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At the interface between two fluid layers in relative motion, minimal fluctuations are exponentially amplified, inducing vorticity and laminar flow breakdown. This process, known as Kelvin-Helmholtz instability, is responsible for many well-known phenomena observed in the atmosphere, ocean, and astrophysics, and is one of the exemplary pathways to turbulence in fluid dynamics. is. In classical fluid dynamics, instabilities are governed by universal scaling laws, but the extent to which universality manifests itself in quantum fluids is not yet fully understood. Here we shed light on this question by inducing Kelvin-Helmholtz instabilities of atomic superfluids over widely different regimes, from weakly…
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We consider the problem of steady-state generation of one-dimensional Bose gas tubes that are weakly coupled to each other via density-density interactions. We analyze this development through the Boltzmann collision integral approach. We argue that when single-particle Hall excitations dominate the dominant orders of collision integrals created in individual gases, the state of the gas first evolves to a non-thermal fixed point, that is, a preheating plateau. This order is dominant when pairs of tubes are unequal, for example, at different temperatures or with different effective interaction parameters $\gamma$. We characterize this unheated preheating plateau and construct both a quasi-conserved…
We study the time evolution of the Boltzmann entropy of microstates during nonequilibrium free expansion of a one-dimensional quantum ideal gas. This quantum Boltzmann entropy $S_B$ essentially counts the number of independent wavefunctions (microstates) that give rise to a particular macrostate. In general, it depends on the choice of macrovariables such as the type and amount of coarse-graining and specifies the non-equilibrium macrostate of the system, a large part of which agrees with the thermodynamic entropy of the thermal equilibrium macrostate. Examine his two choices for macro variables. The $U$-macrovariables are local observables in position space, while the $f$-macrovariables also…
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[Submitted on 7 Mar 2022 (v1), last revised 21 Mar 2023 (this version, v2)] Download the PDF of the paper entitled “Bandits Corrupted by Nature: Lower Bounds on Regret and Robust Optimistic Algorithm” by Debabrota Basu and two other authors Download PDF overview: We study the corrupted bandit problem, that is, the stochastic multi-armed bandit problem with unknown reward distributions of $k corrupted in heavy tails by history-independent adversaries or nature. Specifically, the rewards obtained by playing an arm have a corresponding heavy-tailed reward distribution with probability $1-\varepsilon \in (0.5,1]$ and an arbitrary is obtained from the failure distribution of…
[Submitted on 5 Sep 2018 (v1), last revised 21 Mar 2023 (this version, v3)] Download the PDF of the paper on the uniqueness of the Steiner problem by Mikhail Basok and three other authors. Download PDF overview: A set of $n$ point constellations whose solution to the planar Steiner problem is not unique proves that the Hausdorff dimension is at most $2n-1$ (as a subset of $\mathbb{R}^{2n}). $). Furthermore, we show that the Hausdorff dimension of a set of $n$ point constellations in which at least two local minimal trees have the same length is also at most $2n-1$. The…
A model of photoassociation of atoms and molecules at cryogenic temperatures is presented and applied in the case of $^{39}$K and $^{23}$Na$^{39}$K bosons. This model relies on the assumption that photoassociation is governed by long-range interatomic interactions well outside the chemical bonding region. The frequency of the photoassociation laser is chosen close to the boundary-coupled lovibronic transition from the $X^1\Sigma^+$ ground state towards the metastable $b^3\Pi$ lowest excited state of $^{23}$Na. will be $^{39}$K, allowing other excitations that may interfere with photoassociation detection to be ignored. The energy level structure of the long-range $^{39}$K$\cdots$$^{23}$Na$^{39}$K excited superdimer is bound- $^{23}$Na$^{39 }$K…
Permutation synchronization is a key problem in computer science that constitutes a key step in many computer vision tasks. The goal is to recover $n$ latent permutations from noisy and imperfect pairwise measurements. In recent years, spectral methods have grown in popularity due to their simplicity and computational efficiency. The spectral method recovers permutations using the principal eigenspace $U$ of the data matrix and its block submatrices $U_1, U_2, \ldots, U_n$. In this paper, we propose a novel and statistically optimal spectral algorithm. Unlike existing methods that use $\{U_jU_1^\top\}_{j\geq 2}$, we aggregate useful information from all block submatrices to build…
The problem of macroscopic occupation of exciton ensembles and the spontaneous generation of coherence has received renewed attention with the rise of van der Waals heterostructures made of atomically thin semiconductors. Hosted interlayer excitons exhibit nanosecond lifetimes that are long enough to allow exciton thermalization in time. Several experimental studies have reported signs of macroscopic occupation effects in increasing exciton density. Theoretically, excitons are composite particles formed by fermionic components, and there is still no general theoretical discussion of bosonic thermalization of exciton gases beyond the linear regime. Here we derive equations for phonon-mediated thermalization at densities above the classical…