论文标题
尺寸在随机重置和有吸引力的偏见下的第一次传递中的作用
Role of dimensions in first passage of a diffusing particle under stochastic resetting and attractive bias
论文作者
论文摘要
一个维度的最新研究表明，随机重置以扩散粒子在获得第一个通道时所带来的时间优势可能被足够强大的吸引力的潜力消除。我们将结果扩展到更高的维度。对于一个有吸引力的潜在$ v（{r}）= k {r}^n $，一般$ d $ dimensions中的散射粒子，我们研究了关键强度$ k = k_c $，而重置变得不利。即使在重置问题无法解决的情况下，如果不重置问题的前两个时刻，连续过渡的点也可以完全找到。当$ d/n $和$ 2/n $时，我们发现无量纲的临界强度$κ_{C，N}（k_c）$以积极的积分值。也是针对盒子潜力的限制情况（代表$ n \至\ infty $），以及对数潜在的$ k \ ln \ big（\ frac {r} {a} \ big）$的特殊情况，我们找到了相应的过渡点$κ__{c，\ infty} $ and $ n dimistion $和$ ch $ n diceSIST大尺寸$ d $的关键优势的渐近形式很有趣。我们表明，对于（0，\ infty）$中的任何$ n \，在大$ d $中，对于任何$ n \ in（0，\ infty）$的任何$ n \ in（0，\ infty）$，无量纲的关键强度$κ_{c，n} \ sim d^{\ frac {\ frac {1} {n}}} $。对于盒子的潜力，差异是$κ_{c，\ infty} \ sim（1 - \ ln（\ frac {d} {2} {2}）/d）$，而对数潜力，$κ__{c，c，l} \ sim d $。
Recent studies in one dimension have revealed that the temporal advantage rendered by stochastic resetting to diffusing particles in attaining first passage, may be annulled by a sufficiently strong attractive potential. We extend the results to higher dimensions. For a diffusing particle in an attractive potential $V({R})=k {R}^n$, in general $d$ dimensions, we study the critical strength $k = k_c$ above which resetting becomes disadvantageous. The point of continuous transition may be exactly found even in cases where the problem with resetting is not solvable, provided the first two moments of the problem without resetting are known. We find the dimensionless critical strength $κ_{c,n}(k_c)$ exactly when $d/n$ and $2/n$ take positive integral values. Also for the limiting case of a box potential (representing $n \to \infty$), and the special case of a logarithmic potential $k \ln\big(\frac{R}{a}\big)$, we find the corresponding transition points $κ_{c,\infty}$ and $κ_{c,l}$ exactly for any dimension $d$. The asymptotic forms of the critical strengths at large dimensions $d$ are interesting. We show that for the power law potential, for any $n \in (0,\infty)$, the dimensionless critical strength $κ_{c,n} \sim d^{\frac{1}{n}}$ at large $d$. For the box potential, asymptotically, $κ_{c,\infty} \sim (1 - \ln(\frac{d}{2})/d)$, while for the logarithmic potential, $κ_{c,l} \sim d$.
