Timeline for Independent boson model with an arbitrary finite-dimensional impurity
Current License: CC BY-SA 3.0
6 events
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| Jun 3, 2015 at 17:36 | comment | added | Mark Mitchison | Actually the Hamiltonian $\hat{n}\hat{x}$ describes, for example, the radiation pressure force in cavity optomechanics. This was precisely the system in which I was originally interested, before being distracted by this multi-mode problem. In the single-mode case, I expect that the unboundedness is probably remedied by non-linearities of the opto-mechanical oscillator (i.e. the $b$ mode in your notation) when the displacements are large. | |
| May 24, 2015 at 20:52 | comment | added | Emilio Pisanty | Fair enough ;). I guess adding a term $C(\hat n)^2$ to the hamiltonian, with $C>g^2/\omega_b$ would probably fix it, but you're going to have an interesting time finding physical models which implement that. It's a bizarre hamiltonian in the first place - I can see why you'd want it for finite systems, but the bosonic case is just weird. A coupling of the form $\hat x\,\hat n$? No wonder it's unbounded. | |
| May 24, 2015 at 20:45 | comment | added | Mark Mitchison | Excellent answer, thanks Emilio. I guess the unboundedness of the Hamiltonian could be remedied by a sufficiently strong non-linearity in the impurity Hamiltonian. Regarding my reasons for believing the bosonic case fails, they can be summarised succinctly as "laziness". | |
| May 24, 2015 at 20:39 | comment | added | Emilio Pisanty | @MarkMitchison I'm hoping I didn't miss anything. Did you have stronger reasons to think the bosonic case fails? | |
| May 24, 2015 at 20:38 | vote | accept | Mark Mitchison | ||
| May 19, 2015 at 15:57 | history | answered | Emilio Pisanty | CC BY-SA 3.0 |