Due to entropic effects, it is possible that generic high-energy states of a quantum or classical system are ordered. This leads to spontaneous symmetry breaking at arbitrarily high temperatures. We present minimal models of entropic order that arise from very simple interactions. Our main examples are the Arithmetic Ising Model (AIM) and its quantum analogue, where usual Ising spins are replaced by non-negative integers. Using a large-flavor expansion together with numerical simulations, we find that the high-temperature phase is ordered in the classical and quantum models. We also introduce classical gas models whose interactions drive the system to a crystal at high temperatures.
Abstract Spin-dependent effects in atomic processes can be caused by the spin–orbit interaction or/and by the requirement that the wave function of identical electrons is antisymmetric. Such effects are usually neglected in strong-field physics. We show two examples, supported by theoretical results and numerical calculations, in which these effects are important. The first one is based on strong-field ionization of Xe atoms by a bicircular field. The corresponding momentum distribution of spin-polarized electrons emitted in the above-threshold ionization process exhibits wavelength-dependent fast oscillations. For longer wavelengths and small electron emission angle there is a wide photoelectron kinetic energy region in which the spin asymmetry parameter changes continuously from large positive to large negative values. In addition, the emission time of such electrons in high-order above-threshold ionization is determined on the attosecond time scale. The second process considered is high-order above-threshold ionization of excited Li + ions. We have found that in this case, even in the absence of spin–orbit coupling, the photoelectron momentum distribution strongly depends on the initial spin state. In the singlet state we have characteristic minima, which are caused by the destructive interference of the direct and exchange rescattering amplitudes. Such minima are absent in the triplet state.
Spin relaxation due to atom--atom collisions is measured for magnetically trapped erbium and thulium atoms at a temperature near 500 mK. The rate constants for Er--Er and Tm--Tm collisions are $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ and $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ cm
3 ${\mathrm{s}}^{\ensuremath{-}1}$, respectively,
2−−3 orders of magnitude larger than those observed for highly magnetic
S-state atoms. This is strong evidence for an additional, dominant, spin relaxation mechanism, electronic interaction anisotropy, in collisions between these ``submerged-shell,'' $L\ensuremath{\ne}0$ atoms. These large spin relaxation rates imply that evaporative cooling of these atoms in a magnetic trap will be highly inefficient.