Timeline for Solving $T^2 = -\kappa\, \mathrm{Tr}\, (\log(e^{i T \hat{H}_0} \hat{O}) )^2$ equation
Current License: CC BY-SA 3.0
26 events
| when toggle format | what | by | license | comment | |
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| S Jul 13, 2014 at 23:26 | history | bounty ended | CommunityBot | ||
| S Jul 13, 2014 at 23:26 | history | notice removed | CommunityBot | ||
| S Jul 12, 2014 at 17:50 | history | suggested | user35458 | CC BY-SA 3.0 |
fixed title question
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| Jul 12, 2014 at 17:37 | review | Suggested edits | |||
| S Jul 12, 2014 at 17:50 | |||||
| Jul 12, 2014 at 17:06 | history | edited | Benjamin | CC BY-SA 3.0 |
edited title
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| Jul 6, 2014 at 7:21 | comment | added | Carlo Beenakker | @VítTuček --- if $H_0$ and $O$ commute, the trace depends only on the $N$ eigenvalues of each of these two matrices; once you abandon that, the eigenvectors enter as well so knowing the spectra of $H_0$ and $O$ will not suffice. | |
| Jul 6, 2014 at 0:56 | comment | added | Benjamin | Yes, I do mean that. | |
| Jul 6, 2014 at 0:49 | comment | added | user44191 | Also, when you say the square of the log, do you mean the Killing form on two copies of that log? | |
| Jul 6, 2014 at 0:37 | comment | added | user44191 | We can get rid of $\kappa$; let $T' = T/\sqrt\kappa$ and $H'_0 = H_0/\sqrt\kappa$. | |
| Jul 6, 2014 at 0:01 | comment | added | Vít Tuček | @user44191: Thanks for spotting my error. I've deleted the parenthesis. | |
| Jul 6, 2014 at 0:00 | comment | added | Vít Tuček | @CarloBeenakker: Perhaps there could be a closed form solution in terms of spectra of $H_0$ and $\widehat{O}$. Since the OP claims that he obtained some formula in the case when these two operators commute, it is probably time to investigate spectral mapping theorem in the context of functional calculus in several variables for non-commuting operators. ;) | |
| Jul 5, 2014 at 23:56 | history | edited | Vít Tuček | CC BY-SA 3.0 |
parenthesis fix
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| Jul 5, 2014 at 23:14 | comment | added | user44191 | You seem to be missing an open parenthesis. I'm guessing it's before the log? | |
| Jul 5, 2014 at 23:08 | comment | added | Carlo Beenakker | you want a closed form solution without specifying $H_0$ and $O$? not much hope for that... | |
| Jul 5, 2014 at 22:58 | comment | added | Vít Tuček | OK. That means that $T$ is a scalar. I took the liberty and edited the equation in your question. | |
| Jul 5, 2014 at 22:57 | history | edited | Vít Tuček | CC BY-SA 3.0 |
Tr -> trace
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| Jul 5, 2014 at 22:17 | comment | added | Benjamin | The $Tr$ together means the matrix trace. | |
| Jul 5, 2014 at 22:14 | comment | added | Vít Tuček | What are $r$ and $T$? | |
| S Jul 5, 2014 at 21:33 | history | bounty started | Benjamin | ||
| S Jul 5, 2014 at 21:33 | history | notice added | Benjamin | Authoritative reference needed | |
| Jun 28, 2014 at 8:28 | review | Close votes | |||
| Jul 5, 2014 at 21:40 | |||||
| Jun 27, 2014 at 16:00 | history | edited | Benjamin | CC BY-SA 3.0 |
edited body
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| May 21, 2014 at 15:26 | history | edited | Benjamin |
edited tags
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| May 21, 2014 at 12:59 | history | edited | Benjamin | CC BY-SA 3.0 |
added 7 characters in body; edited title
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| May 21, 2014 at 12:20 | history | edited | Benjamin | CC BY-SA 3.0 |
added 168 characters in body
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| May 21, 2014 at 11:39 | history | asked | Benjamin | CC BY-SA 3.0 |