Adiabatic versus instantaneous transitions from a harmonic oscillator to an inverted oscillator
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913397828747264 |
|---|---|
| author | Dodonov, Viktor V. Dodonov, Alexandre V. |
| author_facet | Dodonov, Viktor V. Dodonov, Alexandre V. |
| contents | We have obtained explicit analytical formulas for the mean energy and its variance (characterizing the energy fluctuations) of a quantum harmonic oscillator with time-dependent frequency in the adiabatic regimes after the frequency passes through zero. The behavior of energy turns out to be quite different in two cases: when the frequency remains real and when it becomes imaginary. In the first case, the mean energy always increases when the frequency returns to its initial value, and the increment coefficient is determined by the exponent in the power law of the frequency crossing zero. On the other hand, if the frequency becomes imaginary, the absolute value of mean energy increases exponentially, even in the adiabatic regime, unless the Hamiltonian becomes time independent. Small corrections to the leading terms of simple adiabatic approximate formulas are crucial in this case, due to the unstable nature of the motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adiabatic versus instantaneous transitions from a harmonic oscillator to an inverted oscillator Dodonov, Viktor V. Dodonov, Alexandre V. Quantum Physics Mathematical Physics We have obtained explicit analytical formulas for the mean energy and its variance (characterizing the energy fluctuations) of a quantum harmonic oscillator with time-dependent frequency in the adiabatic regimes after the frequency passes through zero. The behavior of energy turns out to be quite different in two cases: when the frequency remains real and when it becomes imaginary. In the first case, the mean energy always increases when the frequency returns to its initial value, and the increment coefficient is determined by the exponent in the power law of the frequency crossing zero. On the other hand, if the frequency becomes imaginary, the absolute value of mean energy increases exponentially, even in the adiabatic regime, unless the Hamiltonian becomes time independent. Small corrections to the leading terms of simple adiabatic approximate formulas are crucial in this case, due to the unstable nature of the motion. |
| title | Adiabatic versus instantaneous transitions from a harmonic oscillator to an inverted oscillator |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2403.06377 |