Semiclassical dynamics and long time asymptotics of the central-spin problem in a quantum dot

The spin of an electron trapped in a quantum dot is a promising candidate implementation of a qubit for quantum information processing. We study the central spin problem of the effect of the hyperfine interaction between such an electron and a large number of nuclear moments. Using a spin coherent path integral, we show that in this limit the electron spin evolution is well described by classical dynamics of both the nuclear and electron spins. We then introduce approximate yet systematic methods to analyze aspects of the classical dynamics, and discuss the importance of the exact integrability of the central spin Hamiltonian. This is compared with numerical simulation. Finally, we obtain the asymptotic long time decay of the electron spin polarization. We show that this is insensitive to integrability, and determined instead by the transfer of angular momentum to very weakly coupled spins far from the center of the quantum dot. The specific form of the decay is shown to depend sensitively on the form of the electronic wavefunction.Comment: 13 pages, 4 figures, accepted by PR

CHAMMI: A benchmark for channel-adaptive models in microscopy imaging

Most neural networks assume that input images have a fixed number of channels (three for RGB images). However, there are many settings where the number of channels may vary, such as microscopy images where the number of channels changes depending on instruments and experimental goals. Yet, there has not been a systemic attempt to create and evaluate neural networks that are invariant to the number and type of channels. As a result, trained models remain specific to individual studies and are hardly reusable for other microscopy settings. In this paper, we present a benchmark for investigating channel-adaptive models in microscopy imaging, which consists of 1) a dataset of varied-channel single-cell images, and 2) a biologically relevant evaluation framework. In addition, we adapted several existing techniques to create channel-adaptive models and compared their performance on this benchmark to fixed-channel, baseline models. We find that channel-adaptive models can generalize better to out-of-domain tasks and can be computationally efficient. We contribute a curated dataset (https://doi.org/10.5281/zenodo.7988357) and an evaluation API (https://github.com/broadinstitute/MorphEm.git) to facilitate objective comparisons in future research and applications.Comment: Accepted at NeurIPS Track on Datasets and Benchmarks, 202

Multipole (E1, M1, E2, M2, E3, M3) transition wavelengths and rates between 3l5l' excited and ground states in nickel-like ions

A relativistic many-body method is developed to calculate energy and transition rates for multipole transitions in many-electron ions. This method is based on relativistic many-body perturbation theory (RMBPT), agrees with MCDF calculations in lowest-order, includes all second-order correlation corrections and includes corrections from negative energy states. Reduced matrix elements, oscillator strengths, and transition rates are calculated for electric-multipole (dipole (E1), quadrupole (E2), and octupole (E3)) and magnetic-multipole (dipole (M1), quadrupole (M2), and octupole (M3)) transitions between 3l5l' excited and ground states in Ni-like ions with nuclear charges ranging from Z = 30 to 100. The calculations start from a 1s22s22p63s23p63d10} Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. A detailed discussion of the various contributions to the dipole matrix elements and energy levels is given for nickellike tungsten (Z = 74). The contributions from negative-energy states are included in the second-order E1, M1, E2 M2, E3, and M3 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. These atomic data are important in modeling of M-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in M-shell diagnostics of plasmas.Comment: 21 pages, 8 figures, 11 table

Quantum mechanical analysis of the equilateral triangle billiard: periodic orbit theory and wave packet revivals

Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by $T_{rev} = 9 \mu a^2/4\hbar \pi$ where $a$ and $\mu$ are the length of one side and the mass of the point particle respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral ($60^{\circ}-60^{\circ}-60^{\circ}$) triangle, such as the half equilateral ($30^{\circ}-60^{\circ}-90^{\circ}$) triangle and other `foldings', which have related energy spectra and revival structures.Comment: 34 pages, 9 embedded .eps figure