Non-Hermitian dynamics from Hermitian systems: Do-it-yourself

Braulio M. Villegas-Martínez; Francisco Soto-Eguibar; Héctor M. Moya-Cessa; Sergio A. Hojman; Felipe A. Asenjo

doi:10.1142/S0217984924501781

Non-Hermitian dynamics from Hermitian systems: Do-it-yourself

Braulio M. Villegas-Martínez
, Francisco Soto-Eguibar
, Héctor M. Moya-Cessa
, Sergio A. Hojman
, Felipe A. Asenjo

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We show that several Hamiltonians that are symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. Therefore, a recipe to produce tractable non-Hermitian Hamiltonians is given (a set of instructions to do it yourself). We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.

Original language	English
Article number	2450178
Journal	Modern Physics Letters B
Volume	38
Issue number	22
DOIs	https://doi.org/10.1142/S0217984924501781
State	Published - 10 Aug 2024
Externally published	Yes

Keywords

PT symmetric Hamiltonians
Wick rotation
non-unitary transformations

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10.1142/S0217984924501781

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abstract = "We show that several Hamiltonians that are symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. Therefore, a recipe to produce tractable non-Hermitian Hamiltonians is given (a set of instructions to do it yourself). We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.",

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AU - Villegas-Martínez, Braulio M.

AU - Soto-Eguibar, Francisco

AU - Moya-Cessa, Héctor M.

AU - Hojman, Sergio A.

AU - Asenjo, Felipe A.

PY - 2024/8/10

Y1 - 2024/8/10

N2 - We show that several Hamiltonians that are symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. Therefore, a recipe to produce tractable non-Hermitian Hamiltonians is given (a set of instructions to do it yourself). We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.

AB - We show that several Hamiltonians that are symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. Therefore, a recipe to produce tractable non-Hermitian Hamiltonians is given (a set of instructions to do it yourself). We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.

KW - PT symmetric Hamiltonians

KW - Wick rotation

KW - non-unitary transformations

UR - https://www.scopus.com/pages/publications/85184512828

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DO - 10.1142/S0217984924501781

M3 - Article

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JO - Modern Physics Letters B

JF - Modern Physics Letters B

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M1 - 2450178

ER -

Non-Hermitian dynamics from Hermitian systems: Do-it-yourself

Abstract

Keywords

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