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To represent the two-dimensional $N$-body delta-Bose gas for any integer $N\geq 2$, we construct an It\^{o} diffusion satisfying the strong Markov property and establish an associated Feynman-Kac-type formula. Among several properties, the diffusion is singular to the Brownian motion for showing almost sure contacts of particles and has a supercritical drift coefficient in the sense of a Ladyzhenskaya-Prodi-Serrin-type condition. Despite the supercriticality, the construction of the diffusion process and the relevant distributional properties for the Feynman-Kac-type formula are obtained by locally transforming the relative motions in two-body interactions and the necessary free motions. The central mechanism making this reduction to two-body interaction possible is the "no triple contacts" of particles, observed earlier in the functional integrals of the two-dimensional delta-Bose gas and now extended to the stochastic process level., Comment: 122 pages

A novel defect control approach based on laminated HfO$_2$/ZrO$_2$ with multifunctional TiN/Mo/TiOxNy electrode is proposed to significantly improve the endurance and data retention in HZO-based ferroelectric capacitor. The O-rich interface reduces leakage current and prolong the endurance up to 1011 cycles while retaining a 2Pr value of 34 ($\mu$C/cm$^2$ ) at 3.4MV/cm. Using first-principles calculations and experiments, we demonstrate that the enhancement of endurance is ascribed to the higher migration barrier of oxygen vacancies within the laminated HZO film and higher work function of MoO$_x$/TiO$_x$N$_y$ between top electrode and the insulating oxide. This 2.5-nm-thick TiOxNy barrier further increase the grain size of HZO, lowering the activation field and thus improving polarization reversal speed. This interfacial layer further decreases the overall capacitance, increases the depolarization field, thereby enhancing the data retention. By fitting the data using the Arrhenius equation, we demonstrate a 10-year data retention is achieved at 109.6 $^\circ$C, surpassing traditional SS-HZO of 78.2 $^\circ$C with a 450$^\circ$C RTA (required by backend-of-the-line). This work elucidates that interfacial engineering serves as a crucial technology capable of resolving the endurance, storage capability, and high-temperature data retention issues for ferroelectric memory., Comment: 7 pages, 6 figures

Sodium-ion batteries exhibit significant promise as a viable alternative to current lithium-ion technologies owing to their sustainability, low cost per energy density, reliability, and safety. Despite recent advancements in cathode materials for this category of energy storage systems, the primary challenge in realizing practical applications of sodium-ion systems is the absence of an anode system with high energy density and durability. Although Na metal is the ultimate anode that can facilitate high-energy sodium-ion batteries, its use remains limited due to safety concerns and the high-capacity loss associated with the high reactivity of Na metal. In this study, titration gas chromatography is employed to accurately quantify the sodium inventory loss in ether- and carbonate-based electrolytes. Uniaxial pressure is developed as a powerful tool to control the deposition of sodium metal with dense morphology, thereby enabling high initial coulombic efficiencies. In ether-based electrolytes, the Na metal surface exhibits the presence of a uniform solid electrolyte interphase layer, primarily characterized by favorable inorganic chemical components with close-packed structures. The full cell, utilizing a controlled electroplated sodium metal in ether-based electrolyte, provides capacity retention of 91.84% after 500 cycles at 2C current rate and delivers 86 mAh/g discharge capacity at 45C current rate, suggesting the potential to enable Na metal in the next generation of sodium-ion technologies with specifications close to practical requirements.

We propose and experimentally demonstrate an analog scheme for generating XY-type ($J_{ij}^x \sigma_x^i \sigma_x^j \;$ + $J_{ij}^y \sigma_y^i \sigma_y^j \;$) Hamiltonians on trapped ion spins with independent control over the $J_{ij}^x$ and $J_{ij}^y$ terms. The Ising-type interactions $\sigma_x^i \sigma_x^j \;$ and $\sigma_y^i \sigma_y^j \;$ are simultaneously generated by employing two spin-dependent forces operating in parallel on the same set of normal modes. We analytically calculate the region of validity of this scheme, and provide numerical and experimental validation with $^{171}\rm{Yb}^+\;$ ions. This scheme inherits the programmability and scalability of the Ising-type interactions with trapped ions that have been explored in numerous quantum simulation experiments. Our approach extends the capabilities of existing trapped ion quantum simulators to access a large class of spin Hamiltonians relevant for exploring exotic quantum phases such as superfluidity and spin liquids.

Controlling the spin transport at the single-molecule level, especially without the use of ferromagnetic contacts, becomes a focus of research in spintronics. Inspired by the progress on atomic-level molecular synthesis, through first-principles calculations, we investigate the spin-dependent electronic transport of graphene nanoflakes with side-bonded functional groups, contacted by atomic carbon chain electrodes. It is found that, by rotating the functional group, the spin polarization of the transmission at the Fermi level could be switched between completely polarized and unpolarized states. Moreover, the transition between spin-up and spin-down polarized states can also be achieved, operating as a dual-spin filter. Further analysis shows that, it is the spin-dependent shift of density of states, caused by the rotation, that triggers the shift of transmission peaks, and then results in the variation of spin polarization. Such a feature is found to be robust to the of the nanoflake and the electrode material, showing great application potential. Those findings may throw light on the development of spintronic devices.

