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The motion of a lazy Pearson walker is studied with different probability ($p$) of jump in two and three dimensions. The probability of exit ($P_e$) from a zone of radius $r_e$, is studied as a function of $r_e$ with different values of…
Nucleation phenomena commonly observed in our every day life are of fundamental, technological and societal importance in many areas, but some of their most intimate mechanisms remain however to be unravelled. Crystal nucleation, the early…
We investigate how entanglement spreads along small Bose-Hubbard chains, with only the first well initially occupied by a mesoscopic number of atoms, as the number of sites increases. For two- and three-well chains in the non-interacting…
The basic physics of nucleation in solid \hl{single-crystal} nanoparticles is revealed by a phase-field theory that includes surface energy, chemical reactions and coherency strain. In contrast to binary fluids, which form arbitrary contact…
We study the first hitting time statistics between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the…
For more than half a century, nucleons are considered to move continuously in the nuclei. Recent electron-scattering experiments indicate about 20$\sim$25\% nucleons in heavier nuclei are involved in the neutron-proton short-range…
The classical nucleation theory for homogeneous nucleation is formulated as a theory for a density fluctuation in a supersaturated gas at a given temperature. But Molecular Dynamics simulations reveal that it is small cold clusters which…
The nucleation rate derived in the classical theory contains at least one undetermined parameter, which may be expressed in terms of the Langer first-principles theory. But the uncertainties in the accounting for fluctuation modes, which…
Prediction of nucleation rates in first order phase transitions requires the knowledge of the barrier associated to the free energy profile $W$. Molecular simulations offer a direct route through $W = -kT \ln p_a$, where $k$ is Boltzmann's…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
Nucleation and growth is the dominant relaxation mechanism driving first order phase transitions. In two-dimensional at systems nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study…
We investigate quantum persistence by analyzing amplitude and phase fluctuations of the wave function governed by the time-dependent free-particle Schr\"odinger equation. The quantum system is initialized with local random uncorrelated…
Bubble-nucleation processes of a Lennard-Jones liquid are studied by molecular dynamics simulations. Waiting time, which is the lifetime of a superheated liquid, is determined for several system sizes, and the apparent finite-size effect of…
We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite…
The spontaneous formation of tiny bubbles in a liquid is at the root of the nucleation mechanism during the liquid-to-vapor transition of a metastable liquid. The smaller the bubbles the larger their probability to appear, and even for…
We consider the quantum creation of a closed universe within the Euclidean path-integral formalism. An analytical expression for the tunneling probability is derived, including both the exponential suppression and the exact Gaussian…
The buildup process of the probability density inside the quantum well of a double-barrier resonant structure is studied by considering the analytic solution of the time dependent Schr\"{o}dinger equation with the initial condition of a…
Time analysis of oscillations of a particle between wells in the one-dimensional double-well potential with infinite high outside walls, based on wave packet use and energy spectrum analysis, is presented. For the double-well potential of…
We investigate specific features in the Wigner time behavior for slow electron elastic scattering by shallow potential wells. We considered two types of potentials wells, the small changes in the parameters of which lead to arising bound…
We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial…