More Like this

1. Vortex structure and spectrum of an atomic Fermi superfluid in a spherical bubble trap

   https://doi.org/10.1103/PhysRevA.108.053303  

   He, Yan; Chien, Chih-Chun (November 2023, Physical Review A)

   The structures of multiply quantized vortices (MQVs) of an equal-population atomic Fermi superfluid in a rotating spherical bubble trap approximated as a thin shell are analyzed by solving the Bogoliubov-de Gennes (BdG) equation throughout the BCS-Bose Einstein condensation (BEC) crossover. Consistent with the Poincare-Hopf theorem, a pair of vortices emerge at the poles of the rotation axis in the presence of azimuthal symmetry, and the compact geometry provides confinement for the MQVs. While the single-vorticity vortex structure is similar to that in a planar geometry, higher-vorticity vortices exhibit interesting phenomena at the vortex center, such as a density peak due to accumulation of a normal Fermi gas and reversed circulation of current due to in-gap states carrying angular momentum, in the BCS regime but not the BEC regime because of the subtle relations between the order parameter and density. The energy spectrum shows the number of the in-gap state branches corresponds to the vorticity of a vortex, and an explanation based on a topological correspondence is provided. 

   more » « less
2. Neural-network quantum states for ultra-cold Fermi gases

   https://doi.org/10.1038/s42005-024-01613-w  

   Kim, Jane; Pescia, Gabriel; Fore, Bryce; Nys, Jannes; Carleo, Giuseppe; Gandolfi, Stefano; Hjorth-Jensen, Morten; Lovato, Alessandro (May 2024, Communications Physics)

   Abstract Ultra-cold Fermi gases exhibit a rich array of quantum mechanical properties, including the transition from a fermionic superfluid Bardeen-Cooper-Schrieffer (BCS) state to a bosonic superfluid Bose-Einstein condensate (BEC). While these properties can be precisely probed experimentally, accurately describing them poses significant theoretical challenges due to strong pairing correlations and the non-perturbative nature of particle interactions. In this work, we introduce a Pfaffian-Jastrow neural-network quantum state featuring a message-passing architecture to efficiently capture pairing and backflow correlations. We benchmark our approach on existing Slater-Jastrow frameworks and state-of-the-art diffusion Monte Carlo methods, demonstrating a performance advantage and the scalability of our scheme. We show that transfer learning stabilizes the training process in the presence of strong, short-ranged interactions, and allows for an effective exploration of the BCS-BEC crossover region. Our findings highlight the potential of neural-network quantum states as a promising strategy for investigating ultra-cold Fermi gases. 

   more » « less
3. The Permeability of Volcanic Mixtures—Implications for Pyroclastic Currents

   https://doi.org/10.1029/2018JB016544  

   Breard, Eric C. P.; Jones, Jim R.; Fullard, Luke; Lube, Gert; Davies, Clive; Dufek, Josef (February 2019, Journal of Geophysical Research: Solid Earth)

   Abstract Geophysical fluid‐granular flows, such as pyroclastic currents and debris flows, owe much of their runout and hazard behavior to the occurrence and time‐variant decay of a flow‐internal fluid pore pressure. However, modeling the effects of fluid pore pressure to forecast hazards is challenging because a unified method in Earth Sciences to quantitatively determine the permeability of these natural mixtures is currently missing. Here we combine experiments on fluidization and defluidization of pyroclastic materials, eolian sediments, and glass beads mixtures with numerical multiphase simulations to compare previous attempts to compute the permeability of complex natural particle‐fluid mixtures. In analogy to particle‐engineering studies on simple gas‐particle mixtures, we demonstrate that the effective length‐scale in the characterization of the fluid‐particle interaction of complex natural mixtures is the product of the Sauter mean diameter and the particle sphericity. Its use in the Kozeny‐Carman equation allows accurate prediction of mixture permeability, and we suggest the routine calculation of the Sauter mean from grain size distributions of the deposits of geophysical mass flows in Earth Sciences. We also show, through defluidization experiments, that the duration of gas retention in natural mixtures is well described when using the Sauter mean as the effective particle size. Further, we show through multiphase simulations that initial bed expansion extends the pore pressure diffusion timescale up to nine times. These results can be applied to small‐to‐large volume dense pyroclastic currents where the ranges of Sauter mean diameter predict gas retention for long duration and to debris flows and snow avalanches. 

