Recent content by Opus_723

Okay, that makes sense, but I'm having trouble seeing how the two pictures connect. If I measure <p(dp/dt)> for one particle, it should be zero, and yet the motion of that particle could be well described by a Langevin equation that has a nonzero <p(dp/dt)> due to the drag term. Is it just that...

If I have a many-body Hamiltonian, and I choose a coordinate x with canonical momentum p, I can say that by the generalized equipartition theorem that <p(dH/dx)> = -<p(dp/dt)> = 0 Since p and x are distinct phase space variables, and since by the Hamiltonian equations of motion the force...

Thanks for responding! I'm actually pretty familiar with curvilinear coordinates, where you have families of surfaces. I should probably be more specific about what I'm interested in: In this case the space I am starting with is actually a 2N-dimensional Hamiltonian phase space, with positions...

Disclaimer: I am a physics student and I have very little knowledge of topology or differential geometry. I don't necessarily expect a complete answer to this question, but I haven't really found any reference that approaches what I'm trying to ask, so I'd be quite happy to simply be pointed in...

I'm trying to come up with a proof of the operator identity typically used in the Mori projector operator formalism for Generalized Langevin Equations, e^{tL} = e^{t(1-P)L}+\int_{0}^{t}dse^{(t-s)L}PLe^{s(1-P)L}, where L is the Liouville operator and P is a projection operator that projects...

Thank you. This is exactly what I needed, and in retrospect makes a lot of sense. I will note that the Kronecker delta *is* necessary in my particular problem as I have uncorrelated forces acting on different particles, but I probably didn't make that very clear. Thanks again!

Suppose I have Gaussian white noise, with the usual dirac-delta autocorrelation function, <F1(t1)F2(t2)> = s2*d(t1-t2)*D12 Where s is the standard deviation of the Gaussian, little d is the delta function, and big D is the kronecker delta. For concreteness and to keep track of units, say F...

And naturally, after puzzling over what was happening all day, I think it finally clicked about 10 seconds after posting this question, and I feel really silly. If I'm right, the appearance of that degenerate propagator is completely fine, since it corresponds to the loop in the tadpole? This...

I am studying the terms in the dual Taylor expansion of Z_{1}(J) in \phi^{3} theory, and being introduced to Feynman diagrams in the process. I thought I would try to simplify one of the terms in the expansion so that, after taking derivatives of all the sources, I ended up with integrals that...

If it's just defined that way for any state, I haven't seen a text explicitly state that. In Shankar, for example, the closest I can find in the postulates is this: "If the particle is in a state |ψ>, measurement of the variable (corresponding to) Ω will yield one of the eigenvalues ω with...

Okay, for definiteness, say that |ψ> is a wave packet with some spread of momentum. Then, for example, <x|eiHt/ħ|ψ> makes sense to me as the probability amplitude of finding the particle at position x after a time t, during which the wave packet propagated, dispersed, etc. This makes sense to me...

I have a question about probability amplitudes to go from one state to another. I think it'll be clearest if I start with the case that I understand. Suppose I start in some initial state |ψ>, and I let it evolve over time t to some state eiHt/ħ|ψ>. Now, if I want to know the probability that...

I am going through Shankar's treatment of Feynman Integrals right now, and I have one lingering doubt that I can't quite seem to work out. I was pretty happy with the idea of discretizing time, then doing independent sums over xi at each time. But Shankar simply says that we can consider the...

I'm afraid my Google-fu is failing me. Try as I might, I can only find very basic descriptions online of how RFID tags (specifically passive ones) work. I'd like to actually know what the microcontroller in the tag does, and how it creates a signal the reader can pick up and decode. For example...

I've heard a lot about different schools having stellar reputations in certain subfields of physics, and that this likely matters more for career advancement than how "highly ranked" the school is overall. My question is, as someone who isn't currently plugged into an academic community, how can...