Energy-level pinning and the 0.7 spin state in one dimension: GaAs quantum wires studied using finite-bias spectroscopy
We study the effects of electron-electron interactions on the energy levels of GaAs quantum wires (QWs) using finite-bias spectroscopy. We probe the energy spectrum at zero magnetic field, and at crossings of opposite-spin-levels in high in-plane magnetic field B. Our results constitute direct evidence that spin-up (higher energy) levels pin to the chemical potential as they populate. We also show that spin-up and spin-down levels abruptly rearrange at the crossing in a manner resembling the magnetic phase transitions predicted to occur at crossings of Landau levels. This rearranging and pinning of subbands provides a phenomenological explanation for the 0.7 structure, a one-dimensional (1D) nanomagnetic state, and its high-B variants.
We show that Variational Autoencoders consistently fail to learn marginal distributions in latent and visible space. We ask whether this is a consequence of matching conditional distributions, or a limitation of explicit model and posterior distributions. We explore alternatives provided by marginal distribution matching and implicit distributions through the use of Generative Adversarial Networks in variational inference. We perform a large-scale evaluation of several VAE-GAN hybrids and explore the implications of class probability estimation for learning distributions. We conclude that at present VAE-GAN hybrids have limited applicability: they are harder to scale, evaluate, and use for inference compared to VAEs; and they do not improve over the generation quality of GANs.