{
  "id": "1603.08267",
  "version": "v1",
  "published": "2016-03-27T22:51:14.000Z",
  "updated": "2016-03-27T22:51:14.000Z",
  "title": "Quantum Revivals in Conformal Field Theories in Higher Dimensions",
  "authors": [
    "John Cardy"
  ],
  "comment": "19 pages, 14 figures",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "We investigate the behavior of the return amplitude ${\\cal F}(t)= |\\langle\\Psi(0)|\\Psi(t)\\rangle|$ following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension $d-1$ and linear size $O(L)$, from a state $|\\Psi(0)\\rangle$ of extensive energy with short-range correlations. After an initial gaussian decay ${\\cal F}(t)$ reaches a plateau value related to the density of available states at the initial energy. However for $d=3,4$ this value is attained from below after a single oscillation. For a holographic CFT the plateau persists up to times at least $O(\\sigma^{1/(d-1)} L)$, where $\\sigma\\gg1$ is the dimensionless Stefan-Boltzmann constant. On the other hand for a free field theory on manifolds with high symmetry there are typically revivals at times $t\\sim\\mbox{integer}\\times L$. In particular, on a sphere $S_{d-1}$ of circumference $2\\pi L$, there is an action of the modular group on ${\\cal F}(t)$ implying structure near all rational values of $t/L$, similarly to what happens for rational CFTs in $d=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-27T22:51:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal field theory",
      "quantum revivals",
      "higher dimensions",
      "free field theory",
      "compact spatial manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160308267C",
      "inspire": 1435081
    }
  }
}