Stochastic Shrodinger equations.

  • Thread starter Thread starter Alexey
  • Start date Start date
  • Tags Tags
    Stochastic
AI Thread Summary
The discussion focuses on the Schrodinger equation with a stochastic Gaussian delta-correlated potential that is both time-dependent and space-dependent, characterized by a zero average. Participants seek references on the average wave function and the implications of such a potential, specifically in relation to quantum Brownian motion. The potential is defined by a correlation function involving delta functions and a constant A, while the probability density follows a Gaussian distribution. The conversation highlights the challenges in finding relevant literature on this specific topic. Overall, the exploration of stochastic effects in quantum mechanics remains a complex and under-researched area.
Alexey
Messages
8
Reaction score
0
Dear frends!
Prompt please references to works in which it was considered the Schrodinger equation with stochastic (random) Gaussian delta-correlated potential which
time-dependent and spaces-dependent and with zero average (gaussian delta-correlated noise). I am interesting what average wave function is equal.

U - potential.
<> - simbol of average.

P(F) - density of probability of existence of size F.

Delta-correlated potential which
time-dependent and spaces-dependent:
<U(x,t)U(x`,t`)>=A*delta(x-x`) *delta(t-t`)
delta - delta-function of Dirack.
A - const.

Zero average:
<U(x,t)>=0

Gaussian potential (existence of probability is distributed on Gauss law):
P(U)=C*exp(U^2/delU^2)

C - normalizing constant.
delU - root-mean-square fluctuation of U.
 
Physics news on Phys.org
Are you talking about quantum Brownian motion??
 
Originally posted by arcnets
Are you talking about quantum Brownian motion??

Yes it is.
 
Google gives some hits on "quantum Brownian motion", maybe there's what you're looking for.
 
Originally posted by arcnets
Google gives some hits on "quantum Brownian motion", maybe there's what you're looking for.

Thanck you! I find any-thing.
 

Thread 'Thinking Outside The Box Versus Knowing What’s In The Box'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Someone who shows interest in science is initially a welcome development. So are fresh ideas from unexpected quarters. In contrast, there is a scientific community that is meticulously organized down to the last detail, allowing little to no external influence. With the invention of social media and other sites on the internet competing for content, unprecedented opportunities have opened up for...
View full post »

Thread 'Bilateral and unilateral constraints'

I am going through this course on collision detection: https://siggraphcontact.github.io/ In this link is a PDF called course notes. Scrolling down to section 1.3, called constraints. In this section it is said that we can write bilateral constraints as ##\phi(\mathbf{x}) = 0## and unilateral constraints as ##\phi(\mathbf{x}) \ge 0##. I understand that, but then it says that these constraints call also be written as: $$\mathbf{J} \mathbf{u} = 0, \mathbf{J} \mathbf{u} \ge 0,$$ where...
View full post »

Similar threads

Algorithm of the numerical decision of stochastic Shrodinger equation.
Replies
1
Views
3K
A Brownian Motion (Langevin equation) correlation function
Replies
2
Views
1K
I Some notes on stochastic physics
Replies
1
Views
2K
B Showing that formulae are invariant for all values in the domain
Replies
2
Views
2K
A Karhunen–Loève theorem expansion random variables
Replies
1
Views
2K
Verify Green's Formula for a Simple DE
Replies
1
Views
1K
I To rejuvenate the plausibility of stochastic mechanics
Replies
1
Views
2K
I Stopping Time in layman's words
Replies
6
Views
2K
Expectation Value of a Stochastic Quantity
Replies
8
Views
2K
I About stochastic differential equation and probability density
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top