A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians

DOI10.1063/1.525329zbMath0515.70018OpenAlexW2105721771MaRDI QIDQ3662666

Publication date: 1982

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.525329

zbMATH Keywords

autonomous system exact invariants arbitrary time dependent potential linear or quadratic series in positive powers of p

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (54)

First integrals for the modified Emden equation q̈+α(t) q̇+q n =0 ⋮ Conserved vectors for the autonomous system \(\ddot r+g(r,\theta)\hat r+h(r,\theta){\hat \theta}=0\) ⋮ Time-dependent invariants and quantum mechanics in two dimensions ⋮ Investigating non-integrability and chaos in complex time ⋮ Dynamical algebraic approach and invariants for time-dependent Hamiltonian systems in two dimensions ⋮ Representations of one-dimensional Hamiltonians in terms of their invariants ⋮ Comment on an aspect of a paper by G. Thompson ⋮ Adiabatic and nonadiabatic evolution of a generalized damped harmonic oscillator ⋮ GENERALIZED ERMAKOV SYSTEMS IN TERMS OFsl(2,R) INVARIANTS ⋮ Invariants for time-dependent potentials: Use of self-similar techniques ⋮ Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap ⋮ Search for first integrals in relativistic time-dependent Hamiltonian systems ⋮ Completely integrable one-dimensional classical and relativistic time-dependent Hamiltonians ⋮ Hamiltonian structure and integrability of the stationary Kuramoto–Sivashinsky equation ⋮ Lie symmetries and invariants of the Lotka–Volterra system ⋮ Lie transformation group solutions of the nonlinear one-dimensional Vlasov equation ⋮ Entanglement Hamiltonian during a domain wall melting in the free Fermi chain ⋮ Partial Noether Operators and First Integrals for a System with two Degrees of Freedom ⋮ Optimal controls of invariant-based population transfer in a superconducting qutrit ⋮ Quantum uncertainty as an intrinsic clock ⋮ One-dimensional nonautonomous dynamical systems with exact transcendental invariants ⋮ One-dimensional Bose gas driven by a slow time-dependent harmonic trap ⋮ Noether’s theorem, the Rund–Trautman function, and adiabatic invariance ⋮ First integrals for two linearly coupled nonlinear Duffing oscillators ⋮ Noether symmetries and conserved quantities for spaces with a section of zero curvature ⋮ Dirac's method for the two-dimensional damped harmonic oscillator in the extended phase space ⋮ Shortcuts to adiabaticity using flow fields ⋮ On the solution of the Schrödinger equation with time dependent boundary conditions ⋮ Fast transport of Bose–Einstein condensates ⋮ Controlling the transport of an ion: classical and quantum mechanical solutions ⋮ Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant ⋮ Reduced phase space optics for general relativity: symplectic ray bundle transfer ⋮ Time-dependent vector constants of motion, symmetries, and orbit equations for the dynamical system r̈=îr{[Ü(t)/U(t)r −[μ/U(t)]r−2}] ⋮ Noether, partial Noether operators and first integrals for a linear system ⋮ Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Basic theory ⋮ Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Two- and three-resonance cases ⋮ Generalized canonical transformations for time-dependent systems ⋮ Generalised Symmetries and the Ermakov-Lewis Invariant ⋮ First integrals via polynomial canonical transformations ⋮ Invariants for dissipative nonlinear systems by using rescaling ⋮ Ermakov-Lewis invariants and Reid systems ⋮ Generalisations of the LaplaceRungeLenz Vector ⋮ Extension of Giacomini’s results concerning invariants for one-dimensional time-dependent potentials ⋮ A second invariant for one-degree-of-freedom, time-dependent Hamiltonians given a first invariant ⋮ Single resonance integrals for two-dimensional Hamiltonians ⋮ Integrable time-dependent central potentials ⋮ Separation of variables treatment of the invariant quadratic in momentum for any admissible potential ⋮ Approximate partial Noether operators and first integrals for coupled nonlinear oscillators ⋮ A theory of exact and approximate configurational invariants ⋮ A resonance formulation for invariants of particle motion in a one- dimensional time-dependent potential ⋮ First integrals versus configurational invariants and a weak form of complete integrability ⋮ Entanglement dynamics of a hard-core quantum gas during a Joule expansion ⋮ Two-dimensional time-dependent Hamiltonian systems with an exact invariant ⋮ Classes of potentials of time-dependent central force fields which possess first integrals quadratic in the momenta

Cites Work

This page was built for publication: A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians