dorsal/arxiv
View SchemaResonance Photon Generation in a Vibrating Cavity
| Authors | V. V. Dodonov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9810077 |
| URL | https://arxiv.org/abs/quant-ph/9810077 |
| DOI | 10.1088/0305-4470/31/49/008 |
| Journal | J.Phys.A31:9835-9854,1998 |
Abstract
The problem of photon creation from vacuum due to the nonstationary Casimir effect in an ideal one-dimensional Fabry--Perot cavity with vibrating walls is solved in the resonance case, when the frequency of vibrations is close to the frequency of some unperturbed electromagnetic mode: $\omega_w=p(\pi c/L_0)(1+\delta)$, $|\delta|\ll 1$, (p=1,2,...). An explicit analytical expression for the total energy in all the modes shows an exponential growth if $|\delta|$ is less than the dimensionless amplitude of vibrations $\epsilon\ll 1$, the increment being proportional to $p\sqrt{\epsilon^2-\delta^2}$. The rate of photon generation from vacuum in the (j+ps)th mode goes asymptotically to a constant value $cp^2\sin^2(\pi j/p)\sqrt{\epsilon^2-\delta^2}/[\pi L_0 (j+ps)]$, the numbers of photons in the modes with indices p,2p,3p,... being the integrals of motion. The total number of photons in all the modes is proportional to $p^3(\epsilon^2-\delta^2) t^2$ in the short-time and in the long-time limits. In the case of strong detuning $|\delta|>\epsilon$ the total energy and the total number of photons generated from vacuum oscillate with the amplitudes decreasing as $(\epsilon/\delta)^2$ for $\epsilon\ll|\delta|$. The special cases of p=1 and p=2 are studied in detail.
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"abstract": "The problem of photon creation from vacuum due to the nonstationary Casimir\neffect in an ideal one-dimensional Fabry--Perot cavity with vibrating walls is\nsolved in the resonance case, when the frequency of vibrations is close to the\nfrequency of some unperturbed electromagnetic mode: $\\omega_w=p(\\pi\nc/L_0)(1+\\delta)$, $|\\delta|\\ll 1$, (p=1,2,...). An explicit analytical\nexpression for the total energy in all the modes shows an exponential growth if\n$|\\delta|$ is less than the dimensionless amplitude of vibrations $\\epsilon\\ll\n1$, the increment being proportional to $p\\sqrt{\\epsilon^2-\\delta^2}$. The rate\nof photon generation from vacuum in the (j+ps)th mode goes asymptotically to a\nconstant value $cp^2\\sin^2(\\pi j/p)\\sqrt{\\epsilon^2-\\delta^2}/[\\pi L_0\n(j+ps)]$, the numbers of photons in the modes with indices p,2p,3p,... being\nthe integrals of motion. The total number of photons in all the modes is\nproportional to $p^3(\\epsilon^2-\\delta^2) t^2$ in the short-time and in the\nlong-time limits. In the case of strong detuning $|\\delta|\u003e\\epsilon$ the total\nenergy and the total number of photons generated from vacuum oscillate with the\namplitudes decreasing as $(\\epsilon/\\delta)^2$ for $\\epsilon\\ll|\\delta|$. The\nspecial cases of p=1 and p=2 are studied in detail.",
"arxiv_id": "quant-ph/9810077",
"authors": [
"V. V. Dodonov"
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"doi": "10.1088/0305-4470/31/49/008",
"journal_ref": "J.Phys.A31:9835-9854,1998",
"title": "Resonance Photon Generation in a Vibrating Cavity",
"url": "https://arxiv.org/abs/quant-ph/9810077"
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