Effective potentials from semiclassical truncations

Abstract

Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order in moments for a single classical degree of freedom and to second order for a pair of classical degrees of freedom are derived and applied to several model systems. It is shown that these new canonical variables facilitate the derivation of quantum-statistical quantities and effective potentials. Moreover, by formulating quantum dynamics in classical language, these methods result in new heuristic pictures, for instance of tunneling, that can guide further investigations.

arXiv comment35 pages, 5 figures

References in corpus (10)

• Tunneling Time in Ultrafast Science is Real and Probabilistic
• Experimental evidence for Wigner's tunneling time
• Effective Equations of Motion for Quantum Systems
• Moment Closure - A Brief Review
• Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization
• Quantum Gravity and Higher Curvature Actions
• High-order quantum back-reaction and quantum cosmology with a positive cosmological constant
• Dynamics of Tunneling Ionization using Bohmian Mechanics
• Canonical Tunneling Time in Ionization Experiments
• Semiclassical States on Lie Algebras

Cited by in corpus (28)

• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Faithful realizations of semiclassical truncations
• Canonical description of cosmological backreaction
• Equivalence of models in loop quantum cosmology and group field theory
• Quantum Higgs Inflation
• Canonical description of quantum dynamics
• Quasiclassical model of inhomogeneous cosmology
• Quasiclassical solutions for static quantum black holes
• Multi-field inflation from single-field models
• Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe
• Quantum approach to a Bianchi I singularity
• Tunneling dynamics in cosmological bounce models
• Adherence and violation of the equivalence principle from classical to quantum mechanics
• Quantum fluctuations and semiclassicality in an inflaton-driven evolution
• Moments and saturation properties of eigenstates
• Geometry and proper time of a relativistic quantum clock
• Quantum Uncertainty as an Intrinsic Clock
• Quantum proper time: A Finsler space from entropy and purity
• Semiclassical Backreaction: A Qualitative Assessment
• Space-time superpositions as fluctuating geometries
• Effective dynamics of quantum fluctuations in field theory: with applications to cosmology
• Evolution of the wave-function's shape in a time-dependent harmonic potential
• Tunneling dynamics of an oscillating universe model
• Minisuperspace results for causal dynamical triangulations
• Semiclassical study of the Mixmaster model: the quantum Kasner map
• Chaos in a tunneling universe
• Relativistic implications of entropy and purity
• Quantum dynamics in Weyl-Heisenberg coherent states