The PCA-seq method applied to analyze of the dynamics of COVID-19 epidemic indicators

In time series analysis using the SSA method, a univariate series is converted into the multivariate one by shifts. The resulting trajectory matrix is subjected to principal component analysis (PCA). However, the principal components can also be computed using the PCA-Seq method if segments of the original series are selected as objects. The matrix of Euclidean distances between the objects can be obtained using any method, which offers additional opportunities for time series analysis compared to the conventional SSA. In this study, the PCA-Seq method was used to analyze the dynamics of COVID-19 epidemic indicators

Analytic Confinement and Regge Trajectories

A simple relativistic quantum field model with the Yukawa-type interaction is considered to demonstrate that the analytic confinement of the constituent ("quarks") and carrier ("gluons") particles explains qualitatively the basic dynamical properties of the spectrum of mesons considered as two-particle stable bound states of quarks and gluons: the quarks and gluons are confined, the glueballs represent bound states of massless gluons, the masses of mesons are larger than the sum of the constituent quark masses and the Regge trajectories of mesonic orbital excitations are almost linear.Comment: RevTeX, 16 pages, 3 figures and 2 table

Illustration of universal relations for trapped four-fermion system with arbitrary s-wave scattering length

A two-component four-fermion system with equal masses, interspecies s-wave scattering length a and vanishing intraspecies interactions under external spherically symmetric harmonic confinement is considered. Using a correlated Gaussian basis set expansion approach, we determine the energies and various structural properties of the energetically lowest-lying gas-like state throughout the crossover for various ranges of the underlying two-body potential. Extrapolating to the zero-range limit, our numerical results show explicitly that the total energy, the trap energy as well as certain aspects of the pair distribution function and of the momentum distribution are related through the so-called integrated contact intensity I(a). Furthermore, it is shown explicitly that the total energy and the trap energy are related through a generalized virial theorem that accounts for a non-zero range.Comment: 9 figures with several subfigure

Three-body problem in Fermi gases with short-range interparticle interaction

We discuss 3-body processes in ultracold two-component Fermi gases with short-range intercomponent interaction characterized by a large and positive scattering length $a$. It is found that in most cases the probability of 3-body recombination is a universal function of the mass ratio and $a$, and is independent of short-range physics. We also calculate the scattering length corresponding to the atom-dimer interaction.Comment: 4 pages, 2 figure

Time-Dependent Density-Functional Theory for Trapped Strongly-Interacting Fermionic Atoms

The dynamics of strongly interacting trapped dilute Fermi gases (dilute in the sense that the range of interatomic potential is small compared with inter-particle spacing) is investigated in a single-equation approach to the time-dependent density-functional theory. Our results are in good agreement with recent experimental data in the BCS-BEC crossover regime. It is also shown that the calculated corrections to the hydrodynamic approximation may be important even for systems with a rather large number of atoms.Comment: Resubmitted to PRA in response to referee's comments. Abstract is changed. Added new figure

How to observe the Efimov effect

We propose to observe the Efimov effect experimentally by applying an external electric field on atomic three-body systems. We first derive the lowest order effective two-body interaction for two spin zero atoms in the field. Then we solve the three-body problem and search for the extreme spatially extended Efimov states. We use helium trimers as an illustrative numerical example and estimate the necessary field strength to be less than 2.7 V/angstrom.Comment: 4 pages, 2 postscript figures, psfig.sty, revte

Resonant Atom-Dimer Relaxation in Ultracold Atoms

Three-body systems with large scattering length display universal phenomena associated with a discrete scaling symmetry. These phenomena include resonant enhancement of three-body loss rates when an Efimov three-body resonance is at the scattering threshold. In particular, there can be resonant peaks in the atom-dimer relaxation rate for large positive scattering length. We improve upon earlier studies and calculate the atom-dimer relaxation rate as a function of temperature using a Bose-Einstein distribution for the thermal average. As input, we use calculations of the atom-dimer scattering phase shifts from effective field theory.Comment: 5 pages, 2 figures, published version, minor change in result

Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory

We examine in non-Abelian gauge theory the heavy quark limit in the presence of the (anti-)self-dual homogeneous background field and see that a confining potential emerges, consistent with the Wilson criterion, although the potential is quadratic and not linear in the quark separation. This builds upon the well-known feature that propagators in such a background field are entire functions. The way in which deconfinement can occur at finite temperature is then studied in the static temporal gauge by calculation of the effective potential at high temperature. Finally we discuss the problems to be surmounted in setting up the calculation of the effective potential nonperturbatively on the lattice.Comment: 31 pages, LaTeX, expanded discussion and derivations in Sections 2 and

Stability of Inhomogeneous Multi-Component Fermi Gases

Two-component equal-mass Fermi gases, in which unlike atoms interact through a short-range two-body potential and like atoms do not interact, are stable even when the interspecies s-wave scattering length becomes infinitely large. Solving the many-body Schroedinger equation within a hyperspherical framework and by Monte Carlo techniques, this paper investigates how the properties of trapped two-component gases change if a third or fourth component are added. If all interspecies scattering lengths are equal and negative, our calculations suggest that both three- and four-component Fermi gases become unstable for a certain critical set of parameters. The relevant length scale associated with the collapse is set by the interspecies scattering length and we argue that the collapse is, similar to the collapse of an attractive trapped Bose gas, a many-body phenomenon. Furthermore, we consider a three-component Fermi gas in which two interspecies scattering lengths are negative while the other interspecies scattering length is zero. In this case, the stability of the Fermi system is predicted to depend appreciably on the range of the underlying two-body potential. We find parameter combinations for which the system appears to become unstable for a finite negative scattering length and parameter combinations for which the system appears to be made up of weakly-bound trimers that consist of one fermion of each species.Comment: 15 pages, 8 figure