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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cause of brownian motion's indeterminacy

Is there a causal link between quantum property indeterminacy (randomness) and a complex molecule's location in space in any moment at larger scales aka brownian motion? This question is void if my ...
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Coupling constant for an object in a photon gas

I want to model a photon gas as a bath of harmonic oscillators, and examine the effects of this bath on a system which is also a harmonic oscillator. The trouble I'm having is in relating the ...
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Understanding various types of motion

In classical statistical mechanics, given a system of particles, one often goes about classifying various dynamics (or types of motion) the system may exhibit on different time scales, but studying ...
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Is Brownian motion truly random? [duplicate]

My question basically is: Is the Brownian motion truly random, in a sense that such feature can be proved/demonstrated or is it considered to be a random phenomenon simply because one cannot take into ...
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95 views

Diffusion coefficient for asymmetric (biased) random walk

I want to obtain a Fokker-Planck like equation by taking the continuous limit of a discrete asymmetric random walk. Let the probability of taking a step to the right be $p$, and the probability of ...
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Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?

Say the diffusion coefficient of the concentration of a particle in a fluid in 3-dimensions is $D_{3\textrm{d}}$. Can we estimate the diffusion coefficient of the same particle in the same fluid, in a ...
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Brownian motion moving nano/micro coils inside a magnetic field

Following experimental setup. We take copper coils which are small enough to be subject to brownian motion. We combine those coils with some other material to make them about as heavy as the liquid ...
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Relation between solvent accessibility and brownian motion

Assume one has a molecule (made of nodes) inside a solvent. If one tries to model the average effect of the interaction between the molecule and the solvent, one has two effects: 1- Friction term on ...
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117 views

Massless brownian particle Langevin equation and FDT

Given the Langevin equation of a massless brownian particle: $$ \gamma \dot{x}=\eta, $$ where $\gamma$ is the friction coefficent and $\eta$ the noise ($\langle\eta \rangle =0$ and $\langle\eta(t)\...
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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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28 views

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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1answer
122 views

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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70 views

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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1answer
45 views

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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1answer
31 views

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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76 views

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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46 views

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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147 views

Langevin Equation - Stochastic Differential Equation. What are the subtleties?

I am trying to find out the motion of a particle in 3D governed by the Langevin equation, numerically. Anyway, the Langevin equation is given by $$m \ddot{x} = -(6\pi a\nu) \dot{x} + F_b $$ where $...
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Stochastic process generating fractional diffusion

One way to generate Brownian motion is as follows: Define a waiting time probability distribution $\psi(t)$ and step length probability distribution $\lambda(x)$. Require also that $\langle \psi \...
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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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107 views

From master equation to Fokker-Planck equation

For the continuous master equation in real space and time, we have for the distribution $f(x,t)$: $$\frac{\partial f(x,t)}{\partial t}=\int_{-\infty}^{\infty}[f(x',t)W(x',x)-f(x,t)W(x,x')]\mathrm{d}x'$...
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How are smoke cells an example of Brownian motion?

I don't get how smoke cells are an example of Brownian motion.
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Expression of heat by the Brownian motion

folks. I was reading a paper from PRE and I'm not sure what's going on about the following equation. So for the system composed of two heat baths governed by Brownian motion, the entropy change of the ...
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52 views

Ewald summation without repeating one particle periodically?

I need to perform an Ewald summation for a Brownian Dynamics simulation. In the normal Ewald summation procedure, all particles in the simulation box are periodically repeated in the neighbouring ...
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288 views

What type of non-differentiable continuous paths contribute for the path integral in quantum mechanics

Consider the path integral for a 1D particle subjected to a potential $V(x)$ in imaginary time $$ \int_{x(0)=x_0}^{x(T)=x_T} [dx] \, e^{- \int_0^T d\tau \left[\frac{1}{2}\dot{x}^2 + V(x(\tau))\right]}...
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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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1answer
153 views

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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1answer
100 views

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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31 views

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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164 views

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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70 views

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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2answers
52 views

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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1answer
101 views

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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1answer
52 views

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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294 views

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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1answer
37 views

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 ...
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1answer
267 views

Langevin equations in translational and rotational direction

I want to describe the following system. A bead is connected with a tether. There is a force $\vec{F}_{up}=F_{up}\hat{y}$ that acts on the bead. The tether acts with a force on the bead, this force $...
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566 views

Is there a modern iteration of Einstein's Brownian motion theory?

I ask this question on math stackexchange but got no answer. Not sure how to move the post so I'm reposting it here. I was arguing with my friend that Brownian motion, in the sense of a pollen moving ...
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What excactly is a “fourier component of a density fluctuation”?

Light scattering texts say depending on the scattering angle, you are seeing a certain fourier component of a density fluctuation. This density fluctuation varies sinusoidally due to Brownian motion ...
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1answer
180 views

Lagrangian description of Brownian motion?

I'm interested in the existence of a Lagrangian field theory description of Bronwnian motion, does such a thing exist? Given a particle of some spin $\sigma$, which has a Lagrangian associated with ...
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65 views

Brownian motion and physical meaning

I have read Stochastic Differential Equations by Bernt Oksendal It constructs Brownian motion by Kolmogorov extension theorem by consider $p(t,x,y)=(2\pi t)^{-n/2} e^{- \frac{|x-y|^{2}}{2t}}$ But I ...
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How loud is the thermal motion of air molecules?

In other words, given a magical room with walls that produce no vibration and transmit zero vibration from the outside, and nothing on the inside except room temperature air, what would be the noise ...
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Can you equate the diffusivity constant in random walks with the one in Brownian motion (Einstein relation)?

In an unbiased random walk in one dimension, the coefficient of diffusion is $D = l^2/2\tau$, where $l$ is the size of the jump and $\tau$ is time taken for that jump. In simple Brownian motion, ...