Dynamical change under slowly changing conditions: the quantum Kruskal–Neishtadt–Henrard theorem
Adiabatic approximations break down classically when a constant-energy contour splits into separate contours, forcing the system to choose which daughter contour to follow; the choices often represent qualitatively different behavior, so that slowly changing conditions induce a sudden and drastic ch...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2022-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aca557 |
| _version_ | 1797748773108056064 |
|---|---|
| author | Peter Stabel James R Anglin |
| author_facet | Peter Stabel James R Anglin |
| author_sort | Peter Stabel |
| collection | DOAJ |
| description | Adiabatic approximations break down classically when a constant-energy contour splits into separate contours, forcing the system to choose which daughter contour to follow; the choices often represent qualitatively different behavior, so that slowly changing conditions induce a sudden and drastic change in dynamics. The Kruskal–Neishtadt–Henrard (KNH) theorem relates the probability of each choice to the rates at which the phase space areas enclosed by the different contours are changing. This represents a connection within closed-system mechanics, and without dynamical chaos, between spontaneous change and increase in phase space measure, as required by the Second Law of Thermodynamics. Quantum mechanically, in contrast, dynamical tunneling allows adiabaticity to persist, for very slow parameter change, through a classical splitting of energy contours; the classical and adiabatic limits fail to commute. Here we show that a quantum form of the KNH theorem holds nonetheless, due to unitarity. |
| first_indexed | 2024-03-12T16:09:38Z |
| format | Article |
| id | doaj.art-8b268585046b4813843c0669cbe01264 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:09:38Z |
| publishDate | 2022-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-8b268585046b4813843c0669cbe012642023-08-09T14:11:16ZengIOP PublishingNew Journal of Physics1367-26302022-01-01241111305210.1088/1367-2630/aca557Dynamical change under slowly changing conditions: the quantum Kruskal–Neishtadt–Henrard theoremPeter Stabel0https://orcid.org/0000-0001-6852-6090James R Anglin1State Research Center, OPTIMAS and Fachbereich Physik, Technische Universität Kaiserslautern , D-67663 Kaiserslautern, GermanyState Research Center, OPTIMAS and Fachbereich Physik, Technische Universität Kaiserslautern , D-67663 Kaiserslautern, GermanyAdiabatic approximations break down classically when a constant-energy contour splits into separate contours, forcing the system to choose which daughter contour to follow; the choices often represent qualitatively different behavior, so that slowly changing conditions induce a sudden and drastic change in dynamics. The Kruskal–Neishtadt–Henrard (KNH) theorem relates the probability of each choice to the rates at which the phase space areas enclosed by the different contours are changing. This represents a connection within closed-system mechanics, and without dynamical chaos, between spontaneous change and increase in phase space measure, as required by the Second Law of Thermodynamics. Quantum mechanically, in contrast, dynamical tunneling allows adiabaticity to persist, for very slow parameter change, through a classical splitting of energy contours; the classical and adiabatic limits fail to commute. Here we show that a quantum form of the KNH theorem holds nonetheless, due to unitarity.https://doi.org/10.1088/1367-2630/aca557quantum mechanicssemi-classical methodsquantum–classical correspondenceadiabatic theoryLandau–Zener avoided crossingsKruskal–Neishstadt–Henrard theorem |
| spellingShingle | Peter Stabel James R Anglin Dynamical change under slowly changing conditions: the quantum Kruskal–Neishtadt–Henrard theorem New Journal of Physics quantum mechanics semi-classical methods quantum–classical correspondence adiabatic theory Landau–Zener avoided crossings Kruskal–Neishstadt–Henrard theorem |
| title | Dynamical change under slowly changing conditions: the quantum Kruskal–Neishtadt–Henrard theorem |
| title_full | Dynamical change under slowly changing conditions: the quantum Kruskal–Neishtadt–Henrard theorem |
| title_fullStr | Dynamical change under slowly changing conditions: the quantum Kruskal–Neishtadt–Henrard theorem |
| title_full_unstemmed | Dynamical change under slowly changing conditions: the quantum Kruskal–Neishtadt–Henrard theorem |
| title_short | Dynamical change under slowly changing conditions: the quantum Kruskal–Neishtadt–Henrard theorem |
| title_sort | dynamical change under slowly changing conditions the quantum kruskal neishtadt henrard theorem |
| topic | quantum mechanics semi-classical methods quantum–classical correspondence adiabatic theory Landau–Zener avoided crossings Kruskal–Neishstadt–Henrard theorem |
| url | https://doi.org/10.1088/1367-2630/aca557 |
| work_keys_str_mv | AT peterstabel dynamicalchangeunderslowlychangingconditionsthequantumkruskalneishtadthenrardtheorem AT jamesranglin dynamicalchangeunderslowlychangingconditionsthequantumkruskalneishtadthenrardtheorem |