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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Is there any aspect of an explosion resulting from a nuclear weapon test that cannot be simulated using super computers?

This Washington Post news article states that with the advent of computer simulation of nuclear tests, live tests are no longer needed. Generally speaking there are 3 aspects of an explosion ...
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3answers
3k views

Programming in physics [closed]

How important is programming in physics? I am studying physics at university and these first years there is actually no approach (as it is understandable) to what working in physics is like. Now, I ...
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5answers
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What do theoretical physicists need from computer scientists?

I recently co-authored a paper (not online yet unfortunately) with some chemists that essentially provided answers to the question, "What do chemists need from computer scientists?" This included the ...
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5answers
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Home-made lattice calculation?

The topic of Lattice QCD or Lattice gauge theory or even Lattice field theory is quite old now. And the main reason for the interest in the topic is the ability to calculate nonperturbative stuff on a ...
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1answer
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Solving Schrödinger's equation with Crank-Nicolson method

I am trying to numerically solve Schrödinger's equation with Cayley's expansion ($\hbar=1$) $$\psi(x,t+\Delta t)=e^{-i H\Delta t}\psi(x,t)\approx\frac{1-\frac{1}{2}i H\Delta t}{1+\frac{1}{2}i H\Delta ...
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What limitations are there in measuring physical properties accurately?

In a StackOverflow answer, I attempted to explain why a 32-bit float was perfectly adequate for representing the questioner's weight measurement: Physical properties are inaccurately measured ...
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2answers
448 views

How do you simulate chiral gauge theories on a computer?

David Tong and Lubos Motl have argued that our universe can't possibly be a digital computer simulation because chiral gauge theories can't be discretized, and the Standard Model is a chiral gauge ...
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3answers
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Correct way to write the eigenvector of a diagonalized hamiltonian in second quantization

I am studying diagonalization of a quadratic bosonic Hamiltonian of the type: $$ H = \displaystyle\sum_{<i,j>} A_{ij} a_i^\dagger a_j + \frac{1}{2}\displaystyle\sum_{<i,j>} [B_{ij} a_i^\...
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5answers
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How useful is programming in physics? [closed]

I have been wondering recently how useful programming is to a physicist. It seems fairly useful (simulations are a lot cheaper than the actual thing in many cases) in some areas (say space programs), ...
11
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3answers
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How are physics and computer science getting united? [closed]

How is theoretical computer science getting united with physics? Phenomena like Quantum Computing uses Quantum Mechanics to be able to compute things, how are computers helping not just to model our ...
10
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1answer
154 views

Consideration of static atomic displacements in electronic structure calculations

I am hoping to discuss some details of electronic structure calculations. I am not an expert on this topic, so please forgive any abuse of terminology. It is my understanding that first principles ...
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4answers
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Why is the canonical ($NVT$) ensemble often used for (classical) molecular dynamics (MD) simulations?

Molecular dynamics (MD) simulation is a common approach to the (classical) many-body problem. It relies on integration of Newton's equations of motion to simulate the trajectories of many (e.g., ~1,...
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2answers
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How do I calculate the Reynolds number in multiphase flows?

I am modeling a gas flowing through a liquid. How do I calculate the Reynolds number in multiphase flows? And, at what Reynolds number should I consider the flow to be turbulent? The problem is of a ...
9
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2answers
254 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(\...
8
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2answers
447 views

Arrhenius Fit: Linear or exponential form?

I have a seemingly easy question about performing an Arrhenius fit to the equation $$y = A \times \exp \left( -\frac{E_A}{RT} \right)$$ I can either fit this in the exponential form using a non-...
8
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1answer
147 views

Minimal Extension of Wave Equation to Include Dispersion

Let's say you are modeling some process with the wave equation $\frac{1}{c^{2}}\frac{\partial^{2}\psi}{\partial t^{2}} = \nabla^{2}\psi$. You wish to improve your model by including dispersive effects,...
8
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1answer
910 views

What is the status of applying numerical analysis to QM/QFT problems

This is something I don't ever seem to hear about, except regarding QCD ("lattice QCD"). What about QED? Is numerical integration always inferior to hand-calculating Feynman diagrams in perturbation ...
8
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1answer
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Riemann invariants…Any physical interpretation?

I am really new to the CFD simulation, and started some simple algorithms recently. I then got introduced to the Riemann Invariants. Can any one provide some physical interpretation? Also, why is ...
8
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1answer
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What are the limitations of Smoothed-Particle Hydrodynamics?

I've been excited by some of the possibilities of Smoothed-Particle Hydrodynamics (SPH). I have seen some very exciting demonstrations of their use in 3D graphics, but I am wondering how well the ...
8
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1answer
2k views

What programming languages would be helpful for a physicist to know? [closed]

From the vantage point of a physicist and the kind of problems he would like a computer program to solve, what are the essential programming languages that a physicist should know. I know C++ and I ...
8
votes
3answers
464 views

Can the Metropolis-Hastings algorithm be generalized to quantum systems?

The Metropolis-Hastings algorithm is an efficient way of simulating classical ensembles using the Monte Carlo method. Is there a generalization of this algorithm to quantum systems? What I DON'T have ...
8
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0answers
500 views

Intuition for when the replica trick should work and why it works

I am a graduate student in mathematics working in probability (without a very good background in physics honestly) and I've started to see arguments based on computations derived from the replica ...
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5answers
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Why do objects in a gravity simulation experience sudden large accelerations?

I'm trying to create a simple program that simulates gravity. The idea is that I have one central sun and several planets that I can create with a swipe gesture on the screen, and I use the initial ...
7
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4answers
969 views

Church-Turing hypothesis as a fundamental law of physics

The Church-Turing hypothesis says one can not build a computing device which has more computing power (in terms of computability) than the abstract model of Turing machine. So, there is something in ...
7
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2answers
273 views

Why do we still use perturbation theory, when we have advanced numerical methods and fast computers?

