Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

In recent years, machine learning (ML) methods have become increasingly popular in computational chemistry. After being trained on appropriate ab initio reference data, these methods allow for accurately predicting the properties of chemical systems, circumventing the need for explicitly solving the electronic Schrodinger equation. Because of their computational efficiency and scalability to large data sets, deep neural networks (DNNs) are a particularly promising ML algorithm for chemical applications. This work introduces PhysNet, a DNN architecture designed for predicting energies, forces, and dipole moments of chemical systems. PhysNet achieves state-of-the-art performance on the QM9, MD17, and ISO17 benchmarks. Further, two new data sets are generated in order to probe the performance of ML models for describing chemical reactions, long-range interactions, and condensed phase systems. It is shown that explicitly including electrostatics in energy predictions is crucial for a qualitatively correct description of the asymptotic regions of a potential energy surface (PES). PhysNet models trained on a systematically constructed set of small peptide fragments (at most eight heavy atoms) are able to generalize to considerably larger proteins like deca-alanine (Ala10): The optimized geometry of helical Ala10 predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 A). By running unbiased molecular dynamics (MD) simulations of Ala10 on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala10 folds into a "wreath-shaped" configuration, which is more stable than the helical form by 0.46 kcal mol-1 according to the reference ab initio calculations.

PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges.

▪ Abstract Laser ablation of in situ metals has recently made it possible to immerse a large number of different metal atoms and ions and small clusters of metal atoms in liquid helium (He) and thus study their absorption and emission spectra in the visible region. Atoms and molecules are readily picked up by large ( ≥ 103 atoms) He droplets, and their spectra are sensitively detected through the use of either beam depletion following absorption or laser-induced fluorescence. Within the past three years, a wide variety of molecules, ranging from OCS to large organic molecules such as amino acids and a number of van der Waals complexes and even large metal clusters, have been embedded in He droplets and studied either in infrared or in the visible region. These results are discussed here in detail, and the evidence for the effect of superfluidity on the spectral features is reviewed.

Spectroscopy of atoms and molecules in liquid helium

Topological Phase Transitions in Strongly Interacting Fermi Systems (J W Clark) Semifluxon Dynamics in Extended Josephson Junctions (H Farhan) On the Quantum Hall Effect in Graphene (S Fujita) Ergodicity and Chaos in a System of Harmonic Oscillators (M H Lee) Fluid Helium-4 in Thermal Equilibrium (M Ristig) On the Generalised Slater Approximation (E Suraud) An Informative Method for the Diagnostics of Superconductors (K Rostami) Numerical Study of Pi-Junction Using Spin Filtering Barriers (S Kawabata) RPA Approach to Nonlinear Transport in Quantum Dots (B Tanatar) and other papers.

Condensed Matter Theories

In recent years, the use of machine learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail, and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.

Machine Learning Force Fields

Long-range Jastrow correlations

An elaborate cluster analysis of the single-particle occupation probability ${n}_{\stackrel{^}{q}}$ and associated one-body density matrix $n(r)$ is performed for a Fermi system described by a Jastrow wave function. A diagrammatic formalism rooted in Ursell-Mayer theory facilitates the analysis. It is conjectured, and demonstrated to convincingly high cluster order, that ${n}_{\stackrel{^}{q}}$ may be written as $n[N(q)+{N}_{1}(q)]$, where $n$ is a strength factor independent of wave number $q$ and the quantities $N(q)$ and ${N}_{1}(q)$ may be expressed as series of irreducible cluster contributions. The strength factor $n$ has the form $n={e}^{Q}$, where $Q$ may also be expressed as a series of irreducible cluster contributions. Massive partial summations on the latter series yield a compact expression for $Q$ in terms of the spatial distribution functions corresponding to the Jastrow wave function. Working with the Fourier inverse of ${n}_{\stackrel{^}{q}}$, it is further demonstrated that $n(r)$ may be cast in the form $\ensuremath{\rho}n[{N}_{1}(r)+{N}_{2}(r)]\mathrm{exp}\mathcal{Q}(r)$, where $\ensuremath{\rho}$ is the particle density and the functions ${N}_{1}(r)$, ${N}_{2}(r)$, and $\mathcal{Q}(r)$ are all given by irreducible cluster series. Massive partial summations are executed in the $\mathcal{Q}(r)$ series to achieve a compact expression of this quantity in terms of the aforementioned spatial distribution functions. One has $\mathcal{Q}(0)=Q$. The leading diagrams necessary for a quantitative evaluation of the momentum distribution of liquid $^{3}\mathrm{He}$ and nuclear matter are displayed. Specialization to infinite degeneracy of the single-particle levels, while shrinking the Fermi wave number to zero (Bose limit), allows liquid $^{4}\mathrm{He}$ to be treated as well. In this limit off-diagonal long-range order appears, the condensate fraction ${\ensuremath{\rho}}^{\ensuremath{-}1}n(\ensuremath{\infty})={n}_{c}$ being just the strength factor $n$. It may also be shown (under certain reasonable assumptions) that the customary ${r}^{\ensuremath{-}2}$ long-range behavior of the two-body correlations implies a singular behavior ${n}_{q}={n}_{c}(\frac{\mathrm{mc}}{2\ensuremath{\hbar}}){q}^{\ensuremath{-}1}$ of the Bose momentum distribution for small $q$.

Manfred L. Ristig

Papers

Long-range Jastrow correlations

Density matrix of quantum fluids

Hypernetted-chain approximation for dense Fermi fluids

Tensor correlations in nuclear matter.

Studies in the method of correlated basis functions