We report a high-finesse bow-tie cavity designed for atomic physics experiments with Rydberg atom arrays. The cavity has a finesse of $51,000$ and a waist of $7.1$ $\mu$m at the cesium D2 line ($852$ nm). With these parameters, the cavity is expected to induce strong coupling between a single atom and a single photon, corresponding to a cooperativity per traveling mode of $35$ at the cavity waist. To trap and image atoms, the cavity setup utilizes two in-vacuum aspheric lenses with numerical aperture ($NA$) of $0.35$ and is capable of housing $NA=0.5$ microscope objectives. In addition, the large atom-mirror distance ($\gtrsim1.5$ cm) provides good optical access and minimizes stray electric fields at the position of the atoms. This cavity setup can operate in tandem with the Rydberg array platform, creating a fully connected system for quantum simulation and computation., Comment: 9 pages, 7 figures

For the two-dimensional delta-Bose gas, we prove the first Feynman-Kac type diffusion representation of the Schr\"odinger semigroup generated by the relative motion of two particles. The representation builds on a unique skew-product diffusion, in the sense of Erickson [22], such that the Markov process ${\rm BES}(0,\beta{\downarrow})$ from Donati-Martin and Yor [20] defines the radial part. Moreover, the law of this skew-product diffusion is singular to the law of planar Brownian motion. As an application, we determine some exact forms of non-Gaussianity for the stochastic heat equation. We give two different proofs of the representation: one applies the original characterization of ${\rm BES}(0,\beta{\downarrow})$ by excursion theory, and the other extends [20] by approximations of SDEs and resolvents. In the latter, we establish a new characterization of ${\rm BES}(0,\beta{\downarrow})$ as a strongly well-posed SDE. The approximations of resolvents construct the two-dimensional delta potentials from local times of lower-dimensional Bessel processes, which may be of independent interest for being an alternative to the long-standing approach of using mollifiers., Comment: 54 pages, 2 figures

We consider the 2D delta-Bose gas by a smooth mollification of the delta potential, where the coupling constant is in the critical window. The main result proves that for two particles, the approximate semigroups on $\mathscr B_b(\Bbb R^2)$ for the Schr\"odinger operator with singular interaction at the origin converge pointwise in the initial condition. This convergence extends earlier functional analytic results for the convergence in the $L_2$-norm resolvent sense. The central methods introduced here apply the excursion theory of the 2D Bessel process and the ergodicity of the winding number of planar Brownian motion. The limiting semigroup thus shows both the Kallianpur--Robbins law for additive functionals of planar Brownian motion and Kasahara's second-order law for the fluctuations. As an application, the mode of convergence is extended to the $N$-particle delta-Bose gas for all $N\geq 3$., Comment: 56 pages, 2 figures

The development of silicon anodes to replace conventional graphite in efforts to increase energy densities of lithium-ion batteries has been largely impeded by poor interfacial stability against liquid electrolytes. Here, stable operation of 99.9 weight% micro-Si (uSi) anode is enabled by utilizing the interface passivating properties of sulfide based solid-electrolytes. Bulk to surface characterization, as well as quantification of interfacial components showed that such an approach eliminates continuous interfacial growth and irreversible lithium losses. In uSi || layered-oxide full cells, high current densities at room temperature (5 mA cm 2), wide operating temperature (-20{\deg}C to 80{\deg}C) and high loadings (>11 mAh cm-2) were demonstrated for both charge and discharge operations. The promising battery performance can be attributed to both the desirable interfacial property between uSi and sulfide electrolytes, as well as the unique chemo-mechanical behavior of the Li-Si alloys., Comment: 13 pages, 5 figures

Temperature scaling has been widely used as an effective approach to control the smoothness of a distribution, which helps the model performance in various tasks. Current practices to apply temperature scaling assume either a fixed, or a manually-crafted dynamically changing schedule. However, our studies indicate that the individual optimal trajectory for each class can change with the context. To this end, we propose contextual temperature, a generalized approach that learns an optimal temperature trajectory for each vocabulary over the context. Experimental results confirm that the proposed method significantly improves state-of-the-art language models, achieving a perplexity of 55.31 and 62.89 on the test set of Penn Treebank and WikiText-2, respectively. In-depth analyses show that the behaviour of the learned temperature schedules varies dramatically by vocabulary, and that the optimal schedules help in controlling the uncertainties. These evidences further justify the need for the proposed method and its advantages over fixed temperature schedules.

We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths satisfying $1/N\ll w\ll 1$. Under appropriate conditions on the space, the limiting density processes of strategy are proven to obey the replicator equation, and the normalized fluctuations converge to a Gaussian process with the Wright-Fisher covariance function in the limiting densities. As an application, we resolve in the positive a conjecture from the biological literature that the expected density processes approximate the replicator equation on many non-regular graphs., Comment: 41 pages

Analog computing hardwares, such as Processing-in-memory (PIM) accelerators, have gradually received more attention for accelerating the neural network computations. However, PIM accelerators often suffer from intrinsic noise in the physical components, making it challenging for neural network models to achieve the same performance as on the digital hardware. Previous works in mitigating intrinsic noise assumed the knowledge of the noise model, and retraining the neural networks accordingly was required. In this paper, we propose a noise-agnostic method to achieve robust neural network performance against any noise setting. Our key observation is that the degradation of performance is due to the distribution shifts in network activations, which are caused by the noise. To properly track the shifts and calibrate the biased distributions, we propose a "noise-aware" batch normalization layer, which is able to align the distributions of the activations under variational noise inherent in the analog environments. Our method is simple, easy to implement, general to various noise settings, and does not need to retrain the models. We conduct experiments on several tasks in computer vision, including classification, object detection and semantic segmentation. The results demonstrate the effectiveness of our method, achieving robust performance under a wide range of noise settings, more reliable than existing methods. We believe that our simple yet general method can facilitate the adoption of analog computing devices for neural networks., Comment: 7 pages, 3 figure