{
  "id": "0810.3540",
  "version": "v1",
  "published": "2008-10-20T11:59:29.000Z",
  "updated": "2008-10-20T11:59:29.000Z",
  "title": "A resonance theory for open quantum systems with time-dependent dynamics",
  "authors": [
    "Marco Merkli",
    "Shannon Starr"
  ],
  "comment": "29 pages",
  "journal": "J. Statist. Phys., 134 (2009) 871--898",
  "doi": "10.1007/s10955-008-9645-5",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed dynamical resonance theory, and we piece them together to obtain the total evolution. The initial state corresponding to one time-interval with constant Hamiltonian is the final state of the system corresponding to the interval before. This results in a non-markovian dynamics. We find a representation of the dynamics in terms of resonance energies and resonance states associated to the Hamiltonians, valid for all times $t\\geq 0$ and for small (but fixed) interaction strengths. The representation has the form of a path integral over resonances. We present applications to a spin-fermion system, where the energy levels of the spin may undergo rather arbitrary crossings in the course of time. In particular, we find the probability for transition between ground- and excited state at all times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-20T11:59:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C10"
    ],
    "keywords": [
      "open quantum systems",
      "time-dependent dynamics",
      "constant hamiltonian",
      "constant bit",
      "spin-fermion system"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2009,
      "month": "Mar",
      "volume": 134,
      "number": "5-6",
      "pages": 871
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JSP...134..871M"
    }
  }
}