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3
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1answer
62 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 + ...
1
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0answers
21 views

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?
2
votes
1answer
66 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 ...
1
vote
1answer
49 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} ...
0
votes
1answer
19 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 ...
0
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3answers
67 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 ...
1
vote
0answers
46 views

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 ...
1
vote
0answers
34 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 ...
1
vote
2answers
39 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 ...
1
vote
0answers
66 views

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 ...
2
votes
1answer
76 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 ...
0
votes
1answer
39 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 ...
0
votes
0answers
49 views

Mean free time vs relaxation time

What is the difference in meaning between relaxation time and mean free time of a Brownian particle in a medium? In this case, we will have mean free time and relaxation time of the medium particles ...
0
votes
1answer
124 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 ...
0
votes
1answer
35 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 ...
2
votes
2answers
57 views

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 ...
2
votes
1answer
145 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 ...
1
vote
0answers
28 views

Floating subject on a surface of water

If We put a small floating object (penoplast granule) on a surface of water it performs spiral like movements and eventually sticks to a side of a vial. What physical forces are involved? I'm ...
4
votes
1answer
401 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 ...
1
vote
0answers
66 views

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 ...
3
votes
1answer
111 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 ...
0
votes
0answers
51 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 ...
11
votes
2answers
370 views

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 ...
1
vote
1answer
61 views

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, ...
0
votes
2answers
84 views

Simulating diffusion from bulk to individual particles

I have a 2 compartment simulation. The first compartment simulates reactions using ODEs. The second compartment uses Brownian motion. I want to be able to have molecules from the ODE compartment ...
0
votes
1answer
67 views

Second law of thermodynamics and motion

The second law of thermodynamics states that the entropy of an isolated system never decreases, because isolated systems spontaneously evolve toward thermodynamic equilibrium—the state of ...
5
votes
2answers
142 views

Counting of brownian particles: Point Process

Imagine a point process defined by the passage time of purely brownian particles through a given point (in 1D), line (2D) or plane (3D). I'm interested in the variance of the counts (number of ...
1
vote
1answer
204 views

Quantum randomness and brownian motion in biological systems, e.g., fertilization

I am looking for examples of physical indeterminacy impacting the macroscopic world. By physical indeterminacy, I mean physical sources of randomness such as quantum indeterminacy or brownian motion. ...
-1
votes
1answer
96 views

Virtual Particles and Quantum Brownian Motion

Does the frequency of virtual particles (creation/annihilation) match with nucleus random paths - known as Quantum Brownian Motion?
1
vote
1answer
503 views

Autocorrelation and Power density spectrum : Continuous Markov Process

I've been reading through the paper from Gillespie on Brownian motion and Johnson Noise (DOI, PDF). He considers $X_s(t)$, a zero-mean stochastic variable, that is stationary in the sense that all of ...
2
votes
1answer
124 views

Integral related to particle diffusion

In the context of particle diffusion, I am trying to understand the equations that describe Brownian motion as a macroscopic process. Assume $N(x,t)$ is a number concentration and $D$ is a diffusion ...
1
vote
2answers
97 views

on Brownian motors

From this review on Brownian motors, there is such a statement without detailed explanation: (I think this statement is general enough so that one does not need to read the article) "Apart from ...
3
votes
0answers
145 views

Impact of the noise distribution on Geometric Brownian motion

I have a problem which includes geometric Brownian motion, with either normally distributed or power-law-distributed noise, and I'm asking for some explanations and if possible references to read in ...
2
votes
1answer
309 views

Is Brownian motion a deterministic system?

Is Brownian motion a deterministic system? I.e the motion of all particles are completely determined or is there an innate indeterminism like quantum systems?
2
votes
0answers
113 views

Expected and maximum likelihood estimate positions of particle in a box

From Causal Entropic Forces, A. D. Wissner-Grossand C. E. Freer, Physical Review Letters Regarding a particle exhibiting brownian motion within a box... ...In contrast, if the particle had merely ...
2
votes
2answers
187 views

Diffusion of probability amplitudes

Let's say I have a probability amplitude $\psi:\Sigma\rightarrow\mathbb{C}$ for some domain $\Sigma$ (so, $\psi$ satisfies $\int_\Sigma |\psi|^2=1$). Is there a way to use $\psi$ as initial ...
0
votes
0answers
155 views

direct conversion of heat to electric potential / current - are there theories that contradict the 'Kelvin Statement'?

In particular, William Thomson (Kelvin) appeared to be wrong about key things in physics (initially X-rays, aether, even aviation feasibility). ...
2
votes
0answers
105 views

Randomly sampling a “well-mixed” solution of Brownian particles

I place $N$ Brownian particles in $V$ liters of solution, shake until I assume that the particles are "well-mixed", and sample and randomly sample an $S$ liter volume. What is the probability ...
3
votes
1answer
397 views

What is the return probability for Brownian motion in three dimensions?

I would like to know the probability of return to the initial point in three dimensional Brownian motion. Does someone know an expression for the diffusion constant? (Suggestions of books on this ...
2
votes
2answers
219 views

Is there an overlap between quantum dynamics and math of brownian motion?

Suppose you have dynamics of a coherent state. The state presents a normal distribution of finding the particle. Does anyone know of any attempts to connect modern advances in the probability theory ...
1
vote
1answer
149 views

SDE for particle, PDE for the density

Given a particle on the plane we can assume that it follows 2D Brownian motion. On the other hand if there is a lot of such a Brownian particles one can be interested in the evolution of the density ...
2
votes
1answer
78 views

What interpretive difference is there between defining a function with or without a differential as a postfactor?

I have thought about this and looked for answers for a long time now, but I do not have any name or label for this problem, which is the reason for the long title of this question. I have come across ...
4
votes
2answers
296 views

What does this observation of instantaneous velocity in Brownian particles mean?

I read this artice: Physicists Prove Einstein Wrong with Observation of Instantaneous Velocity in Brownian Particles “We’ve now observed the instantaneous velocity of a Brownian particle,” says ...
15
votes
5answers
5k views

Which experiments prove atomic theory?

Which experiments prove atomic theory? Sub-atomic theories: atoms have: nuclei; electrons; protons; and neutrons. That the number of electrons atoms have determines their relationship with other ...