Finite-time Unruh effect: Waiting for the transient effects to fade off
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arXiv
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| Format: | Preprint |
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2025
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| author | Stargen, D. Jaffino |
| author_facet | Stargen, D. Jaffino |
| contents | We investigate the transition probability rate of a Unruh-DeWitt (UD) detector interacting with massless scalar field for a finite duration of proper time, $T$, of the detector. For a UD detector moving at a uniform acceleration, $a$, we explicitly show that the finite-time transition probability rate can be written as a sum of purely thermal terms, and non-thermal transient terms. While the thermal terms are independent of time, $T$, the non-thermal transient terms depend on $(ΔET)$, $(aT)$, and $(ΔE/a)$, where $ΔE$ is the energy gap of the detector. Particularly, the non-thermal terms are oscillatory with respect to the variable $(ΔET)$, so that they may be averaged out to be insignificant in the limit $ΔET \gg 1$, irrespective of the values of $(aT)$ and $(ΔE/a)$. To quantify the contribution of non-thermal transient terms to the transition probability rate of a uniformly accelerating detector, we introduce a parameter, $\varepsilon_{\rm nt}$, called non-thermal parameter. Demanding the contribution of non-thermal terms in the finite-time transition probability rate to be negligibly small, \ie, $\varepsilon_{\rm nt}=δ\ll1$, we calculate the thermalization time -- the time required for the detector to interact with the field to arrive at the required non-thermality, $\varepsilon_{\rm nt}=δ$, and the detector to be (almost) thermalized with the Unruh bath in its comoving frame. Specifically, for small accelerations, $a\llΔE$, we find the thermalization time, $τ_{\rm th}$, to be $τ_{\rm th} \sim (ΔE)^{-1} \times {\rm e}^{2π|ΔE|/a}/δ$; and for large accelerations, $a\gg ΔE$, we find the thermalization time to be $τ_{\rm th} \sim (ΔE)^{-1}/δ$. We comment on the possibilities of bringing down the exponentially large thermalization time at small accelerations, $a\llΔE$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09676 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-time Unruh effect: Waiting for the transient effects to fade off Stargen, D. Jaffino General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics We investigate the transition probability rate of a Unruh-DeWitt (UD) detector interacting with massless scalar field for a finite duration of proper time, $T$, of the detector. For a UD detector moving at a uniform acceleration, $a$, we explicitly show that the finite-time transition probability rate can be written as a sum of purely thermal terms, and non-thermal transient terms. While the thermal terms are independent of time, $T$, the non-thermal transient terms depend on $(ΔET)$, $(aT)$, and $(ΔE/a)$, where $ΔE$ is the energy gap of the detector. Particularly, the non-thermal terms are oscillatory with respect to the variable $(ΔET)$, so that they may be averaged out to be insignificant in the limit $ΔET \gg 1$, irrespective of the values of $(aT)$ and $(ΔE/a)$. To quantify the contribution of non-thermal transient terms to the transition probability rate of a uniformly accelerating detector, we introduce a parameter, $\varepsilon_{\rm nt}$, called non-thermal parameter. Demanding the contribution of non-thermal terms in the finite-time transition probability rate to be negligibly small, \ie, $\varepsilon_{\rm nt}=δ\ll1$, we calculate the thermalization time -- the time required for the detector to interact with the field to arrive at the required non-thermality, $\varepsilon_{\rm nt}=δ$, and the detector to be (almost) thermalized with the Unruh bath in its comoving frame. Specifically, for small accelerations, $a\llΔE$, we find the thermalization time, $τ_{\rm th}$, to be $τ_{\rm th} \sim (ΔE)^{-1} \times {\rm e}^{2π|ΔE|/a}/δ$; and for large accelerations, $a\gg ΔE$, we find the thermalization time to be $τ_{\rm th} \sim (ΔE)^{-1}/δ$. We comment on the possibilities of bringing down the exponentially large thermalization time at small accelerations, $a\llΔE$. |
| title | Finite-time Unruh effect: Waiting for the transient effects to fade off |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2501.09676 |