Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions

Occupation Time Statistics in the Quenched Trap Model

We investigate the distribution of occupation times for a particle undergoing a random walk among random energy traps and in the presence of a deterministic potential field $U^{\rm det}(x)$. When the distribution of energy traps is exponential with a width $T_g$ we find that the occupation time statistics behaves according to (i) the canonical Boltzmann theory when $T>T_g$, (ii) while for $T<T_g$ they are distributed according to the Lamperti distribution with the asymmetry of the distribution determined by the Boltzmann factor $\exp(-U^{\rm det}(x)/T_g)$ with $T_g$ and not $T$ being the effec…

Encounter-based reaction-subdiffusion model II: partially absorbing traps and the occupation time propagator

In this paper we develop an encounter-based model of reaction-subdiffusion in a domain $Ω$ with a partially absorbing interior trap $\calU\subset Ω$. We assume that the particle can freely enter and exit $\calU$, but is only absorbed within $\calU$. We take the probability of absorption to depend on the amount of time a particle spends within the trap, which is specified by a Brownian functional known as the occupation time $A(t)$. The first passage time (FPT) for absorption is identified with the point at which the occupation time crosses a random threshold $\widehat{A}$ with probability dens…

Correlations of occupation numbers in the canonical ensemble and application to BEC in a 1D harmonic trap

We study statistical properties of $N$ non-interacting identical bosons or fermions in the canonical ensemble. We derive several general representations for the $p$-point correlation function of occupation numbers $\overline{n_1\cdots n_p}$. We demonstrate that it can be expressed as a ratio of two $p\times p$ determinants involving the (canonical) mean occupations $\overline{n_1}$, ..., $\overline{n_p}$, which can themselves be conveniently expressed in terms of the $k$-body partition functions (with $k\leq N$). We draw some connection with the theory of symmetric functions, and obtain an exp…

Trapping in bottlenecks: interplay between microscopic dynamics and large scale effects

We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow trough a bottleneck via a Zero Range Process on a one dimensional periodic lattice. Particle are removed from the lattice sites with rates proportional to the local occupation numbers. The bottleneck is modelled by a particular site of the lattice where the updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that, for an…

A microfluidic method for passive trapping of sperms in microstructures

Sperm motility is a prerequisite for male fertility. Enhancing the concentration of motile sperms in assisted reproductive technologies - for human and animal reproduction - is typically achieved through aggressive methods such as centrifugation. Here we propose a passive technique for the amplification of motile sperm concentration, with no externally imposed forces or flows. The technique is based upon the disparity between probability rates, for motile cells, of entering in and escaping from complex structures. The effectiveness of the technique is demonstrated in microfluidic experiments w…

玻色-爱因斯坦凝聚气体中激发粒子态占据数的多体涨落量子优越性

Quantum supremacy of the many-body fluctuations in the occupations of the excited particle states in a Bose-Einstein-condensed gas

本研究推导了BEC气体粒子占据数联合分布的特征函数公式与Hafnian主定理，提出多量子比特BEC阱原子玻色采样模型，证明其多体涨落计算为#P难，可用于展示多体相互作用系统的量子优越性。