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**Bachmann, Sven; Roeck, Wojciech de and Fraas, Martin (2018): The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems. In: Communications in Mathematical Physics, Vol. 361, No. 3: pp. 997-1027**

**Full text not available from 'Open Access LMU'.**

## Abstract

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter epsilon. Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One important application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g. for the integer quantum Hall effect.

Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |

Subjects: | 500 Science > 510 Mathematics |

ISSN: | 0010-3616 |

Language: | English |

Item ID: | 66376 |

Date Deposited: | 19. Jul 2019, 12:19 |

Last Modified: | 04. Nov 2020, 13:47 |