   more » « less
4. On finite-length analysis and channel dispersion for broadcast packet erasure channels with feedback

   https://doi.org/10.1109/ISIT45174.2021.9517889  

   Lin, Shih-Chun; Wang, Chih-Chun; Wang, I-Hsiang; Huang, Yu-Chih; Lai, Yi-Chun (July 2021, 2021 IEEE International Symposium on Information Theory (ISIT))

   Motivated by the applications for low-delay communication networks, the finite-length analysis, or channel dispersion identification, of the multi-user channel is very important. Recent studies also incorporate the effects of feedback in point-to-point and common-message broadcast channels (BCs). However, with private messages and feedback, finite-length results for BCs are much more scarce. Though it is known that feedback can strictly enlarge the capacity, the ultimate feedback capacity regions remain unknown for even some classical channels including Gaussian BCs. In this work, we study the two-user broadcast packet erasure channel (PEC) with causal feedback, which is one of the cleanest feedback capacity results and the capacity region can be achieved by elegant linear network coding (LNC). We first derive a new finite-length outer bound for any LNCs and then accompanying inner bound by analyzing a three-phase LNC. For the outer-bound, we adopt a linear-space-based framework, which can successfully find the LNC capacity. However, naively applying this method in finite-length regime will result in a loose outer bound. Thus a new bounding technique based on carefully labelling each time slot according to the type of LNC transmitted is proposed. Simulation results show that the sum-rate gap between our inner and outer bounds is within 0.02 bits/channel use. Asymptotic analysis also shows that our bounds bracket the channel dispersion of LNC feedback capacity for broadcast PEC to within a factor of Q-l (E/2)/Q-l (E). 

   more » « less
5. Exact results of the one-dimensional repulsive Hubbard model

   https://doi.org/10.1088/1361-6633/ad7b70  

   Luo, Jia-Jia; Pu, Han; Guan, Xi-Wen (October 2024, Reports on Progress in Physics)

   Abstract We present analytical results of the fundamental properties of the one-dimensional (1D) Hubbard model with a repulsive interaction. The new model results with arbitrary external fields include: (I) using the exact solutions of the Bethe ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. We then investigate the gapped excitations in terms of the spin string and the $k-\mathrm{\Lambda }$string bound states at arbitrary driving fields, showing subtle differences in spin magnons and charge $\eta$-pair excitations. (II) For a high-density and high spin magnetization region, i.e. near the quadruple critical point, we further analytically obtain the thermodynamic properties, dimensionless ratios and scaling functions near quantum phase transitions. (III) Importantly, we give the general scaling functions at quantum criticality for arbitrary filling and interaction strength. These can directly apply to other integrable models. (IV) Based on the fractional excitations and the scaling laws, the spin-incoherent Luttinger liquid (SILL) with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of conformal field theory. We also, for the first time, obtain the analytical results of the thermodynamics for the SILL. (V) Finally, to capture deeper insights into the Mott insulator and interaction-driven criticality, we further study the double occupancy and propose its associated contact and contact susceptibilities, through which an adiabatic cooling scheme based upon quantum criticality is proposed. In this scenario, we build up general relations among arbitrary external- and internal-potential-driven quantum phase transitions, providing a comprehensive understanding of quantum criticality. Our methods offer rich perspectives of quantum integrability and offer promising guidance for future experiments with interacting electrons and ultracold atoms, both with and without a lattice. 

   more » « less