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Wasserstein Hamiltonian flows · Around

2019

Wasserstein Hamiltonian flows

Chow, Shui-Nee, Li, Wuchen, Zhou, Haomin

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We establish kinetic Hamiltonian flows in density space embedded with the $L^2$-Wasserstein metric tensor.

We derive the Euler-Lagrange equation in density space, which introduces the associated Hamiltonian flows.
We demonstrate that many classical equations, such as Vlasov equation, Schr{\"o}dinger equation and Schr{\"o}dinger bridge problem, can be rewritten as the formalism of Hamiltonian flows in density space.

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Derivation of the Schrödinger Equation from Newtonian Mechanics
E. Nelson · 1966
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The free Markoff field
E. Nelson · 1973
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Conservative Diffusions
E. A. Carlen · 1984
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Quantum Fluctuations
E. Nelson · 1985
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Field theory and the future of stochastic mechanics
E. Nelson · 1986
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