Timeline for Decoding Fock spaces
Current License: CC BY-SA 4.0
17 events
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| Apr 12, 2020 at 6:37 | comment | added | Alangri | Sorry, in my questions and my comments; probably I am writing one thing and thinking completely about different thing. I am writing about Fock space as an object under computation, but in reality I am thinking about Fock space as a tool to do computation. So my question is wrongly phrased, instead I should write as the following:- " Is there a general known method(scheme),to decode a quantum device;if we know about its Fock space,(we have information about its spectrum topology)".I am not sure if this good question,but this summaries what I am thinking. | |
| Apr 11, 2020 at 21:52 | comment | added | Andreas Blass | I don't see any plausible way to "find" $H$ within its Fock space by giving "simpler" information then just pointing out $H$. @CarloBeenakker has shown that the vacuum state and creation operators are enough information, but they describe a lot more than just $H$. | |
| Apr 11, 2020 at 21:49 | comment | added | Andreas Blass | From a computational perspective that needs finite inputs and outputs, there's a problem because Fock spaces are often infinite-dimensional. Even if $H$ is one-dimensional (a spin-$0$ boson), the Fock space will be infinite dimensional because of the infinitely many possible occupation numbers. The only way the Fock space can be finite-dimensional is if you're dealing with fermions with a finite-dimensional $H$. | |
| Apr 11, 2020 at 16:45 | comment | added | Alangri | @AndreasBlass, just for curiosity, what extra information we need to add to make H unique; if you know. | |
| Apr 11, 2020 at 16:42 | comment | added | Alangri | @AndreasBlass,I guess,since we are searching for H in computional-complexity context, H is a finite Hilbert space. Second, the question does not require uniqueness of H. I am not expert in any of all this. | |
| Apr 11, 2020 at 13:30 | comment | added | Andreas Blass | It seems to me that, if you are given a Fock space with its vacuum state and creation operators, then the first comment by @CarloBeenakker answers the question. If you're given only a Fock space, as an abstract Hilbert space, without a specified vacuum state and creation operators, then this is not enough information to recover the one-particle space $H$ as a subspace of Fock space. Even some non-isomorphic $H$'s can produce isomorphic Fock spaces. Example: any infinite-dimensional $H$ and any nontrivial finite-dimensional boson $H$ (i.e., use symmetric powers). | |
| Apr 11, 2020 at 12:05 | review | Close votes | |||
| Apr 19, 2020 at 3:03 | |||||
| Apr 11, 2020 at 11:43 | history | edited | Alangri | CC BY-SA 4.0 |
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| S Apr 11, 2020 at 10:38 | history | suggested | CommunityBot | CC BY-SA 4.0 |
I clarified my question more
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| Apr 11, 2020 at 10:35 | review | Suggested edits | |||
| S Apr 11, 2020 at 10:38 | |||||
| Apr 11, 2020 at 9:11 | comment | added | Alangri | I am asking how to write a Hilbert space if it is a Fock space as (the Hilbert space completion of) the direct sum of the symmetric or antisymmetric tensors in the tensor powers of a single-particle Hilbert space H. How to search for H?. | |
| Apr 11, 2020 at 9:00 | comment | added | Carlo Beenakker | I assume the Fock space is formed out of all linear combinations of states $a_{p_1}^\dagger a_{p_2}^\dagger\cdots a_{p_k}^\dagger|0\rangle$, $k=1,2,\ldots$. | |
| Apr 11, 2020 at 8:54 | comment | added | gmvh | How is your already-give Fock space supposed to be specified? | |
| Apr 11, 2020 at 8:49 | comment | added | Carlo Beenakker | I am perhaps still not quite understanding the issue: a Fock space is specified by a vacuum state $|0\rangle$ and a set of creation operators $a^\dagger_p$; the single-particle Hilbert space has basis states $a^\dagger_p|0\rangle$. | |
| Apr 11, 2020 at 8:44 | history | edited | Alangri | CC BY-SA 4.0 |
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| Apr 11, 2020 at 6:34 | history | edited | Alangri | CC BY-SA 4.0 |
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| Apr 11, 2020 at 6:07 | history | asked | Alangri | CC BY-SA 4.0 |