Higher-order and fractional discrete time crystals in clean long-range interacting systems

Discrete time crystals are periodically driven systems characterized by a response with periodicity nT, with T the period of the drive and n > 1. Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here, we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different ‘higher-order’ discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.

Spectral Gap in Mean-Field $${\mathcal {O}}(n)$$-Model

We study the dependence of the spectral gap for the generator of the Ginzburg–Landau dynamics for all $$\mathcal O(n)$$ O ( n ) -models with mean-field interaction and magnetic field, below and at the critical temperature on the number N of particles. For our analysis of the Gibbs measure, we use a one-step renormalization approach and semiclassical methods to study the eigenvalue-spacing of an auxiliary Schrödinger operator.

Formation of CO+ by radiative association II

ABSTRACT Radiative association of an oxygen atom with a carbon cation is investigated using quantal and semiclassical methods. The total rate coefficient for spontaneous radiative association of O(2s22p4, 3P) with C+(2s22p, 2P) on the doublet manifold is determined from the corresponding cross-sections. The cross-sections for the ${\rm 1}^2\, \Sigma ^-\rightarrow {\rm A}^2\Pi$, ${\rm 2}^2\, \Sigma ^-\rightarrow {\rm A}^2\Pi$, and ${\rm C}^2\, \Delta \rightarrow {\rm A}^2\Pi$ continuum-bound processes are calculated either semiclassically, in combination with the Breit–Wigner approach, or fully quantum mechanically. In the temperature range 10–10 000 K, our recommended total rate coefficient, obtained from these calculations and the data of Zámečníková et al. (2019), slowly increases from 7.5 × 10−18 cm3s−1 to 2.1 × 10−17 cm3s−1. Corresponding aspects of the CO+ and CO formations in SN 1987A are discussed.

A classical and semiclassical study of collisions between Xq+ ions and water molecules

He2+, Li3+ and C3+ collisions with H2O are studied with three different classical and semiclassical methods, which agree for target net electron loss. The relevance of two- and three-electron removal in the fragmentation is shown.

How quantum is radical pair magnetoreception?

Semiclassical methods cannot accurately simulate magnetic field effects relevant to avian magnetoreception, which may therefore deserve the label “quantum biology”.

Ignatyuk damping factor: A semiclassical formula

Data on nuclear-level densities extracted from transmission data or gamma energy spectrum store the basic statistical information about nuclei at various temperatures. Generally, this extracted data goes through model fitting using computer codes like CASCADE. However, recently established semiclassical methods involving no adjustable parameters to determine the level density parameter for magic and semi-magic nuclei give a good agreement with the experimental values. One of the popular ways to paramaterize the level density parameter which includes the shell effects and its damping was given by Ignatyuk. This damping factor is usually fitted from the experimental data on nuclear-level density and it comes around 0.05 [Formula: see text]. In this work, we calculate the Ignatyuk damping factor for various nuclei using semiclassical methods.