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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2405.18988 |
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| _version_ | 1866916650034397184 |
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| author | Nath, Sujit Kumar Sabhapandit, Sanjib |
| author_facet | Nath, Sujit Kumar Sabhapandit, Sanjib |
| contents | We study the late time exponential decay of the survival probability $S_\pm(t,a|x_0)\sim e^{-θ(a)t}$, of a one-dimensional run and tumble particle starting from $x_0<a$ with an initial orientation $σ(0)=\pm 1$, under a confining potential $U(x)=α|x|$ with an absorbing boundary at $x=a>0$. We find that the decay rate $θ(a)$ of the survival probability has strong dependence on the location $a$ of the absorbing boundary, which undergoes a freezing transition at a critical value $a=a_c=(v_0-α)\sqrt{v_0^2-α^2}/(2αγ)$, where $v_0>α$ is the self-propulsion speed and $γ$ is the tumbling rate of the particle. For $a>a_c$, the value of $θ(a)$ increases monotonically from zero, as $a$ decreases from infinity, till it attains the maximum value $θ(a_c)$ at $a=a_c$. For $0<a<a_c$, the value of $θ(a)$ freezes to the value $θ(a)=θ(a_c)$. We also obtain the propagator with the absorbing boundary condition at $x=a$. Our analytical results are supported by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18988 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Survival probability and position distribution of a run and tumble particle in $U(x)=α|x|$ potential with an absorbing boundary Nath, Sujit Kumar Sabhapandit, Sanjib Statistical Mechanics We study the late time exponential decay of the survival probability $S_\pm(t,a|x_0)\sim e^{-θ(a)t}$, of a one-dimensional run and tumble particle starting from $x_0<a$ with an initial orientation $σ(0)=\pm 1$, under a confining potential $U(x)=α|x|$ with an absorbing boundary at $x=a>0$. We find that the decay rate $θ(a)$ of the survival probability has strong dependence on the location $a$ of the absorbing boundary, which undergoes a freezing transition at a critical value $a=a_c=(v_0-α)\sqrt{v_0^2-α^2}/(2αγ)$, where $v_0>α$ is the self-propulsion speed and $γ$ is the tumbling rate of the particle. For $a>a_c$, the value of $θ(a)$ increases monotonically from zero, as $a$ decreases from infinity, till it attains the maximum value $θ(a_c)$ at $a=a_c$. For $0<a<a_c$, the value of $θ(a)$ freezes to the value $θ(a)=θ(a_c)$. We also obtain the propagator with the absorbing boundary condition at $x=a$. Our analytical results are supported by numerical simulations. |
| title | Survival probability and position distribution of a run and tumble particle in $U(x)=α|x|$ potential with an absorbing boundary |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2405.18988 |