Historical methods of functional development in density functional theory have often been guided by analytic conditions that constrain the exact functional one is trying to approximate. Recently, machine-learned functionals have been created by interpolating the results from a small number of exactly solved systems to unsolved systems that are similar in nature. For a simple one-dimensional system, using an exact condition, we find improvements in the learning curves of a machine learning approximation to the non-interacting kinetic energy functional. We also find that the significance of the improvement depends on the nature of the interpolation manifold of the machine-learned functional.
We excite ultracold rubidium atoms in a magneto-optical trap to a coherent superposition of the three |m j | sublevels of the 37d 5/2 Rydberg state. After some delay, during which the relative phases of the superposition components can evolve, we apply an electric field pulse to ionize the Rydberg electron and send it to a detector. The electron traverses many avoided crossings in the Stark levels as it ionizes. The net effect of the transitions at these crossings is to mix the amplitudes of the initial superposition into the same final states at ionization. Similar to a Mach-Zehnder interferometer, the three initial superposition components have multiple paths by which they can arrive at ionization and, since the phases of those paths differ, we observe quantum beats as a function of the delay time between excitation and initiation of the ionization pulse. We present a fully quantum-mechanical calculation of the electron's path to ionization and the resulting interference pattern.
Models of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental results project onto a subspace of parameters that are consistent with those observations, but mapping these constraints to the underlying parameters is also typically intractable. Instead, physicists often resort to scanning small subsets of the full parameter space and testing for experimental consistency. We propose an alternative approach that uses generative models to significantly improve the computational efficiency of sampling high-dimensional parameter spaces. To demonstrate this, we sample the constrained and phenomenological Minimal Supersymmetric Standard Models subject to the requirement that the sampled points are consistent with the measured Higgs boson mass. Our method achieves orders of magnitude improvements in sampling efficiency compared to a brute force search.
We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics using a Bloch vector-e.g., a magnetic field causes it to precess and dissipation causes it to shrink-one can reason similarly about the shapes we use to visualize correlations. This visualization demonstrates its usefulness by unveiling the hidden structure in the correlations. For example, seemingly complex correlation dynamics can be described as simple motions of the shapes. We demonstrate the simplicity of the dynamics, which is obscured in conventional analyses, by analyzing several physical systems of relevance to cold atoms.
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