Realizing time crystals in discrete quantum few-body systems

The exotic phenomenon of time translation symmetry breaking under periodic driving - the time crystal - has been shown to occur in many-body systems even in clean setups where disorder is absent. In this work, we propose the realization of time-crystals in few-body systems, both in the context of trapped cold atoms with strong interactions and of a circuit of superconducting qubits. We show how these two models can be treated in a fairly similar way by adopting an effective spin chain description, to which we apply a simple driving protocol. We focus on the response of the magnetization in the presence of imperfect pulses and interactions, and show how the results can be interpreted, in the cold atomic case, in the context of experiments with trapped bosons and fermions. Furthermore, we provide a set of realistic parameters for the implementation of the superconducting circuit.Comment: 6 pages, 4 figure

Analytic Harmonic Approach to the N-body problem

We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the energy spectrum and radius of the relevant two-body problem which gives frequency, center position, and zero point energy of the corresponding harmonic oscillator. Adding external harmonic one-body terms, we proceed to solve the full quantum mechanical N-body problem analytically for arbitrary masses. Energy eigenvalues, eigenmodes, and correlation functions like density matrices can then be computed analytically. As a first application of our formalism, we consider the N-boson problem in two- and three dimensions where we fit the two-body interactions to agree with the well-known zero-range model for two particles in a harmonic trap. Subsequently, condensate fractions, spectra, radii, and eigenmodes are discussed as function of dimension, boson number N, and scattering length obtained in the zero-range model. We find that energies, radii, and condensate fraction increase with scattering length as well as boson number, while radii decrease with increasing boson number. Our formalism is completely general and can also be applied to fermions, Bose-Fermi mixtures, and to more exotic geometries.Comment: 30 pages, 12 figures, updated reference

Review and analysis of the DNW/Model 360 rotor acoustic data base

A comprehensive model rotor aeroacoustic data base was collected in a large anechoic wind tunnel in 1986. Twenty-six microphones were positioned around the azimuth to collect acoustic data for approximately 150 different test conditions. A dynamically scaled, blade-pressure-instrumented model of the forward rotor of the BH360 helicopter simultaneously provided blade pressures for correlation with the acoustic data. High-speed impulsive noise, blade-vortex interaction noise, low-frequency noise, and broadband noise were all captured in this extensive data base. Trends are presentes for each noise source, with important parametric variations. The purpose of this paper is to introduce this data base and illustrate its potential for predictive code validation

A Solvable Model for Decoupling of Interacting Clusters

We consider M clusters of interacting particles, whose in-group interactions are arbitrary, and inter-group interactions are approximated by oscillator potentials. We show that there are masses and frequencies that decouple the in-group and inter-group degrees of freedom, which reduces the initial problem to M independent problems that describe each of the relative in-group systems. The dynamics of the M center-of-mass coordinates is described by the analytically solvable problem of M coupled harmonic oscillators. This paper derives and discusses these decoupling conditions. Furthermore, to illustrate our findings, we consider a charged impurity interacting with a ring of ions. We argue that the impurity can be used to probe the center-of-mass dynamics of the ions.Comment: Version accepted for publication in EP

Bound states of Dipolar Bosons in One-dimensional Systems

We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole-dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments with respect to the symmetry axis of the tubes. The few-body structures in this geometry are determined as function of polarization angles and dipole strength by using both essentially exact stochastic variational methods and the harmonic approximation. The main focus is on the three, four, and five-body problems in two or more tubes. Our results indicate that in the weakly-coupled limit the inter-tube interaction is similar to a zero-range term with a suitable rescaled strength. This allows us to address the corresponding many-body physics of the system by constructing a model where bound chains with one molecule in each tube are the effective degrees of freedom. This model can be mapped onto one-dimensional Hamiltonians for which exact solutions are known.Comment: 22 pages, 7 figures, revised versio

Bound States and Universality in Layers of Cold Polar Molecules

The recent experimental realization of cold polar molecules in the rotational and vibrational ground state opens the door to the study of a wealth of phenomena involving long-range interactions. By applying an optical lattice to a gas of cold polar molecules one can create a layered system of planar traps. Due to the long-range dipole-dipole interaction one expects a rich structure of bound complexes in this geometry. We study the bilayer case and determine the two-body bound state properties as a function of the interaction strength. The results clearly show that a least one bound state will always be present in the system. In addition, bound states at zero energy show universal behavior and extend to very large radii. These results suggest that non-trivial bound complexes of more than two particles are likely in the bilayer and in more complicated chain structures in multi-layer systems.Comment: 6 pages, 5 figures. Revised version to be publishe

Carbon-rich presolar grains from massive stars : subsolar ¹²C/¹³C and ¹⁴N/¹⁵N ratios and the mystery of ¹⁵N

Carbon-rich grains with isotopic anomalies compared to the Sun are found in primitive meteorites. They were made by stars, and carry the original stellar nucleosynthesis signature. Silicon carbide grains of Type X and C and low-density (LD) graphites condensed in the ejecta of core-collapse supernovae. We present a new set of models for the explosive He shell and compare them with the grains showing ¹²C/¹³C and ¹⁴N/¹⁵N ratios lower than solar. In the stellar progenitor H was ingested into the He shell and not fully destroyed before the explosion. Different explosion energies and H concentrations are considered. If the supernova shock hits the He-shell region with some H still present, the models can reproduce the C and N isotopic signatures in C-rich grains. Hot-CNO cycle isotopic signatures are obtained, including a large production of ¹³C and ¹⁵N. The short-lived radionuclides ²²Na and ²⁶Al are increased by orders of magnitude. The production of radiogenic ²²Ne from the decay of ²²Na in the He shell might solve the puzzle of the Ne-E(L) component in LD graphite grains. This scenario is attractive for the SiC grains of type AB with ¹⁴N/¹⁵N ratios lower than solar, and provides an alternative solution for SiC grains originally classified as nova grains. Finally, this process may contribute to the production of ¹⁴N and ¹⁵N in the Galaxy, helping to produce the ¹⁴N/¹⁵N ratio in the solar system