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Control-affine Schr\"odinger Bridge and Generalized Bohm Potential
Alexis M. H. Teter, Abhishek Halder, Michael D. Schneider, Alexx S. Perloff, Jane Pratt, Conor M. Artman, Maria Demireva
https://arxiv.org/abs/2508.08511

Control-affine Schrödinger Bridge and Generalized Bohm Potential
The control-affine Schrödinger bridge concerns with a stochastic optimal control problem. Its solution is a controlled evolution of joint state probability density subject to a control-affine Itô diffusion with a given deadline connecting a given pair of initial and terminal densities. In this work, we recast the necessary conditions of optimality for the control-affine Schrödinger bridge problem as a two point boundary value problem for a quantum mechanical Schrödinger PDE with complex pot…