Quantum Physics |
Authors: Joshua James Farrow
A change of field boundary conditions produces quanta when it mixes positive- and negative-frequency modes, but the boundary motion is usually prescribed externally. We construct a finiteautonomous quantum shutter in which a quantum matter register controls one local bilinear of aone-dimensional bosonic lattice while the complete matter—field Hamiltonian remains fixed and timeindependent. The controller-gated term is C = ηκqℓqr , and at full closure the open and closed fieldHamiltonians obey the exact local identity Hcl − Hop = κqℓqr . An abrupt opening therefore gives acanonical Bogoliubov transformation with nonzero β, so the closed vacuum is squeezed in the openbasis and a closed-basis one-quantum state becomes a one-quantum-added squeezed state. Exactsparse evolution and canonical matrix-product-state evolution show autonomous packet transmissionbetween the static closed and open limits, controller backreaction, matter—field entanglement, andenergy redistribution with total-energy drift below 4 × 10−13 in the canonical benchmark. After fixingoutgoing modes independently from a prescribed smooth-history reference, far local field algebras canbe close at the 10−4—10−6 level while the joint outgoing state remains distinguishable. A collectivecontroller of size M approaches the prescribed classical switch with leading corrections proportionalto 1/M , in agreement with a spin-coherent fluctuation expansion. The controller register also has anexact embedding into ordinary matter qubits through frustration projectors and a unary clock sector.The construction is a regulated scalar/bosonic realization of standard dynamical-Casimir physics; itis not a derivation of electromagnetic U (1) or of an unregulated infinite particle-number tail.
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