## Abstract

A number of physical problems, including statistical mechanics of 1D multivalent Coulomb gases, may be formulated in terms of non-Hermitian quantum mechanics. We use this example to develop a non-perturbative method of instanton calculus for non-Hermitian Hamiltonians. This can be seen as an extension of semiclassical methods in conventional quantum mechanics. Treating momentum and coordinate as complex variables yields a Riemann surface of constant complex energy. The classical and instanton actions are given by periods of this surface; we show how to obtain these via methods from algebraic topology. We demonstrate the accuracy of this analytic procedure in comparison with numerical simulations for a class of periodic non-Hermitian Hamiltonians, as well as the validity of the Bohr-Sommerfeld quantization and Gamow's formula in these cases.

Original language | English (US) |
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Article number | 085001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 8 |

DOIs | |

State | Published - Feb 28 2014 |

## Keywords

- algebraic topology
- ion channels
- non-Hermitian quantum theory
- statistical mechanics