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location United Kingdom
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visits member for 2 years, 10 months
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Currently doing a PhD in Controlled Quantum Dynamics at Imperial College and the University of Oxford.


Aug
24
comment Pair Production in Entangled Photons
@Jim Are you sure it's correct to say that the entanglement is "cancelled"? I would imagine that if the photons were entangled in momentum, for example, then the momentum of the remaining photon would still be correlated with the centre-of-mass momentum of the electron-positron pair.
Aug
20
revised Ten-ping bowling: Can a ping pong ball knock over a bowling pin?
The original title was not a typo: it was intended to be a (very bad) pun. I believe that this small humorous addition does not significantly reduce the intelligibility of the title.
Aug
15
comment What is the relationship between the Drude form and the exponential form of Ohmic spectral density?
@TanMath For open quantum systems whose dynamics are (approximately) Markovian, yes.
Aug
15
revised What is the relationship between the Drude form and the exponential form of Ohmic spectral density?
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Aug
14
comment Polarizability and the Clausius-Mossotti Relation
@baptiste OK I will try when I get some time. I remember struggling a little with the argument myself. It has been more than 5 years since I understood this paper so I am not sure how helpful I will be.
Aug
14
revised What is the relationship between the Drude form and the exponential form of Ohmic spectral density?
added 63 characters in body
Aug
14
answered What is the relationship between the Drude form and the exponential form of Ohmic spectral density?
Aug
14
revised Polarizability and the Clausius-Mossotti Relation
deleted 34 characters in body
Aug
14
comment Polarizability and the Clausius-Mossotti Relation
@baptiste You are correct, full citation added to the answer.
Aug
6
comment Plants and quantum mechanics!
@DanielSank I'm not sure there is a simple answer here, also I'm still not entirely sure what you mean by the classical limit. But it will depend on how fast the barrier heights fluctuate (e.g. is it white noise) and how far, and exactly what you mean by the classical limit. Maybe we could discuss in chat, I will be in America for a week or so starting tomorrow afternoon so it might be easier then.
Aug
6
comment Plants and quantum mechanics!
@DanielSank Oh, well here it is an electronic excitation (an exciton) hopping on a lattice of chromophores. The important environmental fluctuations then come from vibrations of the protein scaffolding.
Aug
6
comment Plants and quantum mechanics!
Not sure if that's what you were getting at!
Aug
6
comment Plants and quantum mechanics!
@DanielSank Well, my understanding is that the diffusion equation is fine for predicting mean(-square) values so long as the environmental dynamics is approximately Markovian. I am not sure if this really means that one must have many collisions, but rather that the memory time of the environment is much smaller than the mean free time. Of course, if there are not many collisions within the given time period, then each individual trajectory will display large fluctuations around the diffusion equation result. Then the diffusion eqn. result only applies to averages over many trajectories.
Jul
28
comment Is Hamiltonian a differential operator in second quantization?
@Minethlos Yes but you only determine the constants once you add both the homogeneous and particular solutions. So the relative weight of the homogeneous and particular solutions is determined by the boundary conditions or other constraints. The general solution is just that: the most general thing you can write down that solves the equation. Afraid I don't have any mathematical references. However one does frequently see Green's functions techniques used in finite-dimensional scattering problems, e.g. the Landauer-Buttiker transport formalism.
Jul
27
comment Is Hamiltonian a differential operator in second quantization?
@Minethlos Exactly the same question arises in the differential equation case. Strictly speaking you should add some undefined multiple $\alpha \lvert \phi\rangle$. The solution is then determined up to an unknown constant $\alpha$. It is never OK to just choose the prefactor ad hoc. Generally, the solution of such an equation is undetermined up to an arbitrary vector from the kernel of $(E - H_0)$. In the case of a differential equation this vector is determined by boundary conditions. For a scattering problem, this should probably be that the state is asymptotically an incoming plane wave.
Jul
27
comment Is Hamiltonian a differential operator in second quantization?
@Minethlos The homogeneous solution is just a zero eigenvector of the linear operator $(E - H_0)$. It is clear that one can always add such a zero eigenvector to the solution of $(E - H_0)\lvert \psi\rangle = V\lvert\psi\rangle$. So I don't see any need to restrict the conclusions to a statement about differential/infinite-dimensional operators.
Jul
27
comment Is Hamiltonian a differential operator in second quantization?
Note that the derivation in the linked answer does not need to make any assumptions about whether $H$ is a differential operator. Exactly the same manipulations could be performed for a finite-dimensional matrix: it is just matrix inversion, after all. In the case of an infinite-dimensional matrix the "inverse" is more frequently called the Green's function, but the principle is the same.
Jul
26
comment How is this possible that photons are absorbed?
To clarify: are you asking how it is possible that two different electrons can have exactly the same energy, so that a photon emitted by one can be absorbed by the other? The answer to this is indeed a sort of uncertainty principle argument: the photons emitted by atomic transitions do not have a perfectly sharp energy, but rather a range of energies. This is due to the finite lifetime of the atomic states which decay.
Jul
24
comment bose einstein phase transition
$\mu$ is implicitly a function of temperature. The phase transition occurs at $\mu = 0$ (for a non-interacting Bose gas).
Jul
24
comment How to Derive Atomic Hamiltonian and Cavity Hamiltonian?
You can use LaTeX style code pretty much everywhere. As far as I know \ket{} is not a standard LaTeX macro and you would need to define it yourself.