Tagged Questions

Brownian motion is a stochastic process, continuous in space and time, used in several domains in physics. It is the motion followed by a point which velocity is a white Gaussian noise. This tag sould be used for questions concerning the properties of Brownian motion, white Gaussian noise and ...

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trying to figure out an expansion in Brownian motion derivation

In the derivation for the diffusion equation on the wikipedia article for Brownian motion, they have these equations: I can't figure out how $\rho(x+\Delta,t)$ gets expanded, though. For a Taylor ...
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Entropic forces in Brownian motion

Reading Entropic forces in Brownian motion I'm having trouble to understand how the author makes a computation. He needs to calculate the number of ways a particle that is released from the origin can ...
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Why is it so hard to explain that the Brownian Ratchet doesn't work?

The Brownian Ratchet stood up to a lot of scrutiny before it was finally shown why it would not work as a perpetual motion machine, but it seems weird to me that all of that was necessary. If the ...
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Distinction between time-local, time-homogeneous, and Markov

In the context of quantum Brownian motion, I have read people describe what's apparently the same model as "non-Markovian but local in time" while others describe it as "Markovian but time-...
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Heuristics behind Dirac delta function in Master equation for probability?

I'm reading this paper [Phys. Rev. Lett. 106, 160601 (2011)] and it studies simple diffusion where a particle stochastically resets to its initial position $x_0$ at a constant rate $r$. As you can see,...
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Particle damping at low pressures

I'm looking for references on the topic of particle damping at low pressures, where the interactions are rare enough so that collisions are discrete, and the effective damping has to be integrated in ...
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Variation in Entropy in Einstein's Brownian Motion Paper

In Einstein's Brownian motion paper, he derives a formula for the diffusion coefficient of suspended particles by assuming the system is in dynamic equilibrium and thus, for a variation $\delta x$ (...
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How to add Langevin terms to the semiclassical Bose-Hubbard model?

I would like to add Langevin terms to the Hamilton equations of motion of the semiclassical Bose-Hubbard model. Here's what I have: I start with the standard example of Brownian motion, a particle ...
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Stability of a system of Brownian particles with non-physical collision

A few months ago I wrote this simulation of a system of circles bouncing off each other. It's a two-dimensional box with elastic balls in it that bounce off each other. I came back to it and noticed ...
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Brownian motion, net displacement, and diffusion - conceptual

I'm having trouble reconciling some conceptual issues of brownian motion. Let's say we have a box with two compartments separated by a membrane. Solute is at a high concentration on one side, and at ...
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What are pre-requisites for studying Brownian Motion? [closed]

I know Classical Mechanics (Feynman Lectures of Physics), Fluid mechanics (BR Munson) and basic Thermodynamics (not the part which includes statistical mechanics). Can I study Brownian motion on this ...
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What is thermophoresis?

I read wikipedia article and I saw a bad youtube presentation on thermophoresis, however I don't have a clear insight about the subject. I assume the forces are basically Brownian molecular forces ...
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Probability of collision of brownian particles

2 Brownian particles in a volume $V$. I wish to compute the probability that a collision occurs during a time $dt$. This should be a function of $V$ and the diffusion coefficient $D$. The result ...
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In the process of Diffusion Limited Aggregation (DLA), why do the particles prefer to form something which has the shape of a tree?

In the process of Diffusion Limited Aggregation (DLA), why do the particles prefer to form something which has the shape of a tree instead of just a front line?
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White noise and Fourier transform

I try to solve a Langevin equation in the Fourier space. My understanding of the white noise in the Fourier space seems to be wrong. Suppose I have a particle with its time evolution of the position ...
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Solving for the density operator in the quantum Brownian motion master equation

I want to solve for the density operator in the quantum Brownian motion master equation, \begin{align} \begin{aligned} \frac{d\rho_S(t)}{dt}=&-\left(\frac{i}{\hbar}\right)\Big[H_S+\frac{1}{2}M\...
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What is an expression/physical law that relates high frequency thermal fluctuations to gas pressure?

When a gas is compressed the 'ideal gas law' can predict what the increase in gas temperature will be. But that's just a mean temperature, right? At a quantum level the frequency of molecular ...
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Force causing diffusion

I was curious if there was an equation describing the force acting on a particle (say, sitting in a fluid) that causes it to diffuse. If so, does it include the diffusion coefficient D? Based on ...
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Delta correlated white noise

I am studying Brownian motion, specifically Langevin equation. This equation includes a force expressed by a white noise, say $\xi(t)$. One of the hypothesis is that it is $\delta$-correlated (since ...
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Brownian Ratchet Plausibility

Alright I'm going to throw whatever reputation I have on the line here. And yes this is a serious question. Apologies for the shoddy imagery. I had a couple ideas to get the Brownian Ratchet to ...
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Particle motion characteristic

I'm making a particle motion raffling normal numbers. The normal random numbers raffled are the angles of the directions that the particle is going. The particle speed is constant. Look how this is ...
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What is a stochastic process in a physics context? [closed]

In my mind, a stochastic process is simply a "random" process, one where the outcome is informed by initial conditions but not in a deterministic way. Is this a correct definition? What are some ...
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Curvature of a particle move

I'm simulating a particle movement following a normal distribution. How this is done: My particle has a constant speed v and every step the particle move, I ...
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Randomness of submolecular phenomena

Why do models of submolecular phenomena involving randomness work? Do these phenomena appear random to other submolecular particles? For example, people can use Einstein-Smoluchowski to characterize ...
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Time for a particle undergoing brownian motion to reach a point in a volume

I was wondering how one could calculate the average time a particle needs to reach a random point in a small sphere (filled by water) with a radius of maybe $10 \mu m$. I thought of using the Stokes-...
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Will the particle reach other end?

I place a container at rest in vaccum and filled it with air (STP conditions). Suppose a moving particle(sphere of dia 2mm) is placed at one end of the container without disturbing anything, will the ...
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Why should $\langle xf_r\rangle=0$ but $\langle\dot{x}f_r\rangle\ne 0$?

All the $\langle\rangle$ in this question is the mean value theorem over a large number of experiments. Consider a Brownian particle moving in a liquid with the viscosity $\mu$. The equation of ...