Boundary-Induced Collapse (BIC) in Spectral Language
Year: 2026
Type: article
Abstract: We propose that in physical systems, structural stability is not an intrinsic property but a consequence of boundary-induced spectral selection. In this work, we formalize the Boundary-Induced Collapse (BIC) by analyzing a quantum system S interacting with a boundary environment B through a total Hamiltonian $hat{H}_{text{tot}} = hat{H}_S + hat{H}_B + hat{H}_{SB}$. We demonstrate that the effective dynamics of S is governed by an induced Hermitian operator $\hat{G} = \text{Tr}_B(\hat{H}_{\text{SB}} \rho_B \hat{H}_{\text{SB}}^\dagger)$, which encodes the structural constraints of the boundary. By applying the spectral theorem to hat{G}, we show that the system’s density matrix necessarily collapses into the spectral basis defined by the operator’s eigenstates $(|\phi_i\rangle)$, which we term Ontological Deltas. This process provides a unified framework where quantum decoherence and measurement are seen as specific cases of a more general principle of spectral necessity. Furthermore, we establish that this Hamiltonian-based collapse is the formal quantum analog of the classical $A^T$ normalization in linear systems. We conclude that diagonalization is the universal physical mechanism through which nature translates incoherent interactions into stable, observable states of residency. Diagram https://drive.google.com/file/d/1TxZtBJpwCAzkOGBU3sEpLwhV7DoC3tFA/view?usp=drive_link
Author: Bresciano, Claudio
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7124990738
FWCI:
Cites:
Cited by:
Related to: