Recent content by Type1civ

Graphene's Hamiltonian contains first order derivatives (from the momentum operators) which aren't invariant under simple spatial rotations. So it initially appears to me that it isn't invariant under rotation. From reading around I see that we also have to perform a rotation on the Pauli...

How is a top gate used to change electron density in 2D semi conductors? I get the principle, you are just shifting the chemical potential by some voltage so that there are more or less electrons in the specific bands. But how is it physically done? Thanks.

Does anybody know where I can find solutions to the problems in Wen's 'Quantum Field Theory of Many-Body Systems'?

Sorry I have mixed notation here I should have written my normal dotted with my stress tensor as t_{ij}n_j=0

Firstly, thank you so much for taking the time to help me, I need to get this done tonight and was worried that I had no chance of doing so. Ok, so I would just end up with: \mathbf{t}\cdot\mathbf{n}=(-1+\frac{\partial h}{\partial x_1}+\frac{\partial h}{\partial x_2})p=0 Since the components...

Thanks for the reply, The normal is just \mathbf{n}=\frac{\nabla F}{|\nabla F|} isn't it? (where F is the function of the surface) so with my function (but no time dependence) my normal vector would be: \mathbf{\hat n}=-\mathbf{\hat x_3}+\frac{\partial h}{\partial x_1}\mathbf{\hat...

Homework Statement Stuck on two similar problems: "State the normal stress boundary condition at an interface x_3-h(x_1,x_2,t)=0between an invisicid incompressible fluid and a vacuum. You may assume that the interface has a constant tension." The second question in the same but the fluid is...

Yeah, sorry! It is: x_3-h(x_1,x_2)=0 So then in this case my direction normal would be: \nabla_h=\hat x_3 -\frac{\partial h}{\partial x_1} \hat x_1 -\frac{\partial h}{\partial x_2} \hat x_2 and I can dot this with the velocity of the fluid to get zero. So that: \mathbf{u}\cdot\nabla_h=...

This is my first post so I hope this in the right place. I am fairly sure this is quite a straight forward question but I having trouble working out the details of it. "State the boundary conditions for an inviscid fluid at an impermeable fixed boundary x_3-h(x_1,x_3)=0 where we do...