12 papers
Solvent Inertia Changes Product Probability by Relocating the Phase-Space Reactivity Boundary
Stephen Wiggins
Changing solvent inertia changes the kinetic part of a molecular Hamiltonian and hence its flow in phase space, without requiring a change in the potential energy surface (PES). We…
From Transition-State Geometry to Gap Times: What Lagrangian Betweenness Measures in Chemical Reaction Dynamics
Stephen Wiggins
A chemical transition state is a phase-space bottleneck: trajectories approach along stable directions and leave along unstable directions. Lagrangian betweenness (LB), introduced…
What solvable models reveal about Born-Oppenheimer, Born-Huang, and exact factorization
Stephen Wiggins
The Born-Oppenheimer (BO) and single-surface Born-Huang (BH) approximations replace the full molecular problem by nuclear motion associated with one clamped electronic state, where…
Rare Fluctuations from Normally Hyperbolic Invariant Manifolds
Stephen Wiggins
Freidlin--Wentzell theory converts weak-noise large deviations into a Hamiltonian variational problem. We study how a -dimensional normally hyperbolic invariant manifold (NHIM)…
A Three-Degree-of-Freedom Chesnavich Model for Roaming: Derivation, Phase-Space Geometry, NHIM-Anchored Dividing Surfaces, and Roaming Transport
Stephen Wiggins
Roaming reactions, in which a dissociating fragment moves through a flat region of the potential surface rather than down the minimum-energy path, lie outside the assumptions of co…
An entropic bottleneck, dynamical gating, and outward redistribution of roaming in a designed Chesnavich-type model
Stephen Wiggins
Roaming reactions are organized not by potential-energy saddles but by transition states that are unstable invariant objects in phase space, periodic orbits in the two degrees of f…
Preparation-Space Diagnostics and Logical Information Loss in a Driven Kerr-Cat Qubit
Stephen Wiggins
A Kerr-cat qubit encodes a logical bit in the two wells of a parametrically driven nonlinear oscillator, and a logic gate is a transient change of the drive. In the phase plane the…
A Phase Space Signature of Quantum Roaming in Chesnavich's Model
Stephen Wiggins
Roaming reactions occur when a molecule enters a near-dissociation region, avoids immediate separation, and later forms products by a pathway not controlled by the conventional tig…
A cusp criterion for a local phase-space bottleneck in a minimal adiabatic Marcus Hamiltonian
Stephen Wiggins
Marcus--Hush theory describes electron transfer through reorganization energies, driving forces, and electronic coupling, but it does not by itself determine when an adiabatic mode…
Lobe Dynamics, Phase-Space Transport, and Non-Adiabatic Leakage Thresholds in the Nonautonomous Kerr-Cat Qubit
Stephen Wiggins
The Kerr-nonlinear parametric oscillator (KPO) provides a foundational semiclassical model for cat-state quantum hardware. Standard analyses of the KPO typically rely on autonomous…
A Periodic Orbit Trace Formula for Quantum Scrambling: The Role of the Normally Hyperbolic Invariant Manifold
Stephen Wiggins
Out-of-Time-Order Correlators (OTOCs) quantify quantum information scrambling, but their connection to localized phase-space structures, such as chemical transition states, require…
Bridging Classical Sensitivity and Quantum Scrambling: A Tutorial on Out-of-Time-Ordered Correlators
Stephen Wiggins
In classical dynamical systems, chaotic behavior is often associated with exponential sensitivity to initial conditions together with global phase-space structure. Translating this…