Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems
Quantum characteristics of a mass-accreting oscillator are investigated using the invariant operator theory, which is a rigorous mathematical tool for unfolding quantum theory for time-dependent Hamiltonian systems. In particular, the quantum energy of the system is analyzed in detail and compared t...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-07-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/10/3/153 |
| _version_ | 1829453355634655232 |
|---|---|
| author | Jeong Ryeol Choi |
| author_facet | Jeong Ryeol Choi |
| author_sort | Jeong Ryeol Choi |
| collection | DOAJ |
| description | Quantum characteristics of a mass-accreting oscillator are investigated using the invariant operator theory, which is a rigorous mathematical tool for unfolding quantum theory for time-dependent Hamiltonian systems. In particular, the quantum energy of the system is analyzed in detail and compared to the classical one. We focus on two particular cases; one is a linearly mass-accreting oscillator and the other is an exponentially mass-accreting one. It is confirmed that the quantum energy is in agreement with the classical one in the limit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>ℏ</mo><mo>→</mo><mn>0</mn></mrow></semantics></math></inline-formula>. We showed that not only the classical but also the quantum energy oscillates with time. It is carefully analyzed why the energy oscillates with time, and a reasonable explanation for that outcome is given. |
| first_indexed | 2024-03-10T07:54:32Z |
| format | Article |
| id | doaj.art-c702776e0bd04877893501545165e01e |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T07:54:32Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-c702776e0bd04877893501545165e01e2023-11-22T12:02:10ZengMDPI AGAxioms2075-16802021-07-0110315310.3390/axioms10030153Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator SystemsJeong Ryeol Choi0Department of Nanoengineering, Kyonggi University, Yeongtong-gu, Suwon 16227, Gyeonggi-do, KoreaQuantum characteristics of a mass-accreting oscillator are investigated using the invariant operator theory, which is a rigorous mathematical tool for unfolding quantum theory for time-dependent Hamiltonian systems. In particular, the quantum energy of the system is analyzed in detail and compared to the classical one. We focus on two particular cases; one is a linearly mass-accreting oscillator and the other is an exponentially mass-accreting one. It is confirmed that the quantum energy is in agreement with the classical one in the limit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>ℏ</mo><mo>→</mo><mn>0</mn></mrow></semantics></math></inline-formula>. We showed that not only the classical but also the quantum energy oscillates with time. It is carefully analyzed why the energy oscillates with time, and a reasonable explanation for that outcome is given.https://www.mdpi.com/2075-1680/10/3/153quantum energymass accretionlinear invariant operatorHamiltonian |
| spellingShingle | Jeong Ryeol Choi Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems Axioms quantum energy mass accretion linear invariant operator Hamiltonian |
| title | Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems |
| title_full | Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems |
| title_fullStr | Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems |
| title_full_unstemmed | Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems |
| title_short | Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems |
| title_sort | analysis of novel oscillations of quantized mechanical energy in mass accreting nano oscillator systems |
| topic | quantum energy mass accretion linear invariant operator Hamiltonian |
| url | https://www.mdpi.com/2075-1680/10/3/153 |
| work_keys_str_mv | AT jeongryeolchoi analysisofnoveloscillationsofquantizedmechanicalenergyinmassaccretingnanooscillatorsystems |