Subdiscipline of theoretical physics which consists in the study of physics problems using numerical algorithms. PLEASE NOTE that questions about computational methods and/or programming are OFF-TOPIC on Physics.SE.

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9
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2answers
250 views

In a Monte Carlo NVT simulation How do I determine equilibration

I'm running an NVT (constant number of particles, volume and temperature) Monte Carlo simulation (Metropolis algorithm) of particles in two dimensions interacting via Lennard-Jonse potential ($U = 4(\...
1
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0answers
29 views

How to plot numerically the wave functions according to the Hamiltonian?

It is often difficult to analytically solve the Schrodinger equation, and so we need to obtain a solution numerically. An example plot is shown below. Here, the wave functions for a three junction ...
-1
votes
0answers
46 views

Plotting a Function [on hold]

I have the following result: $$ n_z(t) = 1 - 8 \sum_{k = 0}^{\infty} |g_{k}|^{2} \frac{\sin^2 \Big (\frac{(w_k - w_{0})t}{2} \Big)}{(w_k - w_{0})^2} $$ I want to figure out the dependence ...
-1
votes
0answers
38 views

Does modern science discussed the concept of knowledge and the process of gaining it? [on hold]

I though of an idea is some extrapolation of the law of conservation of energy, and the second law of thermodynamics. It may come a bit philosophical, and I'm really interested if there is any field ...
1
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0answers
36 views

What is the best order of learning mathematics before start Monte Carlo Methods for Physics simulation? [on hold]

I doing medical physics masters and hope to start my research in Monte Carlo methods to simulate some particle interaction and hence to calculate some unknown physical quantities ( Stopping power and ...
1
vote
1answer
251 views

Position based dynamics constraint scaling factor

Reading through Müller et al., Position Based Dynamics, 2007 I got lost when passing from equation (5) $$\Delta p = \frac{C(p)}{|\nabla_pC(p)|^2}\nabla_pC(p)$$ to equation (6) (and applying the ...
0
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0answers
24 views

Mathematica code for self-consistent field loop in Hartree-Fock method

I want to write a Mathematica code for Hartree-Fock treatment of helium (or hydrogen molecule-> namely two electrons systems) , but I don't know how to write a loop for self consistent field procedure....
5
votes
1answer
313 views

Exact diagonalization to resolve ground state degeneracies

I am studying a perturbed Toric Code model that is not analytically solvable. On a torus the ground state degeneracy of the unperturbed model is 4. Once we turn on the perturbation there is a change ...
2
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0answers
52 views

Efficient Method for Multiplying Angular Momentum Operators

I'm doing a calculation that involves canonical symmetrization of angular momentum. For example: $H_{\text{classical}} = J_x J_y \rightarrow \hat{H}_{\text{quantum}} = \frac{1}{2}(\hat{J_x}\cdot \...
-3
votes
0answers
14 views

bounds_z() missing 2 required positional arguments: 'x' and 'y' [closed]

I need to calculate the gravitational potential along the journey through the center of the earth, here is the code: but I get this error: TypeError: bounds_z() missing 2 required positional ...
4
votes
1answer
54 views

Finding $\pm 2 \pi$ defects in 2-D lattice nematic simulation

I'm working on a Monte Carlo simulation of a two-dimensional nematic system (XY-like model with even-order Legendre polynomial interactions, such that the director angle $\theta$ obeys $\theta \equiv \...
1
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0answers
14 views

Modelling a flow due to an oscillating hemisphere?

Say I have a long cylinder filled with air, closed at one end and open at the other. Now say I place a compressible hemisphere at the closed end and make it oscillate (compression and expansion of the ...
0
votes
0answers
31 views

Friedmann Equations on MATLAB [closed]

i'm trying to resolve the Friedmann equations on MATLAB. If you don't know it, they have the form: \begin{eqnarray} \frac{da}{dt}= a\sqrt{\frac{8\pi}{3}G\rho}-\sqrt{k} \\ \frac{d\rho}{dt}=-3\frac{da}{...
0
votes
1answer
41 views

Lattice QFT: Non-homogenous lattice spacing

I am interested why we fix the lattice spacing, $a$ to be homogenous in all dimensions. After a Wick rotation, $a=i \epsilon$ where $\epsilon=t_{i+1} - t_{i}$ and with euclidean time given by $\tau = ...
0
votes
0answers
37 views

C libraries for Solid State Physics

During last year I've attended courses of solid state physics, and I studied methods for bands structure calculations in the Hartree Fock framework. However, I know only theoretical aspects of these ...
3
votes
0answers
50 views

Simulation of plasma in tokamak

I am reading some papers on numerical algorithms for simulation of plasma in the context of nuclear fusion in a tokamak. I am getting a little lost as there is a huge number of references, and it is ...
0
votes
0answers
36 views

“Instantaneous” time stepping with time dependent Hamiltonian Schrodinger equation

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ I know that the "instantaneous" solution of this equation is $$\psi(t+dt) = e^{-\frac{i}{...
0
votes
0answers
38 views

How to make an equal flow rate in 4 glass tubes with different inner diameters?

I would like to ask a question regarding a flow rate project I've been working on that required pneumatic software to solve. Unfortunately, I don't have the software, and I don't know how to control ...
0
votes
2answers
276 views

Modelling multiple heat sources?

I am working on a project to model heat transfer in a data center. I have basic models for a one dimensional heat transfer using conduction and convection. Such as, taking a server and modelling the ...
3
votes
0answers
28 views

The definition of fidelity for fermion

The definition of fidelity for two mixed ensembles is $F=Tr\sqrt{\sqrt{\rho_1}\rho_2\sqrt{\rho_1}}$. Now I came across a problem in numerical calculation, Systems A,B are identical, but attached to ...
0
votes
1answer
116 views

Is there any way to find difference between two same sounds of different people?

I am trying to understand and find a way to distinguish two same sounds of different people by some physics formula, so could you guys help me? OK I'll try to explain my question in this way that, ...
0
votes
0answers
28 views

Finding the initial state in the power method for Hamiltonian diagonalization

In section III of the lecture note Chapter 1: Exact Diagonalization, Weimer has described the Power method for Hamiltonian diagonalization. The process requires the choice of an random initial state ...
4
votes
1answer
73 views

Finding explicit unimodular transformations for Chern-Simons K-matrices

An invertible, symmetric matrix with integer entries, $K$, that encodes the braiding and statistics of an Abelian topologically ordered state, is equivalent to another such matrix, $K'$, if there ...
0
votes
0answers
30 views

Heliocentric Cartesian position of moons

I have a working Kepler orbit system that is GPU accelerated to allow precision, speed and parallelism and more importantly allow as many factors as possible in calculation. For various reasons I ...
0
votes
4answers
150 views

Schrodinger equation for time-dependent Hamiltonian?

Can I write a Schrodinger equation for time-dependent Hamiltonian like this: $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t)$$ and then perform Euler integration like this: $$\psi(t+\Delta t) = (1-\frac{...
0
votes
0answers
89 views

Why does the method below work?

Please explain why this method works. I get this idea when try to solve adiabatic gas expansion by using numerical method. The analytic/exact solution for the expansion will be $PV^\gamma$=constant. ...
0
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0answers
27 views

Implementing fixed-temperature, solid-wall boundary conditions

I wish to simulate the behaviour of a fluid along one dimension, where the right boundary is transmissive and the left boundary is a solid wall at a fixed temperature. Temperature is not one of my ...
1
vote
1answer
115 views

Molecular dynamics and detailed balance

In developing methods to perform Monte Carlo simulations one sufficient condition to preserve the stationarity of the target probability distribution is to impose detailed balance i.e. [Gardiner page ...
0
votes
2answers
86 views

Molecular Dynamics simulation question

In molecular dynamics simulations you apply and solve Newton’s equations of motion for a set of atoms to obtain real dynamical information on how individual atomic positions change as a function of ...
-3
votes
1answer
30 views

Data transmission in optical fibers

Im reading though my Network Architecture lecture notes and it states optical fibers need a repeater every >10km. Repeaters are used to amplify digital signals but the notes do not explain or state ...
1
vote
1answer
308 views

Determing Velocity of Moons

I have a question that I believe is relatively easy to answer, I am working on an $N$-body simulation of a fictional star system and am having trouble finding the velocity of moons so that they will ...
1
vote
2answers
67 views

Which timestep should I use for a $N$-body simulation of the Solar system?

I am trying to implement a $N$-body simulation of the Solar system and I am stuck on the issue of the simulation timestep size. At first I would like to use a simple Euler stepping scheme. Knowing ...
6
votes
1answer
76 views

What is the BG Equation?

About 45 years ago or so I was a Physics department staff computer programmer when I was a physics major undergrad. I worked with a professor doing research on nuclear shell models -- he was ...
3
votes
0answers
40 views

How are boundary consitions implemented correctly in time dependent hydrodynamics?

I posted this question more than one year ago and got an answer recently. This answer looks good to me, but indicates that something is wrong in my original approach to the problem. Can someone tell ...
3
votes
2answers
128 views

Numerical Tools to find Braiding Statistics of Quasiparticles

While certain classes of systems that exhibit topological order can be solved exactly (such as the Toric Code, Abelian FQH Edges, etc.) there also exist systems (think of perturbed versions of the ...
3
votes
1answer
60 views

Collision between a “spring” and a particle

I am currently attempting to create a simple 2D physics engine, and I just need to know how to solve a certain collision. I have particles, and between any two particles, springs can be connected. ...
1
vote
1answer
141 views

How does the Lennard Jones Potential changes for interaction between particles of different sizes?

I am interested in incorporating a Lennard-Jones potential in a simulation. When the interaction only involves the same type of particle, with same characteristics, we can use reduced units, scaling ...
0
votes
1answer
216 views

Tight binding Hamiltonian for 2D finite dimensional lattice and nanowire

The Hamiltonian of a 1D lattice having finite $N$ atoms, (if we consider one basis per atom) is given by the following $N\times N$ matrix- Here $E$ is the onsite energy and $t$ is the hopping ...
0
votes
0answers
36 views

How to calculate the string order parameter (for Haldane phase) in density matrix renormalization group?

The ground state of the spin-1 chain is the Haldane phase, which is known to be a symmetry protected topological phase and cannot be detected by conventional order parameter (beyond the Landau-...
0
votes
0answers
26 views

How Periodic Boundary Condition (PBC) is related to Band Structure of Quantum Dot?

I am reading about relationship between different lattices and their band structures.I have few questions about them: Q 1. Is is possible to find out band structure of a quantum dot (which is a ...
0
votes
1answer
112 views

Using the Fourier transform to find the natural frequencies of coupled oscillators

How can I find the natural frequencies of a system consisting of a pair of coupled oscillators using Fourier transforms? The System consists of two masses and three springs. One of the springs ...
1
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0answers
21 views

Master curve of the 3D Ising model

I am currently doing some grand canonical Monte Carlo simulations for LJ particles and my professor has asked me to map the normalized probability distribution of density on to a master curve of the ...
0
votes
0answers
25 views

Mixed Neumann/Dirichlet BCs in Poisson-Schrodinger self-consistent solver

I'm currently in the process of writing a self-consistent Schrodinger-Poisson solver for a device heterstructure (High Mobility Electron Transistor). I am having a few difficulties however. It seems ...
0
votes
1answer
80 views

Finite Difference Method (FDM) solution to heat equation in material having two different conductivity

I am not from a mechanical engineering background and I have not taken any courses in PDE so this may seem trivial for many. and I am writing a Matlab code with the objective to solve for the ...
0
votes
0answers
12 views

Computing the dynamics with a bilateral constraint in position

Let's says I have a dynamical system of generalized coordinates $x$, subject to a bilateral constraint $g(x(t),t)=x_1(t)-d(t)=0$ where $d$ is a prescribed displacement. I am looking for the ...
0
votes
1answer
40 views

Laser resonator modes

For a resonator, plot the intensity as a function of time for (i) when the modes have identical phases, and (ii) when the modes have random phases. Attempt Here is the equation for intensity (p. ...