If my question sounds ignorant or even insulting, I apologise. I may be completely wrong, since I'm not a theoretical physicist. So, I understand why perturbation theory was originally used in ...
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1answer
987 views

Numerical analytic continuation for Green's function

Recently, I happened to hear about the possibility of doing analytic continuation numerically. That sounds attractive for the ubiquitous $\mathrm{i}\omega_n\rightarrow\omega+\mathrm{i}0^+$ procedure, ...
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2answers
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Solving one dimensional Schrodinger equation with finite difference method

Consider the one-dimensional Schrodinger equation $$-\frac{1}{2}D^2 \psi(x)+V(x)\psi(x)=E\psi(x)$$ where $D^2=\dfrac{d^2}{dx^2},V(x)=-\dfrac{1}{|x|}$. I want to calculate the ground state energy(...
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2answers
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Physics of simple collisions

I'm building a physics simulator for a graphics course, and so far I have it implementing gravitational and Coulomb forces. I want to add collisions next, but I'm not exactly sure how to go about ...
7
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1answer
632 views

Numerical schemes, time integration algorithms and energy conservation

What does it mean when someone says a numerical scheme or a time integration algorithm is "energy conserving". How can a numerical scheme "gain" or "lose" or "conserve" energy apart from the numerical ...
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4answers
1k views

Dirac equation on general geometries?

I have a numerical method for computing solutions to the Dirac equation for a spin 1/2 particle constrained to an arbitrary surface and am interested in finding applications where the configuration ...
7
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2answers
914 views

Diifference between real time propagation and imaginary time propagation?

Suppose I want to solve Nonlinear Schrodinger equation using imaginary time propagation to get the ground state solution. I choose $t = - i t$, and then solve the equation using split step Crank ...
7
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2answers
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Should acceleration be included in state vector of a Kalman filter?

I'm developing (actually adopting existing solution) a Kalman filter to model motion of a vehicle (UAV or automobile). The state vector will include position, velocity, and, possibly, acceleration. ...
7
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1answer
231 views

Feynman's infinite amount of logic for one tiny bit of space

Watching one of Feynman's lectures, I came across something that puzzled me. What was Feynman referring to when he said the following? What goes on in no matter how tiny a region of space and no ...
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2answers
235 views

Monte-Carlo and $O(n)$ models for non-integer n

$O(n)$ lattice statistical models can be generalized to non integer values of n, starting from their (expanded and resumed in graphs) partition function: $$Z = \sum_{\text{loop configurations}} n^{\# \...
7
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3answers
362 views

Runge Kutta Method for a Lindblad Equation

I am solving a Lindblad equation for a dissipative Harmonic Oscillator. My Hamiltonian is time dependent, My Lindblad Equation can be written as \begin{equation} \frac{d\rho}{dt}=\frac{[H(t),\rho]}{i\...
6
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5answers
454 views

Resolving General relativity and Newtonian mechanics to a computer [closed]

I know this is considered an old subject long ridiculed by many as the folly of layman. But I work in the field of computer simulation, specifically in producing fully functional 3D interactive ...
6
votes
2answers
374 views

Ising model observables

Is there a formula or equation relating $\langle E\rangle$ and $\langle M\rangle$ (average spin per site) and $\langle E^2\rangle$ to temperature $T$ for the square lattice Ising model at zero ...
6
votes
2answers
452 views

Difference between Monte Carlo and Quantum Monte Carlo methods?

What are the differences between Classical Monte Carlo methods and Quantum Monte Carlo methods in condensed matter physics? If one want to study strongly correlated systems with Quantum Monte Carlo ...
6
votes
3answers
582 views

How to include random force in the simulation (Classical Molecular Dynamics)

I need to implement a random force in my code according to the fluctuation dissipation theorem. I have a Gaussian distribution function ready width average 0 and distribution 1 and I know I need to ...
6
votes
2answers
282 views

Eigenvalue problem for differential equations in QM

I have a very simple question with regard to numerical methods in physics. I want to solve the eigenvalue problem for a particle moving in an arbitrary potential. Let's take 1D to be concrete. I.e. I ...
6
votes
1answer
90 views

FCC-to-BCC phase transition in NaCl, Buckingham or Lennard-Jones potentials?

Background The transformation from B1 (face centered cubic (FCC) type) to B2 (body centered cubic (body centered cubic (BCC) type) structures is one of the best documented high pressure phase ...
6
votes
1answer
493 views

The use of Artificial Intelligence in physics resarch [closed]

I have been reading about a machine that observed a double pendulum and created equations that both described its motion and associated conservation laws. The authors claims: We have developed a ...
6
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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 ...
5
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1answer
382 views

Discretizing the Wave Equation in polar coordinates

I want to discretize the wave equation $$\frac{1}{c^2}\frac{\partial^2\psi\left(\vec{r},t\right)}{\partial t^2}=\triangle\psi\left(\vec{r},t\right)$$ in polar coordinates. I find the following ...
5
votes
1answer
60k views

How does force relate to velocity?

I had originally asked this question on math overflow and it was suggested that I ask it here. So I know that a force will change the magnitude of velocity if it is at an angle other that 90 degrees. ...
5
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1answer
66 views

Methods for handling close approaches in $N$-body simulations

In direct gravitational $N$-body simulations, what are the preferred methods for handling close approaches between bodies in order to preserve the accuracy of the evolution of the system?
5
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2answers
116 views

Is it possible to propagate a relativistic system of particles in time using Verlet?

The Verlet algorithm and its derivations are very popular methods to integrate Newton's equations of motion in time and obtain a trajectory for a system with $N$ particles. I work with classical ...