Hamiltonian Monte Carlo (HMC) is a state-of-the-art method for sampling from unnormalized, high-dimensional target distributions, and is the cornerstone for most probabilistic programming routines. By formulating the target density as the potential energy of a Hamiltonian system, HMC is able to generate distant proposals from high density regions; however, HMC is known to mix poorly when modes are separated by low-density regions. In this talk we present HaRAM as an extension of HMC geared for multimodal distributions. Notably, HaRAM departs from the "real-world physical analogy” underpinning existing enhancements to HMC, and is based on conformal symplectic dynamics; this perspective leads to several favorable properties. This talk is based on joint work with Hyungsuk Tak.