Contact Hamiltonian mechanics
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Publication:2628211
DOI10.1016/j.aop.2016.11.003zbMath1364.37138arXiv1604.08266OpenAlexW2345020298MaRDI QIDQ2628211
Diego Tapias, Alessandro Bravetti, Hans Cruz
Publication date: 13 June 2017
Published in: Annals of Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.08266
Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Contact systems (37J55)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Completely integrable contact Hamiltonian systems and toric contact structures on \(S^{2}\times S^{3}\)
- Geometry and structure of quantum phase space
- Time-evolution of quantum systems via a complex nonlinear Riccati equation. I: Conservative systems with time-independent Hamiltonian
- Contact symmetries and Hamiltonian thermodynamics
- On the geometric quantization of contact manifolds
- A Hamilton-Jacobi formalism for thermodynamics
- Time-evolution of quantum systems via a complex nonlinear Riccati equation. II: Dissipative systems
- Quantization of contact manifolds and thermodynamics
- Nonlinear Schrödinger-type field equation for the description of dissipative systems. I. Derivation of the nonlinear field equation and one-dimensional example
- Statistical Mechanics of Nonequilibrium Liquids
- The Ermakov equation: A commentary
- Duality and the geometry of quantum mechanics
- Liouville’s theorem and the canonical measure for nonconservative systems from contact geometry
- Exact Quantization Conditions. II
- Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic Oscillators
- Stochastic Problems in Physics and Astronomy
- Geometric quantum mechanics
- Dynamical systems. IV. Symplectic geometry and its applications. Transl. from the Russian by G. Wassermann.
- The quantum damped harmonic oscillator
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