiconductor inverse design. The framework’s eigenvalue solve is the analytic alternative to the SCF-and-finite-difference loop that currently dominates inverse-design workflows. The morphological structure underlying the eigenvalue problem is the same morphological engine that produces several independently developed branches of mathematical physics, with bounded molecular electronic structure as one of its natural projections — a unifying picture rather than a domain-specific tool.
Quantum and Topological Materials (QTM)
FSU Today
FSU’s QTM activity addresses quantum electronic and magnetic phenomena arising from dimensional confinement, electronic correlation, spatial symmetry, and nontrivial band topology — with the goal of harnessing these phenomena for quantum sensing, memory, and computation. Changlani, Dobrosavljevic, and Shatruk lead the strongly correlated and topological theory and synthesis effort, with the National MagLab providing experimental infrastructure. The Moon, McKeever, and Balicas 2024 result on writing and detecting topological charges in exfoliated Fe\(_{5-x}\)GeTe\(_2\) (ACS Nano 18, 4216) is the signature demonstration of the theme’s reach into engineered topological materials.
Morphological Physics
Existing Results. Spatial symmetry of the molecular domain transfers to symmetry of the eigenstates by construction. Validated on benzene: the framework recovers the e\(_{2u}\) LUMO degeneracy with the correct \(90^\circ\)-rotated lobe pattern from hexagonal boundary geometry alone, with no chemistry input beyond atom positions. Benzene HOMO–LUMO computes to within 2.9% of the literature value. The same operator is geometry-agnostic across dimensionality — the planar molecular case and the higher-dimensional extension are the same machinery on different domains.
Direct extensions. Electronic correlation enters the operator through the density weight rather than as a perturbative correction. The eigenvalue problem inherits correlation structure from the underlying density without separation of single-particle and correlated contributions. Application to the larger conjugated and fused-ring systems that define the OSC and emerging topological-organic materials catalog requires only running the existing operator on the corresponding molecular boundaries.
Structural predictions. Topological invariants of band structures — winding numbers, Chern-like quantities — have natural analogs as winding numbers of eigenstates over the bounded molecular domain. The framework’s existing structure carries the geometric information required for this derivation; explicit equivalence to standard band-theoretic invariants is theoretically supported and outstanding as a written result.
Qubit Design and Measurements (QDM)
FSU Today
FSU’s QDM activity focuses on bottom-up synthesis of molecular spin qubits, linking individual qubits into dimers and trimers that mimic simple quantum logic gates, and characterizing coherence in diluted spin systems through advanced spectroscopy — electron paramagnetic resonance, X-ray diffraction, optical spectroscopy, and on-chip detection. The Hill, Kundu, and Shatruk groups are central to this work, with Hanson contributing photophysical characterization. The signature recent result is the Kundu/Hill 9.2 GHz clock transition arising from a 3,467 MHz hyperfine interaction in a Lu(II) molecular spin qubit (Nature Chemistry 14, 392, 2022) — a level structure that lives entirely in the molecular electronic-and-nuclear eigenvalue problem.
Morphological Physics
Existing Results. The Bell correlation function for two-qubit measurements is recovered analytically from the framework’s geometric structure, without invoking the Born rule or any quantum postulate as input. Validated molecular spectrum recovery: the electronic structure of all four DNA bases is reproduced from molecular geometry with a single scaling constant held to \(\pm 3\%\) across the four bases, and the HOMO–LUMO ordering matches the known oxidation sequence (G \(>\) A \(>\) C \(>\) T) with chance probability below \(10^{-6}\).
Direct extensions. The two-level structure of a molecular spin qubit is recoverable from the same eigenvalue machinery that produces the validated DNA spectra. The hyperfine tensor — Fermi contact and dipolar terms — follows from overlap integrals between electronic and nuclear eigenstates on the combined molecular domain; the derivation parallels the validated DNA work and requires application of existing machinery rather than new theoretical framework.
Structural predictions. Coherence in extended molecular spin systems is governed by the same operator that defines the spin states themselves. The framework’s structure suggests analytic scaling laws for coherence as a function of system extent and dilution. Multi-qubit systems (dimers, trimers) are not coupled qubits in the framework’s language; they are single domains whose combined geometry produces multi-level spectra with exchange and coupling structure as direct eigenvalue outputs.
