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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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 ...
14
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5answers
574 views

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 ...
11
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1answer
2k views

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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3answers
2k views

How are physics and computer science getting united?

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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2answers
332 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 ...
10
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1answer
119 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 ...
9
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5answers
2k views

How useful is programming in physics?

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), ...
8
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1answer
578 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
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
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3answers
308 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 ...
7
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4answers
494 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
1k views

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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2answers
3k views

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 ...
7
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4answers
789 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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1answer
156 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 ...
7
votes
1answer
114 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 ...
7
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1answer
571 views

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 ...
7
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2answers
1k views

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
votes
2answers
303 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 ...
6
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1answer
514 views

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 ...
5
votes
3answers
2k views

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., ...
5
votes
3answers
337 views

Supergravity calculation using computer algebra system in early days

I was having a look at the original paper on supergravity by Ferrara, Freedman and van Nieuwenhuizen available here. The abstract has an interesting line saying that Added note: This term has now ...
5
votes
2answers
298 views

In condensed matter simulations, how is particle number density computed in practice?

I have been reading a recent paper. In it, the authors performed molecular dynamics (MD) simulations of parallel-plate supercapacitors, in which liquid resides between the parallel-plate electrodes. ...
5
votes
1answer
211 views

What equation describes the electrostatic potential in these circumstances?

I have a solver for Poisson's equation and it works nicely. It uses finite differences. It works in the presence of multiple dielectrics. It also solves the Poisson Boltzmann equation. That is, fixed ...
5
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3answers
234 views

Simulate a physical impact of objects made of finite, small elements

I want to simulate an impact between two bodies according to gravity, and eventually considering other forces to stick matter together. I'd like to use python to do this, but I am open to ...
5
votes
3answers
336 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 ...
5
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2answers
124 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 ...
5
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0answers
478 views

Interpretation of Stiffness Matrix and Mass Matrix in Finite Element Method

I would like to have a general interpretation of the coefficients of the stiffness matrix that appears in FEM. For instance if we are solving a linear elasticity problem and we modelize the relation ...
4
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3answers
324 views

Future Computer Performance

Moore's law has succesfully predicted up to now that integrated circuit transister density doubles every two years. However, computer performance is dependent on additional factors like architecture, ...
4
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3answers
533 views

Nanorobots. What stops us from producing them yet?

If we can already predicts accuratelly motion on molecular levels, what stops us from developing small robots to, for instance, navigate through our blood vessels looking for cancerous cells and ...
4
votes
2answers
225 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 ...
4
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1answer
438 views

Industry application of computational quantum mechanics?

I was wondering if anybody knew of an industry application of computational quantum mechanics. For example, the efficient placement of circuit elements on a PCB is in part motivated by classical FDTD ...
4
votes
2answers
799 views

Radial Schrodinger equation with inverse power law potential

Recently I read a paper about solving radial Schrodinger equation with inverse power law potential. Consider the radial Schrodinger equation(simply set $\mu=\hbar=1$): ...
4
votes
1answer
155 views

Using the monte carlo method to compute the magnetic field of a curent carrying loop

I have written a program in cpp that computes the magnetic field at a point from a current carrying loop. It uses the biot savart law and the monte carlo technique to carry out the integral. The ...
4
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2answers
1k views

On numerically solving the Schrödinger equation

I just read a paper 'A pocket calculator determination of energy eigenvalues' by J Killingbeck (1979). Link: http://iopscience.iop.org/0305-4470/10/6/001 I have some questions about section 2. Why ...
4
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1answer
309 views

Numeric method to calculate the charge distribution on a conducting surface?

If I have an arbitrary (closed?) conducting surface and a nearby charge density, is there a simple numeric way of computing the induced charge distribution on the surface?
4
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1answer
129 views

How to find positions of $n$ masses in Newton mechanics?

I ran into a problem while doing research. The problem can be described as: consider the original $n$-body problem, and if we fix the position of them(unknowns), no interaction among them, they don't ...
4
votes
1answer
75 views

Can computers accurately model all of the details (to the subatomic level) of macro objects in collisions?

Frequently when trying to solve cosmology questions physicists turn to computer simulations of the universe (albeit massively simplified) in order to verify or disprove their hypotheses. This got me ...
3
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3answers
303 views

Can a wavefunction be solved to any arbitrary precision, given enough computer time?

I learned that the wavefunction for the hydrogen atom can be solved analytically (we did the derivation in class), but that for more complicated atoms it is "impossible" to solve and that only ...
3
votes
2answers
641 views

Can cellular automata be reconcilied with quantum mechanics?

CAs are deterministic representations of the universe, which, according to the Bell's inequality are not entirely accurate. Cells interact "locally" (only with the closest neighbours), while quantum ...
3
votes
1answer
96 views

buiding circuits from color superconductors

caveat: the sort of exotic matter engineering in here is currently beyond the reach of our technology, but, that having been said: Has their been any research on building models of these sorts of ...
3
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2answers
334 views

Mixed conductive and convective heat transfer

I want to make a finite element analysis of a cold airflow through warmer pipes. In particular I want to see how the pipes cool down and the air heats up, as it travels through the pipes. Wich are the ...
3
votes
1answer
151 views

What states are satisfying an entropic area law and why do they satisfy it? More specificly why do matrix product states satisfy it?

I am currently reading some papers concerning the question why the density matrix renormalization group (DMRG) method is working well for simulating one dimensional systems and bad for higher ...
3
votes
2answers
491 views

Implementing simple atom model using density functional theory (DFT)

I am trying to write computer code which will find the energy and density function for an atom with $Z$ protons and $N$ electrons. I am working in 1D for simplicity and would like to make the overall ...
3
votes
2answers
431 views

Can I use imaginary time propagation for many-body problems?

There are various ways to numerically find the ground state energy and wavefunction of a many-body Hamiltonian. You can diagonalize the Hamiltonian and pick out the lowest eigenstate, or you use ...
3
votes
3answers
410 views

Adding rotation to internal coordinates

I'm optimizing the geometry of a system composed of several interacting masses (a molecule). The energy of the system depends on the relative position of the masses, and all velocities are zero. In a ...
3
votes
1answer
422 views

Numerical computation of the Rayleigh-Lamb curves

The Rayleigh-Lamb equations: $$\frac{\tan (pd)}{\tan (qd)}=-\left[\frac{4k^2pq}{\left(k^2-q^2\right)^2}\right]^{\pm 1}$$ (two equations, one with the +1 exponent and the other with the -1 exponent) ...
3
votes
1answer
114 views

Looking for a good introductory-level review of pseudopotential methods

I'm looking for a good introductory-level review of pseudopotential methods. In particular, I'd like to understand how the self-consistent pseudopotential methods work.
3
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1answer
116 views

confusion in discrete transform to solve kronig penney matrix equation in fourier space

I have a periodic potential $$V(x) =\sum_{K}e^{iKx}V_{K} =\sum_{n}e^{\iota2\pi nx/a}V_{n} $$ where $K =\frac{2\pi n}a$ is the reciprocal lattice vector and $a$ is the lattice constant and $n =\pm ...
3
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1answer
116 views

How to determine predicted CP violation for a given SUSY point?

I'm currently studying at the spectra of some supersymmetric models, and would like to know whether the parameter points I'm looking at are ruled out due to excessive CP violation. I am using SPheno, ...