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Neural Ordinary Differential Equations (NeuralODEs) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences. However, these models often display long training times and suboptimal results, especially for longer duration data. While a common strategy in the literature imposes strong constraints to the NeuralODE architecture to inherently promote stable model dynamics, such methods are ill-suited for dynamics discovery as the unknown governing equation is not guaranteed to satisfy the assumed constraints. In this paper, we develop a new training method for NeuralODEs, based on synchronization and homotopy optimization, that does not require changes to the model architecture. We show that synchronizing the model dynamics and the training data tames the originally irregular loss landscape, which homotopy optimization can then leverage to enhance training. Through benchmark experiments, we demonstrate our method achieves competitive or better training loss while often requiring less than half the number of training epochs compared to other model-agnostic techniques. Furthermore, models trained with our method display better extrapolation capabilities, highlighting the effectiveness of our method., Comment: 13 pages, 5 figures, submitted to NeurIPS2023

Surface tension is a key parameter for understanding nucleation from the very initial stage of phase transformation. Although surface tension has been predicted to vary with the curvature of the liquid-vapor interface, particularly at the large curvature of, e.g., the subnanometric critical nucleus, experimental study still remains challenging due to inaccessibility to such a small cluster. Here, by directly measuring the critical size of a single capillary-condensed nanomeniscus using atomic force microscopy, we address the curvature dependence of surface tension of alcohols and observe the surface tension is doubled for ethanol and n-propanol with the radius-of-curvature of ~ -0.46 nm. We also find that the interface of larger negative (positive) curvature exhibits the larger (smaller) surface tension, which evidently governs nucleation at ~ 1 nm scale, indicating more facilitated nucleation than normally expected. Such well characterized curvature effects contribute to better understanding and accurate analysis of nucleation occurring in various fields including material science and atmospheric science., 5 pages, 4 figures and Supplementary Material(pdf)

Surface tension plays a ubiquitous role in phase transitions including condensation or evaporation of atmospheric liquid droplets. Especially, understanding of interfacial thermodynamics of the critical nucleus of 1 nm scale is important for molecular characterization of the activation energy barrier of nucleation. Here, we investigate surface tension of spherical nanodroplets with both molecular dynamics and density functional theory, and find that surface tension decreases appreciably below 1 nm radius, whose analytic expression is consistently derived from the classic Tolman's equation. In particular, the free energy analysis of nanodroplets shows that the change of surface tension originates dominantly from the configurational energy of interfacial molecules, which is evidenced by the increasingly disrupted hydrogen bond network as the droplet size decreases. Our result can be applied to the interface-related phenomena associated with molecular fluctuations such as biomolecule adsorption at sub-nm scale where the macroscopic thermodynamic quantities are ill-defined., Comment: 17 pages, 6 figures

We report on high-resolution photoluminescence (PL) spectroscopic and microscopic study of laterally coupled InAs/GaAs self-assembled quantum dots by using a low-temperature near-field scanning optical microscope. We have observed slightly split PL spectra, which are associated with the bonding (symmetric) and antibonding (antisymmetric) energy states between two coupled quantum dots, closely located each other as confirmed by spatial mapping of the PL intensity. The experimental results are in qualitative agreement with the simple theoretical calculations based on a two-dimensional potential model. This work may open the way to a simultaneous spectroscopy and microscopy study of laterally coupled quantum dots in a high-density quantum dot sample without any articulate sample fabrication., 10 pages, 4 figures

We have observed spontaneous symmetry breaking of atomic populations in the dynamic phase-space double-potential system, which is produced in the parametrically driven magneto-optical trap of atoms. We find that the system exhibits similar characteristics of the Ising-class phase transition and the critical value of the control parameter, which is the total atomic number, can be calculated. In particular, the collective effect of the laser shadow becomes dominant at large atomic number, which is responsible for the population asymmetry of the dynamic two-state system. This study may be useful for investigation of dynamic phase transition and temporal behaviour of critical phenomena., 4 pages, 4 figures

We have investigated noise-induced transition of atoms between double or triple phase-space attractors that are produced in the parametrically driven magneto-optical trap. The transition rates between two or three dynamic attractors, measured for various modulation frequencies and amplitudes, are in good agreement with theoretical calculations and Monte-Carlo simulations based on the Langevin equations. Our experiment may be useful to study nonlinear dynamic problems involving transitions between states far from equilibrium., 4 pages, 4 figures

The theory of Bose-Einstein condensation in a two-dimensional(2D) harmonic trap is developed from 2D Gross-Pitaevskii equation. The 2D interaction strength is obtained from a 2D collision theory. We show the realization of 2D condensation of trapped Bose atoms directly by obtaining the stable solutions for the condensate wave function from the 2D Gross-Pitaevskii equation. We calculate the ground-state energy of the 2D system, and also the wave function of the 2D vortex state. In particular, the 2D energy state becomes less stable than the 3D case with the number of trapped atoms. The results of the 2D Bose condensation are also compared with those of the well-known 3D case., 6 pages, 4 figures

We derive the Gross-Pitaevskii equation in two-dimension from the first principles of two-dimensional scattering theory. Numerical calculation of the condensate wave function shows that atoms in a two-dimensional harmonic trap can be condensed into its ground state. Moreover, the ground state energy and the wave function of two-dimensional vortex state are also obtained. Quantitative comparisons between 2D results and 3D ones are made in detail.

We measure isotope shifts for five Yb$^+$ isotopes with zero nuclear spin on two narrow optical quadrupole transitions ${}^2S_{1/2} \rightarrow {}^2D_{3/2}$, ${}^2S_{1/2} \rightarrow {}^2D_{5/2}$ with an accuracy of $\sim 300$ Hz. The corresponding King plot shows a $3 \times 10^{-7}$ deviation from linearity at the 3 $\sigma$ uncertainty level. Such a nonlinearity can indicate physics beyond the Standard Model (SM) in the form of a new bosonic force carrier, or arise from higher-order nuclear effects within the SM. We identify the quadratic field shift as a possible contributor to the nonlinearity at the observed scale, and show how the nonlinearity pattern can be used in future, more accurate measurements to separate a new-boson signal from nuclear effects.