1,855 reputation
1213
bio website
location
age
visits member for 1 year, 3 months
seen 24 mins ago

Undergrad


Mar
5
comment Valley meaning explanation for foreigner
@BrandonEnright No, that's not right. Valley in this case refers to Dirac points as noted below. Why valley? Because in the most commonly analyzed example of graphene, at zero doping, all the states in the bottom Dirac cone are filled, which leaves the top Dirac cone empty. This empty Dirac cone looks like a valley, like the letter 'V', and the interesting physics comes from exciting electrons into V.
Mar
2
awarded  Nice Question
Feb
16
asked Eigenvalue problem for differential equations in QM
Feb
7
comment Finding the ground state of the toric code Hamiltonian
see socrates.berkeley.edu/~jemoore/Physics_250_files/…
Feb
2
comment Confusion regarding field operators
I fail to understand the point you're trying to make about the Green's function. It is just a matter of convention. Would it help if in the field theory context I wrote $\phi = \phi_+ + \phi_-$ (see P&S)? Obviously $\phi, \pi$ will obey different commutation relations from $\phi_+, \phi_-$, but they are related to one another. Then $\phi_+, \phi_-$ in the field theory context will be equivalent to $\phi, \phi^\dagger$ in the many-body context.
Feb
2
comment What does a $SU(2)$ doublet really mean?
@SanathDevalapurkar The isospin transformation asked in this case is not a gauge transformation, i.e. it does not vary from point to point, but is rather just a global (internal) transformation. Weak isospin on the other hand is a gauge transformation
Feb
1
comment Is the spin 1/2 rotation matrix taken to be counterclockwise?
@Hunter No, what K-boy means is that you take $e^{i \theta S_z}$ (2x2) and act on it to each 2x2 component of the 3x1 column vector $\vec{S}$. You end up with a new column vector which is 3x1 with different 2x2 components. It is fine.
Jan
30
comment A point between two charges has an electric potential of zero, but a charge placed at this point will gain kinetic energy. Why?
@ByronS The two charges (or any collection of charges) will create a potential field that permeates all space. A test charge put into this system will acquire a potential energy, due to this potential field, of strength $q V$, as measured from the potential energy at infinity, $0$.
Jan
30
revised Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
added 141 characters in body
Jan
30
comment A point between two charges has an electric potential of zero, but a charge placed at this point will gain kinetic energy. Why?
@ByronS Not quite, not the charge's location. We say that we calculate the potential due to to an electric field of a point charge at point $r$ by taking another test charge which starts all the way at infinity and then bringing it to a point $r$ infinitesimally slowly. This then just measures the potential difference between infinity and $r$ which we say is the potential of the point charge at distance $r$.
Jan
30
comment A point between two charges has an electric potential of zero, but a charge placed at this point will gain kinetic energy. Why?
@ByronS To reiterate the point. When you say 'this object has $X$ PE', you really mean 'this object has $X$ PE with respect to some special point in the system'. Teachers / books which don't state this point ought to be spanked. Usually the 'special point' is taken to be the point at infinity and the potential set to 0 there.
Jan
30
answered A point between two charges has an electric potential of zero, but a charge placed at this point will gain kinetic energy. Why?
Jan
29
comment Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
(cont.) speedometer. But not all cars (read: models) have speedometers that can be found easily or at all, which is why we have to resort to estimating the speed by looking at the distance/time between the trees (read: perturbation theory). The 1D transverse Ising model is special in that it is an exactly solvable model.
Jan
29
comment Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
(cont.) walls etc.) BUT! That's a separate approach from the JW transformation altogether. To draw an analogy, let's say you are in a car and you want to find out the speed at which you are moving. You have an exact solution: simply look at the speedometer. But there's an approximate way to do it: take your stop watch, measure the time between trees you pass on your way, estimate the distance of your trees, to find your approximate speed. But why do that when you can just look at your speedometer??? For the case of the transverse Ising model, the JW transformation very nicely gives you a
Jan
29
comment Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
(cont.) Translating the first excited state in terms of the spin language will be a pain but you just follow the same recipe i outlined in my answer. This holds even at $h=1$, criticality. Please try to get this point!! The perturbation theory you are talking about is the approach when you start from either limit $h = 0$ or $h = \infty$ and try to work towards $h=1$. And what you mean by the 'vacuum-state becomes highly mixed with excited states' is that the vacuum state in one of those limits (all spins right for e.g.) gets mixed with the excited states of the corresponding limits (domain
Jan
29
comment Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
@VanillaSpinIce As far as getting the ground state and excited states (and in fact the entire Hilbert space) is concerned, the Jordan Wigner transformation gives you an EXACT result. That's what it means to SOLVE the model exactly. There is no need to resort to perturbation theory. Once again, for ANY $h$, the ground state in the fermion language is $|0\rangle$, while the first excited state is $a_0^\dagger |0\rangle$. That's because the dispersion relation has a minimum at 0 and so putting a fermion at $k=0$ gives the lowest excitation above $|0\rangle$.
Jan
29
comment Linear Operators and their representations
@user35952 The existence of a basis for a vector space requires the axiom of choice! proofwiki.org/wiki/Vector_Space_has_Basis
Jan
29
revised Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
added 2444 characters in body
Jan
29
comment Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
@VanillaSpinIce Check out this set of notes: michaelnielsen.org/blog/archive/notes/… equations 31-34 where the JW transformation and its inverse are presented. I have also updated my answer to address your second question.
Jan
28
answered Interpretation of the 1D transverve field Ising model vacuum state in a spin-language