Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition
For a scalar field in an exponentially expanding universe, constituent modes of elementary excitation become unstable consecutively at shorter wavelength. After canonical quantization, a Bogoliubov transformation reduces the minimally coupled scalar field to independent 1D modes of two inequivalent...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/6/943 |
| _version_ | 1797566212248436736 |
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| author | Philip Broadbridge Kathryn Deutscher |
| author_facet | Philip Broadbridge Kathryn Deutscher |
| author_sort | Philip Broadbridge |
| collection | DOAJ |
| description | For a scalar field in an exponentially expanding universe, constituent modes of elementary excitation become unstable consecutively at shorter wavelength. After canonical quantization, a Bogoliubov transformation reduces the minimally coupled scalar field to independent 1D modes of two inequivalent types, leading eventually to a cosmological partitioning of energy. Due to accelerated expansion of the coupled space-time, each underlying mode transits from an attractive oscillator with discrete energy spectrum to a repulsive unit with continuous unbounded energy spectrum. The underlying non-autonomous Schrödinger equation is solved here as the wave function evolves through the attraction-repulsion transition and ceases to oscillate. |
| first_indexed | 2024-03-10T19:23:29Z |
| format | Article |
| id | doaj.art-172309d2daf449c38554e58c03d344cd |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T19:23:29Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-172309d2daf449c38554e58c03d344cd2023-11-20T02:44:46ZengMDPI AGSymmetry2073-89942020-06-0112694310.3390/sym12060943Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion TransitionPhilip Broadbridge0Kathryn Deutscher1Department of Mathematics and Statistics, La Trobe University, Bundoora, VIC 3086, AustraliaSchool of Physical Sciences, University of Adelaide, Adelaide, SA 5005, AustraliaFor a scalar field in an exponentially expanding universe, constituent modes of elementary excitation become unstable consecutively at shorter wavelength. After canonical quantization, a Bogoliubov transformation reduces the minimally coupled scalar field to independent 1D modes of two inequivalent types, leading eventually to a cosmological partitioning of energy. Due to accelerated expansion of the coupled space-time, each underlying mode transits from an attractive oscillator with discrete energy spectrum to a repulsive unit with continuous unbounded energy spectrum. The underlying non-autonomous Schrödinger equation is solved here as the wave function evolves through the attraction-repulsion transition and ceases to oscillate.https://www.mdpi.com/2073-8994/12/6/943non-autonomous Schrödinger equationBogoliubov transformationsdark energy |
| spellingShingle | Philip Broadbridge Kathryn Deutscher Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition Symmetry non-autonomous Schrödinger equation Bogoliubov transformations dark energy |
| title | Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition |
| title_full | Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition |
| title_fullStr | Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition |
| title_full_unstemmed | Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition |
| title_short | Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition |
| title_sort | solution of non autonomous schrodinger equation for quantized de sitter klein gordon oscillator modes undergoing attraction repulsion transition |
| topic | non-autonomous Schrödinger equation Bogoliubov transformations dark energy |
| url | https://www.mdpi.com/2073-8994/12/6/943 |
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