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We study the vortex nucleation dynamics in a heterogeneous atomic boose gas quenched to a superfluid phase and investigate the dependence of the Kibble-Zurek (KZ) scaling exponent on the underlying trap configuration. A characteristic power-law scaling of the vortex number as a function of the thermal quench rate and enhanced vortex suppression in the outer region with low particle density is observed for samples in a number of different inhomogeneous traps, consistent with causal effects. I was. Encapsulated in the Inhomogeneous Kibble Zurek Mechanism (IKZM). However, the measured KZ scaling exponents show significant differences from the theoretical estimates and, moreover,…

The purpose of magnetic relaxometry imaging is to measure the relaxation of the superimposed magnetic field generated by the nanoparticles after first aligning the nanoparticles using an external activating magnetic field and then switching off. is to determine the distribution of magnetic nanoparticles inside the subject. In this study, we applied the technique of Bayesian optimal experimental design to (sequentially) select the positions of the activation coils in order to increase the value of the data and allow more accurate reconstructions with a simplified measurement setup. increase. For the nanoparticle distribution, both Gaussian and total variation prior models are considered.…

[Submitted on 6 Jun 2022 (v1), last revised 31 May 2023 (this version, v2)] Download the PDF of the paper entitled “Tensor join of hypergraphs and its spectra” by R. Vishnupriya and one other author. Download PDF overview: In this paper, we present three operations on hypergraphs using tensors. We show that these three formulations are equivalent and we commonly refer to them as tensor joins. We show that any hypergraph can be seen as a tensor union of hypergraphs. With Tensor Join, we can get some existing and new classes of operations on the hypergraph. Compute the adjacency, Laplacian,…

Conformal dynamics can appear in quantum gases when interactions are fine-tuned to be scale symmetric. One well-known example of such a system is the three-dimensional Fermi gas at the Feschbach resonance. In this letter, we explain how conformal dynamics emerge in the infrared limit for one-dimensional harmonically trapped fermi gases, even if the system does not have exact scale-symmetric interactions. Conformal dynamics are driven by strong renormalization effects due to near-infrared stable scale-invariant interactions. As the system approaches the infrared limit, or the external harmonic trap frequency $\omega_f \rightarrow 0$, the dynamics are not constant as be characterized. General dialogue…

In this work, we study the domain adaptation problem with label shifting. In the label shift context, the marginal distributions of the labels are different across the training and test datasets, but the conditional distributions of the labeled features are the same. Traditional label shift adaptation methods either introduce large estimation errors or require cumbersome post-prediction calibration. To address these issues, we first propose a moment-matching framework to adapt the label shift based on the shape of the influence function. Under this framework, we propose a new method called \underline{E}fficient \underline{L}abel \underline{S}hift \underline{A}daptation (ELSA). This technique allows you to estimate…

We characterize the equation of state (EoS) of the SU($N>2$) Fermi-Hubbard model (FHM) in a two-dimensional monolayer square lattice. We examine the density and site occupancy probability as a function of interaction strength and temperature for N = 3, 4 and 6. Our measurements are Decision Quantum Monte Carlo (DQMC) and Numerically Linked Cluster Extension (NLCE). By investigating the density variation, we compare the temperatures determined in a model-independent manner by fitting the measured values to the numerically calculated EoS results. This represents a particularly interesting new step in the search and characterization of SU($N$) FHMs. Source link

Over the past decades, macroecology has identified large-scale patterns of abundance and diversity in microbial communities and put forward several potential explanations for them. However, these advances are not made possible by a thorough understanding of the dynamic processes behind them. In particular, abundance variations across metagenomic samples have been found to be correlated, but reproducing populations through appropriate population models remains an open challenge. This paper addresses this issue and points to species interactions as a necessary mechanism to explain them. Specifically, we discuss some possibilities for including interactions in population models and recognizing the Lotka–Volterra constant as a…

[Submitted on 21 Jun 2015 (v1), last revised 30 May 2023 (this version, v4)] Download the PDF of the paper by J. Sun and S.B. Download PDF overview: We introduce various quantities that can be defined for any matroid, and certain conditions on these quantities imply that the matroid cannot be expressed over $\mathbb{F}_q$ (where $q$ is a prime power). Indicates that Primarily, for a matroid of rank $r$, we examine the fraction of dependent size $(rk)$ subsets, and the bounds on this fraction in terms of matroid cardinality and $q$ are given below. That is, matroids cannot be represented…

We prove two equilibrium properties of interacting atomic systems in three or more dimensions of continuous space. (i) When particles interact via non-negative Fourier transform pair potentials, self-organization of particles into infinite permutation cycles occurs simultaneously with off-diagonal long-range order. Bose-Einstein condensation also occurs if the cycle length tends to infinity at a rate equal to or greater than the square of the linear elongation of the system. (ii) if the pair potential is also non-negative, a cycle consisting of the non-zero part of the total number of particles appears when the density exceeds a temperature-dependent threshold; Taken together, the…

[Submitted on 23 May 2023 (v1), last revised 30 May 2023 (this version, v2)] Download the PDF of the paper entitled Towards Understanding the Dynamics of Gaussstein Variational Gradient Descent by Tianle Liu and three other authors. Download PDF overview: Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm. Despite its widespread use, understanding the theoretical properties of SVGD remains a difficult problem. For sampling from a Gaussian target, SVGD dynamics with a bilinear kernel remain Gaussian as long as the initializer is Gaussian. Inspired by this fact, we conducted a detailed theoretical study of Gaussian Variational…