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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2402.12124 |
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| _version_ | 1866911779596009472 |
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| author | Plyukhin, Alex V. |
| author_facet | Plyukhin, Alex V. |
| contents | We consider a classical Brownian oscillator of mass $m$ driven from an arbitrary initial state by varying the stiffness $k(t)$ of the harmonic potential according to the protocol $k(t)=k_0+a\,δ(t)$, involving the Dirac delta function. The microscopic work performed on the oscillator is shown to be $W=(a^2/2m)\,q^2-a q v$, where $q$ and $v$ are the coordinate and velocity in the initial state. If the initial distribution of $q$ and $v$ is the equilibrium one with temperature $T$, the average work is $\langle W \rangle=a^2T/(2m\,k_0)$ and the distribution $f(W)$ has the form of the product of exponential and modified Bessel functions. The distribution is asymmetric and diverges as $W\to 0$. The system's response for $t>0$ is evaluated for specific models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Brownian oscillator with time-dependent strength: a delta function protocol Plyukhin, Alex V. Statistical Mechanics Mathematical Physics We consider a classical Brownian oscillator of mass $m$ driven from an arbitrary initial state by varying the stiffness $k(t)$ of the harmonic potential according to the protocol $k(t)=k_0+a\,δ(t)$, involving the Dirac delta function. The microscopic work performed on the oscillator is shown to be $W=(a^2/2m)\,q^2-a q v$, where $q$ and $v$ are the coordinate and velocity in the initial state. If the initial distribution of $q$ and $v$ is the equilibrium one with temperature $T$, the average work is $\langle W \rangle=a^2T/(2m\,k_0)$ and the distribution $f(W)$ has the form of the product of exponential and modified Bessel functions. The distribution is asymmetric and diverges as $W\to 0$. The system's response for $t>0$ is evaluated for specific models. |
| title | Brownian oscillator with time-dependent strength: a delta function protocol |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2402.12124 |