Hyperbolic Inflation Brown, Adam R
Physical review letters,
2018-Dec-21, Volume:
121, Issue:
25
Journal Article
Peer reviewed
Open access
A model of cosmological inflation is proposed in which field space is a hyperbolic plane. The inflaton never slow-rolls, and instead orbits the bottom of the potential, buoyed by a centrifugal force. ...Though initial velocities redshift away during inflation, in negatively curved spaces angular momentum naturally starts exponentially large and remains relevant throughout. Quantum fluctuations produce perturbations that are adiabatic and approximately scale invariant; strikingly, in a certain parameter regime the perturbations can grow double exponentially during horizon crossing.
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Summary
Earth system models must predict forest responses to global change in order to simulate future global climate, hydrology, and ecosystem dynamics. These models are increasingly adopting ...vegetation demographic approaches that explicitly represent tree growth, mortality, and recruitment, enabling advances in the projection of forest vulnerability and resilience, as well as evaluation with field data. To date, simulation of regeneration processes has received far less attention than simulation of processes that affect growth and mortality, in spite of their critical role maintaining forest structure, facilitating turnover in forest composition over space and time, enabling recovery from disturbance, and regulating climate‐driven range shifts. Our critical review of regeneration process representations within current Earth system vegetation demographic models reveals the need to improve parameter values and algorithms for reproductive allocation, dispersal, seed survival and germination, environmental filtering in the seedling layer, and tree regeneration strategies adapted to wind, fire, and anthropogenic disturbance regimes. These improvements require synthesis of existing data, specific field data‐collection protocols, and novel model algorithms compatible with global‐scale simulations. Vegetation demographic models offer the opportunity to more fully integrate ecological understanding into Earth system prediction; regeneration processes need to be a critical part of the effort.
Differential geometry has long found applications in physics in general relativity and related areas. More recently, it was proposed by Nielsen that the tools of differential geometry, when applied ...to the unitary group, might be used to bound the complexity of quantum operations. The Bishop–Gromov bound—a cousin of the focusing lemmas used to prove the Penrose–Hawking black hole singularity theorems—is a differential geometry result that gives an upper bound on the rate of growth of the volume of geodesic balls in terms of the Ricci curvature. Here I apply the Bishop–Gromov bound to Nielsen’s complexity geometry to prove lower bounds on the quantum complexity of a typical unitary. For a broad class of models, the typical complexity is shown to be exponentially large in the number of qubits. This technique gives results that are tighter than all known lower bounds in the literature, as well as establishing lower bounds for a much broader class of complexity geometry metrics than has hitherto been bounded. This method thus realizes the original vision of Nielsen, which was to apply the tools of differential geometry to study quantum complexity.Quantum operations can be considered as points in a high-dimensional space in which distance reflects the similarity of two operations. Applying differential-geometric methods in this picture gives insights into the complexity of quantum systems.
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