Algorithm of the numerical decision of stochastic Shrodinger equation.

In summary, the conversation discusses the search for an algorithm to solve the stochastic Schrodinger equation with a causal potential that has zero average and is delta-correlated in space and time. The equation involves imaginary units, partial derivatives, and a Laplace operator, and the potential is described as delta-correlated and Gaussian distributed. The use of Quantum Monte Carlo methods, specifically Diffusion Monte Carlo, is also mentioned as a possible approach to solving this equation.
  • #1
Alexey
8
0
Prompt please where it is possible to find algorithm of the numerical decision of stochastic Shrodinger equation with casual potential having zero average and delta – correlated in space and time?

The equation:
i*a*dF/dt b*nabla*F-U*F=0

where
i - imaginary unit,
d/dt - partial differential on time,
F=F (x, t) - required complex function,
nabla - Laplas operator,
U=U (x, t)- stochastic potential.
Delta-correlated potential <U(x,t)U(x`,t`)>=A*delta(x-x`) *delta(t-t`) .
where delta - delta-function of Dirack, A – const, <> - simbol of average,
Zero average: <U(x,t)>=0
Gaussian distributed P(U)=C*exp(U^2/delU^2)
Where C, delU - constants.
 
Physics news on Phys.org
  • #2
Not sure if this is what you're looking for...

Quantum Monte Carlo methods are used to solve high dimensional integrals... In Diffusion Monte Carlo (DMC), one rewrites the Schrodinger equation in Integral form. This integral is then solved stochastically.
 

1. What is the purpose of the Algorithm of the numerical decision of stochastic Schrodinger equation?

The purpose of this algorithm is to numerically solve the stochastic Schrodinger equation, which is a mathematical model used to describe the behavior of quantum systems. The algorithm allows scientists to simulate and understand the dynamics of these systems, which can have important applications in fields such as quantum computing and quantum mechanics.

2. How does the algorithm work?

The algorithm works by discretizing the stochastic Schrodinger equation and using numerical methods to solve the resulting system of equations. It involves iteratively solving for the wave function of the system at different time steps, taking into account the effects of stochastic noise on the system's evolution.

3. What are the main challenges in implementing this algorithm?

One of the main challenges in implementing this algorithm is accurately modeling the stochastic noise in the system, which can be difficult due to its random and unpredictable nature. Another challenge is choosing appropriate numerical methods and parameters to ensure the accuracy and stability of the solution.

4. How is this algorithm different from other methods used to solve the stochastic Schrodinger equation?

This algorithm is a numerical method, meaning it uses mathematical calculations and approximations to find a solution. Other methods, such as analytical solutions or Monte Carlo simulations, may provide different types of insights but may not be as efficient for large-scale systems or may rely on simplifying assumptions.

5. What are some potential applications of this algorithm?

This algorithm has potential applications in various fields such as quantum computing, quantum mechanics, and quantum chemistry. It can be used to study the behavior of complex quantum systems, simulate quantum algorithms, and design quantum devices. It can also help improve our understanding of fundamental quantum phenomena and potentially lead to new technological advancements.

Similar threads

I Some notes on stochastic physics
    • Classical Physics
Replies
0
Views
102
A Brownian Motion (Langevin equation) correlation function
    • Classical Physics
Replies
2
Views
831
Linearization Euler's equation
    • Advanced Physics Homework Help
Replies
6
Views
274
B Showing that formulae are invariant for all values in the domain
    • Other Physics Topics
Replies
2
Views
1K
A Green's function for Stokes equation
    • Differential Equations
Replies
1
Views
2K
I On the approximate solution obtained through Euler's method
    • Differential Equations
Replies
1
Views
757
A Numerically solving a transport equation
    • Differential Equations
Replies
3
Views
1K
What is the induced magnetic force on this closed current loop?
    • Introductory Physics Homework Help
Replies
12
Views
187
Stochastic Shrodinger equations.
    • Other Physics Topics
Replies
4
Views
2K
I About stochastic differential equation and probability density
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top