Comment on ‘‘Brownian motion of two interacting particles under a square-well potential’’

1996 ◽  
Vol 53 (1) ◽  
pp. 1291-1292 ◽  
Author(s):  
V. Berdichevsky ◽  
M. Gitterman
Keyword(s):  
Brownian Motion ◽  
Interacting Particles ◽  
Square Well

A perfect probe: Resonance of underdamped scaled Brownian motion

2021 ◽  
Author(s):  
Yuhui Luo ◽  
Chunhua Zeng ◽  
Baowen Li
Keyword(s):  
Brownian Motion ◽  
Single Particle ◽  
Brownian Particle ◽  
Bistable System ◽  
Velocity Autocorrelation Function ◽  
Interacting Particles ◽  
Velocity Autocorrelation ◽  
Spectrum Density ◽  
Coupling Strengths ◽  
And Diffusion

Abstract We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function (VACF) and mean squared displacement (MSD) of a single particle, we find that for the steady state, diffusions are ballistic at short times and then become normal for most of parameter regimes. However, for certain parameter regimes, both VACF and MSD suggest that the transition between superdiffusion and subdiffusion takes place at intermediate times, and diffusion becomes normal at long times. Via the power spectrum density corresponding to the transitions, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we theoretically propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles and for identifying cancer cells or healthy ones.

STICKY SPHERES IN QUANTUM MECHANICS

1994 ◽  
Vol 06 (05a) ◽  
pp. 947-975 ◽  
Author(s):  
M. D. PENROSE ◽  
O. PENROSE ◽  
G. STELL
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Gaseous Phase ◽  
Virial Coefficient ◽  
Hard Spheres ◽  
Second Virial Coefficient ◽  
Dimensional System ◽  
3 Dimensional ◽  
Fermi Statistics ◽  
Square Well

For a 3-dimensional system of hard spheres of diameter D and mass m with an added attractive square-well two-body interaction of width a and depth ε, let BD, a denote the quantum second virial coefficient. Let BD denote the quantum second virial coefficient for hard spheres of diameter D without the added attractive interaction. We show that in the limit a → 0 at constant α: = ℰma2/(2ħ2) with α < π2/8, [Formula: see text] The result is true equally for Boltzmann, Bose and Fermi statistics. The method of proof uses the mathematics of Brownian motion. For α > π2/8, we argue that the gaseous phase disappears in the limit a → 0, so that the second virial coefficient becomes irrelevant.

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