arXiv subjects

Dongshuai Liu

Publications and source records attributed to Dongshuai Liu.

4 recordsLinked to original sources

arXiv2026

Physics-Informed Neural Networks for the Quantum Droplets in Binary Bose-Einstein Condensates

Physics-Informed Neural Networks (PINNs), which integrate deep learning with physical prior knowledge, have proven to be a powerful tool for studying the dynamics of high-dimensional nonlinear systems. The present work utilizes PINNs to analyze the existence and evolution of quantum droplets (QDs) in a binary Bose-Einstein condensate (BEC), revealing the ability of this technique to accurately predict structural features of the QDs, their multipeak profiles, and dynamical behavior. The stable evolution of multipole QDs is thus demonstrated. Comparing different network architectures, including the training time, loss values, and $\mathbb{L_{2}}$ error, PINNs accurately predict specific dynamical characteristics of QDs. Furthermore, the PINN robustness is evaluated by the application of PINN to parameter-discovery tasks, considering both clean training data and data contaminated by $1\%$ random noise. The results highlight the efficiency of PINNs in modeling complex quantum systems and extracting reliable parameters under the noisy conditions.

cond-mat.quant-gas↗

arXiv2025

Robust quantum-droplet necklace clusters in three dimensions

We report the existence of quasi-stable ring-shaped (necklace-shaped) clusters built, in the free space, of 3D quantum droplets (QDs) in a binary Bose-Einstein condensate, modeled by the Gross-Pitaevskii equations with the Lee-Huang-Yang corrections. The QD clusters exhibit diverse dynamical behaviors, including contraction, oscillations, and expansion, depending on the cluster's initial radius. A phase shift between adjacent QDs imparts net angular momentum to the cluster, inducing its permanent rotation. Through the energy-minimization analysis, we predict equilibrium values of the necklace radius that support persistent rotation with negligible radial pulsations. In this regime, the clusters evolve as robust entities, maintaining the azimuthal symmetry in the course of the evolution, even in the presence of considerable perturbations. Necklace "supervortex" clusters, composed of QDs with inner vorticity 1 and global vorticity M, imprinted onto the cluster, may also persist for a long time. The reported findings may facilitate the experimental realization of complex self-sustained quantum states in the 3D free space.

cond-mat.quant-gas↗

arXiv2024

Physics-informed neural network for nonlinear dynamics of self-trapped necklace beams

A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schrödinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution of necklace patterns with integer, half-integer, and fractional reduced orbital angular momenta by means of PINN. The patterns exhibit phenomena similar to rotation of rigid bodies and centrifugal force. Even though the necklaces slowly expand (or shrink), they preserve their structure in the course of the quasi-stable propagation over several diffraction lengths, which is completely different from the ordinary fast diffraction-dominated dynamics. By comparing different ingredients, including the training time, loss value and $\mathbb{L}_{2}$ error, PINN accurately predicts specific nonlinear dynamical properties of the evolving necklace patterns. Furthermore, we perform the data-driven discovery of parameters for both clean and perturbed training data, adding $1\%$ random noise in the latter case. The results reveal that PINN not only effectively emulates the solution of partial differential equations, but also offers applications for predicting the nonlinear dynamics of physically relevant types of patterns.

physics.optics↗

arXiv2024

Rotating dipole and quadrupole quantum droplets in binary Bose-Einstein condensates

Quantum droplets (QDs) are self-trapped modes stabilized by the Lee-Huang-Yang correction to the mean-field Hamiltonian of binary atomic Bose-Einstein condensates. The existence and stability of quiescent and rotating dipole-shaped and vortex QDs with vorticity $S=1$ (DQDs and VQDs, respectively) are numerically studied in the framework of the accordingly modified two-component system. The rotating DQDs trapped in an annular potential are built of two crescent-like components, stretching along the azimuthal direction with the increase of the rotation frequency. Rotating quadrupole QDs (QQDs) bifurcate from the VQDs with $S=2$. Above a certain rotation frequency, they transform back into VQDs with a flat-top shape. Rotating DQDs and QQDs are stable in a broad interval of values of the chemical potential. The results provide the first example of stable modes which are intermediate states between the rotating DQDs and QQDs on the one hand, and VQDs on the other.

cond-mat.quant-gas↗