Quantum Optics and Networks (QON)
FSU Today
FSU’s QON activity addresses light-matter interactions at the quantum level: creation, manipulation, and transmission of quantum states of light, with explicit interest in interfacing photonic states with spin-qubit memories. Dusanowski’s work on telecom-wavelength quantum-dot spin qubits (Nature Communications 13, 748, 2022) is the signature recent result and exemplifies the theme’s central problem — a confined electronic system whose discrete eigenstructure determines coherent photon emission at telecommunication wavelengths. Kudisch and Hanson contribute photophysics and chiral light-matter interaction perspectives.
Morphological Physics
Direct extensions. Coupling between molecular electronic states and electromagnetic modes follows from eigenstate overlap on a combined matter-field domain — the same operator extended to include the electromagnetic field as part of the bounded problem rather than as an external perturbation. Quantum-dot optical emission, the matter side of single-photon generation, and the absorption spectra that determine OSC active-layer behavior all sit inside this construction. The OSC application’s molecular absorption computation, currently in validation against Y6 and ITIC literature, is a quantum-optics calculation in different vocabulary; the underlying machinery is identical.
Structural predictions. Entangled-photon pair generation from correlated emitters corresponds to joint eigenstates on a composite molecular-and-field domain, with the entanglement structure determined by the joint eigenvalue problem rather than imposed by a separate model. Network-scale photonic coherence is governed by the same operator that defines the photon emission, providing a single analytic framework spanning the molecular emitter, the photonic mode, and the network of modes connecting multiple emitters.
What Makes This Possible
The framework’s reach across the four themes is not an aspirational claim about future generality; it is a structural consequence of two pieces of nineteenth-century mathematics that the framework recognizes and applies, rather than invents.
The first is the density-weighted Sturm–Liouville eigenvalue problem on a bounded domain. Sturm–Liouville theory establishes that this problem is a self-adjoint operator with discrete spectrum and a complete orthonormal eigenfunction basis. The mathematics is undisputed and over 150 years old. MP’s claim is recognition, not invention: the eigenvalue problem on the molecular electron-density boundary is the molecular electronic structure — not a model or approximation of it. The boundary and the weight are the input; the eigenstates and the spectrum are determined uniquely by Sturm–Liouville theory.
In two dimensions, Riemann’s 1851 Mapping Theorem reduces any simply-connected bounded planar domain to a canonical reference geometry — the unit disk. This is the classical result that makes the molecular eigenvalue problem analytic on planar molecular cross-sections. The natural next question is what happens in three dimensions, and a careful reader who knows the classical literature knows the answer: Liouville (1850) proved that no analog of the Riemann Mapping Theorem exists in higher dimensions. The conformal-mapping route to canonical reduction is strictly two-dimensional.
Even in two dimensions, however, Riemann’s theorem is an existence result, not a construction — it proves that a canonical mapping exists for any simply-connected bounded domain, but supplies no procedure for computing one. The framework provides the only known constructive solution. An explicit procedure that takes molecular geometry as input and produces the canonical reduced eigenvalue problem as output, applicable in two and higher dimensions alike. This is the operational achievement on which everything else depends. Without a constructive route from molecular boundary to canonical eigenvalue problem, the classical existence theorems tell us only that an answer is possible — not how to compute it. The framework supplies the missing construction.
The higher-dimensional case does not require an analog of the Riemann Mapping Theorem because the construction does not depend on conformal mapping. The analytic structure of the eigenvalue equation itself, combined with the classical theory of orthogonal polynomials on bounded domains, supplies the canonical reduction in three and higher dimensions by a different mathematical route. The framework therefore respects Liouville’s classical impossibility theorem rather than evading it: where conformal mapping cannot reach, the orthogonal-polynomial construction does. The framework’s reach rests on three pillars working together — classical existence theorems that establish the canonical problem is well-posed, the analytic eigenvalue structure of the bounded operator, and the constructive procedure that converts molecular geometry into a computable answer.
The second piece is the morphological principle underlying the eigenvalue problem. The same morphological engine appears, under different boundary conditions, across several independently developed branches of mathematical physics. The framework’s claim to span the four themes reduces to a single observation: the four themes are different observable channels of one morphological engine — not separate physical theories patched together.
The mathematics is canonical; the physics follows; the engineering is downstream.