Analysis Technique for Exceptional Points in Open Quantum Systems and QPT Analogy for the Appearance of Irreversibility View Full Text


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Article Info

DATE

2012-11

AUTHORS

Savannah Garmon, Ingrid Rotter, Naomichi Hatano, Dvira Segal

ABSTRACT

We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate the EPs in OQS, further obtaining an eigenvalue expansion in the vicinity of the EPs that gives rise to characteristic exponents. We also report the precise number of EPs occurring in an OQS with a continuum described by a quadratic dispersion curve. In particular, the number of EPs occurring in a bare discrete Hamiltonian of dimension nD is given by nD(nD−1); if this discrete Hamiltonian is then coupled to continuum (or continua) to form an OQS, the interaction with the continuum generally produces an enlarged discrete solution space that includes a greater number of EPs, specifically , in which nC is the number of (non-degenerate) continua to which the discrete sector is attached. Finally, we offer a heuristic quantum phase transition analogy for the emergence of the resonance (giving rise to irreversibility via exponential decay) in which the decay width plays the role of the order parameter; the associated critical exponent is then determined by the above eigenvalue expansion. More... »

PAGES

3536-3550

References to SciGraph publications

  • 2007-05. Bound states in the continuum in a single-level Fano-Anderson model in THE EUROPEAN PHYSICAL JOURNAL B
  • 2009-09-30. Quantum Post-Exponential Decay in TIME IN QUANTUM MECHANICS II
  • 1999-08. Phases of wave functions and level repulsion in THE EUROPEAN PHYSICAL JOURNAL D
  • 1983. Green’s Functions in Quantum Physics in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10773-012-1240-5

    DOI

    http://dx.doi.org/10.1007/s10773-012-1240-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1026852045


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