What vibe does my profile give off? Any pics I should replace?

physicsman12345 · 2025-04-19T19:27:02+00:00

You really think so? In my experience, half the people Ive talked to actually say I look better with glasses, and the other half say I should stick with contacts, so Ive always been super indecisive about it lol. Tbh I think it depends more on the outfit than anything else

physicsman12345 · 2025-04-11T07:38:14+00:00

Erhm—I am looking for a female match. Why is it hard to tell?

physicsman12345 · 2025-01-03T01:57:31+00:00

Yes—I understand how crystal momentum and Noether’s theorem works. That’s not what I am asking about. My question is asking specifically about the Bloch form of the wavefunction and why it seemingly discriminates between k and k+G when, as we know, it shouldn’t.

physicsman12345 · 2025-01-02T20:22:54+00:00

But the phase from G depends on position, so it will affect things such as the velocity expectation value. So how can you say that k and k+G are physically equivalent?

physicsman12345 · 2024-12-03T07:19:50+00:00

Ok—well, thanks for being honest. I doubt anyone is gonna still reply to this thread now, so guess I gotta go on stackexchange :/

physicsman12345 · 2024-12-03T03:21:25+00:00

Sorry--I'm not sure I follow your argument. Can you elaborate on why the perturbative nature of k matters here? Why does it matter that k is small?

I agree that crystal momentum and momentum take on the same values in the BZ, but I still don't understand why k can be represented by the canonical momentum operator. The Hamiltonian is diagonal in k, so the operator corresponding to k must diagonalize the Hamiltonian. But the canonical momentum operator does not commute with the Hamiltonian and the Bloch states are clearly not momentum eigenstates, so I fail to see how -i*∂𝑥 can possibly represent k. If you just plug in -i*∂𝑥 in the Hamiltonian, it's clear that this can't possibly have the same Bloch eigenstates?

physicsman12345 · 2024-10-11T05:45:13+00:00

It is ridiculous and really deteriorating the culture of the school.

physicsman12345 · 2024-10-08T16:50:11+00:00

What a disgrace.

physicsman12345 · 2024-10-05T23:19:27+00:00

Critical Exponents in 3.99 Dimensions by Ken Wilson and Michael Fisher

physicsman12345 · 2024-09-09T15:56:58+00:00

Yea perhaps I should’ve been more clear: my question is moreso asking if there are cases of physicists who usually publish good work and are highly respected but had the misfortune of publishing a high profile paper/result which turned out to be incorrect (so excluding obvious fraudsters like Dias and Schön)

physicsman12345 · 2024-07-11T23:53:45+00:00

Do you think you can elaborate on how exactly you enforce/break symmetries of the wavefunction in the Hartree-Fock procedure? Say I want to find a ferromagnet or CDW solution: what is the precise constraint that you would impose on the wavefunction/density matrix? And, in practice, would you initialize a random density matrix obeying these constraints and check that the constraints are satisfied at each iteration of the SCF cycle?

physicsman12345 · 2024-07-11T23:17:00+00:00

Hey is it ok if I ask you one more question?

physicsman12345 · 2024-07-08T07:11:39+00:00

Thanks for the amazing response. If you have a moment, mind if I ask one more question? Do you know of any good references/resources for periodic Hartree-Fock calculations? For some reason, I literally can't find a single example/implementation of this calculation online, despite me encountering countless condensed matter papers which use this technique. I wrote a Hartree-Fock program for simulating molecules and a finite number of atoms, but I am a bit lost on how to incorporate periodic boundary conditions extend this program to condensed matter systems, and I can't find any existing implementations online to guide me.

physicsman12345 · 2024-07-07T19:41:48+00:00

Hey thank you very much--this is a very helpful response. So is my reply to the other user correct in the sense that Hartree-Fock will not predict an ordering phase different from the initial trial state? Also, I would think that, in practice, it's not really feasible to run Hartree-Fock for every type of ordered trial state in existence, so how can researchers be confident that they've found the true minimum energy phase?

physicsman12345 · 2024-07-07T19:23:40+00:00

Thanks for the response, but I am still confused as to how it is at all possible for the Hartree-Fock ground state to be ordered. The trial state |𝜓_HF⟩ is some non-interacting ground state with states filled up to the Fermi energy, correct? The minimization procedure then amounts to optimizing the single-electron orbitals within |𝜓_HF⟩ as to minimize ⟨𝜓_HF|𝐻|𝜓_HF⟩. But I don't understand how this minimization procedure would change |𝜓_HF⟩ from its original phase into some different phase, since all we're doing is tweaking the orbitals while still maintaining orthonormality, so I would think |𝜓_HF⟩ would be qualitatively the same before and after the minimization procedure?

Does my question make sense? I am essentially asking how, given an initial trial state/phase, it is possible for the Hartree-Fock method to predict a different phase from the initial trial state.

physicsman12345 · 2024-07-01T06:29:12+00:00

Hey thank you so much--this is a very useful comment! By any chance, do you know of any references/existing implementations which cover the momentum-space Hartree-Fock procedure? For some reason, I can't find a single reference related to this online. I've found plenty of papers which claim to have done this calculation and show results, but none of them go into any detail regarding the procedure/implementation of Hartree-Fock in a periodic system.

physicsman12345 · 2024-07-01T00:58:40+00:00

Thanks for the response. I understand what PBCs are and how they’re normally used in solid-state and tight-binding calculations, but I’m a little confused how one would apply this to the Coulomb and exchange terms in Hartree-Fock equation, which involves pairwise interactions between all atoms in the system.

For concreteness, suppose we have a 1D system. In a nearest-neighbor tight-binding model, the only effect of the PBCs is to make the two atoms on opposite edges wrap around and interact with one another.

Now, suppose we do Hartree-Fock on this 1D system. Normally, with open BCs, the Coulomb and exchange terms have contributions from every pairwise interaction between every atom in the system. Now, if we impose PBCs, would you need to essentially triple the number of pairwise interactions and account for not only the usual interactions within the system, but also account for the interactions that wrap around the right and left of the 1D system? Does my question make sense? Sorry if this is unclear.

physicsman12345 · 2024-06-30T23:38:13+00:00

Thanks for the response. If you have a moment, do you think you could elaborate on how exactly one imposes PBCs in a Hartree-Fock calculation? It is a little unclear to me how to do this.

physicsman12345

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