Tag Info

New answers tagged

2

You can treat the friction term as a perturbation. During all the stages of the motion, the effect of the friction is always small on small time scales. So, it always looks like as if the motion exactly fits the solution of the differential equation where b is set to zero. However, over long periods of time the value of the integration constants will slowly ...


2

The name of DMRG is a bit misleading: the modern view is that it does not really have much to do with the idea of real-space renormalization (although that might be a motivation for Steve White to develop it, following the success of Wilson's numerical RG). DMRG is essentially a variational method based on matrix product state(MPS) representation of the ...


0

Your method is correct. I just followed your approach and successfully observed the localized zero modes at the end of the chain. Following is my Mathematica code. First generate a list of alternating hopping amplitudes with random fluctuation: L = 20; ts = 0.5 + Boole@EvenQ@Range[L-1] + RandomVariate[NormalDistribution[0, 0.1], L-1]; ListLinePlot@ts ...


0

Strictly speaking, a localized state is well defined only on an infinite system. Therefore, the natural idea is to change the size of the system. Localized states respond differently to the size-changing than the extended states. For example, the center-of-mass of the wave function is located at a constant distance to the edge as long as the system size is ...


1

In these modern DMRG algorithms for topological phases, braiding statistics is rarely computed directly. The reason is that it is not clear how to trap a particular anyon in the bulk, and to get braiding statistics requires a careful calculation of adiabatic non-Abelian Berry phase which is often very computationally demanding. Instead, one calculates ...


1

The equations above thus represent conservation of mass, momentum, and energy. Mass density, Flow velocity and pressure are the so-called physical variables, while mass density, momentum density and total energy density are the so-called conserved variables. So three unknowns, right? Actually, there are four variables: density, velocity, pressure ...


2

To integrate the expression over the area you need to write the area of the surface element (the ring of charge that is a distance $r$ away). If we write the position of a point on that surface in spherical coordinates (rather than (x',y',z')) then a little element of surface becomes $$dA = R \sin\theta d\theta R d\phi$$ which they stated explicitly in the ...


3

By the sounds of it you have made a mistake with the units. In fact, you should not be using SI units at all in your simulation; astronomical values in SI units vary by such huge orders of magnitude that they are often a source of floating point errors that can destroy trajectories. You should instead use the astronomical system of units. Specifically, ...


1

You can search for eigenvalues using the bisection method. Priliminaries: To get the eigenvalues from Numerov method you will need to know the wavefunction at the boundaries. Generally this would mean that you need to set the potential to infinity at the boundaries hence putting the wavefunction to zero at those points. For your potential, modify it as ...


0

Here is some documentation for Matlab's fft: https://www.google.nl/url?sa=t&source=web&rct=j&ei=d50VVcCiFumz7gbl54G4Aw&url=http://www.mathworks.com/help/matlab/ref/fft.html&ved=0CBwQFjAA&usg=AFQjCNEW3G7KD5j1-T99VPbdeCb80SHHLg Octave is supposed to be very similar.



Top 50 recent answers are included