Fubini–Study Length Bounds on Particle Creation in Driven Bosonic Systems

Time-dependent quadratic Hamiltonians create quanta from the instantaneous vacuum, as in cosmological particle creation, the dynamical Casimir effect and parametric amplification. We bound the number of created quanta by the quantum geometry of the instantaneous ground state, using the Fubini–Study metric and the intrinsic geometry of the manifold of pure Gaussian states. For any number of coupled bosonic modes with a positive-definite quadratic Hamiltonian, we prove that the number of quasiparticles created from the instantaneous ground state is bounded by sinh²(√2 d), where d is the Gaussian geodesic distance between the evolved state and the instantaneous ground state, and hence by sinh²(√2 L), where L is the Fubini–Study length of the ground-state trajectory. The constant √2 is optimal, and for a single mode the bound reduces to the Boonserm–Visser bound. In a symplectic frame built from the ground-state covariance, an operator-norm refinement and a phase-sensitive bound hold for all such Hamiltonians, and a second integration by parts makes the phase-sensitive bound computable from the Hamiltonian alone. For a defect moved along a ring of oscillators, the phase-sensitive bound follows the exact excitation within a factor 2.1 at all speeds, and motion at finite speed creates more quanta than a sudden displacement. For a conformally coupled massive field in a monotonically expanding universe, the density of created particles is bounded by its sudden-expansion value.