Impurity and soliton dynamics in a Fermi gas with nearest-neighbor interactions

We study spinless fermions with repulsive nearest-neighbor interactions perturbed by an impurity particle or a local potential quench. Using the numerical time-evolving block decimation method and a simplified analytic model, we show that the pertubations create a soliton-antisoliton pair. If solitons are already present in the bath, the two excitations have a drastically different dynamics: The antisoliton does not annihilate with the solitons and is therefore confined close to its origin while the soliton excitation propagates. We discuss the consequences for experiments with ultracold gases.Comment: 12 pages, 16 figure

Sine-Gordon dynamics in spin transport

We study spin transport in a one-dimensional finite-length wire connected to fermionic leads. The interacting wire is described by the sine-Gordon model while the leads are either noninteracting or interacting Luttinger liquids. We calculate the spin current driven by a spin bias by solving numerically the classical equation of motion, and find that the cosine term in the sine-Gordon model gives rise to an oscillating spin current when the spin bias exceeds its critical value. We discuss the results in connection with transport experiments with ultracold atoms.Comment: 13 pages, 7 figure

On Jordan type inequalities for hyperbolic functions

This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.Comment: 16 page

Nonlinear transport in the presence of a local dissipation

We characterize the particle transport, particle loss, and nonequilibrium steady states in a dissipative one-dimensional lattice connected to reservoirs at both ends. The free-fermion reservoirs are fixed at different chemical potentials, giving rise to particle transport. The dissipation is due to a local particle loss acting on the center site. We compute the conserved current and loss current as functions of voltage in the nonlinear regime using a Keldysh description. The currents show step-like features which are affected differently by the local loss: The steps are either smoothened, nearly unaffected, or even enhanced, depending on the spatial symmetry of the single-particle eigenstate giving rise to the step. Additionally, we compute the particle density and momentum distributions in the chain. At a finite voltage, two Fermi momenta can occur, connected to different wavelengths of Friedel oscillations on either side of the lossy site. We find that the wavelengths are determined by the chemical potentials in the reservoirs rather than the average density in the lattice.Comment: 19 pages, 19 figure

Femoral avulsion of the medial patellofemoral ligament after primary traumatic patellar dislocation predicts subsequent instability in men : a mean 7-year nonoperative follow-up study

Peer reviewe

Oort cloud perturbations as a source of hyperbolic Earth impactors

The observation of interstellar objects 1I/'Oumuamua and 2I/Borisov suggests the existence of a larger population of smaller projectiles that impact our planet with unbound orbits. We analyze an asteroidal grazing meteor (FH1) recorded by the Finnish Fireball Network on October 23, 2022. FH1 displayed a likely hyperbolic orbit lying on the ecliptic plane with an estimated velocity excess of $\sim$0.7 km$\,$s$^{-1}$ at impact. FH1 may either be an interstellar object, indicating a high-strength bias in this population, or an Oort cloud object, which would reinforce migration-based solar system models. Furthermore, under the calculated uncertainties, FH1 could potentially be associated with the passage of Scholz's binary star system. Statistical evaluation of uncertainties in the CNEOS database and study of its hyperbolic fireballs reveals an anisotropic geocentric radiant distribution and low orbital inclinations, challenging the assumption of a randomly incoming interstellar population. Orbital integrations suggest that the event on March 9, 2017 (IM2) from CNEOS may have experienced gravitational perturbation during the Scholz fly-by, contingent upon velocity overestimation within the expected range. These findings suggest that apparent interstellar meteors may, in fact, be the result of accelerated meteoroid impacts caused by close encounters with massive objects within or passing through our solar system.Comment: Accepted for publication in Icaru

Spin transport in a one-dimensional quantum wire

We analyze the spin transport through a finite-size one-dimensional interacting wire connected to noninteracting leads. By combining renormalization-group arguments with other analytic considerations such as the memory function technique and instanton tunneling, we find the temperature dependence of the spin conductance in different parameter regimes in terms of interactions and the wire length. The temperature dependence is found to be nonmonotonic. In particular, the system approaches perfect spin conductance at zero temperature for both attractive and repulsive interactions, in contrast with the static spin conductivity. We discuss the connection of our results to recent experiments with ultracold atoms and compare the theoretical prediction to experimental data in the parameter regime where temperature is the largest energy scale.Comment: 16 pages, 10 figure

Robust high-dimensional precision matrix estimation

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in high-dimensions, it cannot be used to obtain a precision matrix estimator. A popular high-dimensional estimator is the graphical lasso, but it lacks robustness. We consider the high-dimensional independent contamination model. Here, even a small percentage of contaminated cells in the data matrix may lead to a high percentage of contaminated rows. Downweighting entire observations, which is done by traditional robust procedures, would then results in a loss of information. In this paper, we formally prove that replacing the sample covariance matrix in the graphical lasso with an elementwise robust covariance matrix leads to an elementwise robust, sparse precision matrix estimator computable in high-dimensions. Examples of such elementwise robust covariance estimators are given. The final precision matrix estimator is positive definite, has a high breakdown point under elementwise contamination and can be computed fast