Severity: Warning
Message: file_get_contents(https://...@gmail.com&api_key=61f08fa0b96a73de8c900d749fcb997acc09&a=1): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests
Filename: helpers/my_audit_helper.php
Line Number: 176
Backtrace:
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 176
Function: file_get_contents
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 250
Function: simplexml_load_file_from_url
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 1034
Function: getPubMedXML
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3152
Function: GetPubMedArticleOutput_2016
File: /var/www/html/application/controllers/Detail.php
Line: 575
Function: pubMedSearch_Global
File: /var/www/html/application/controllers/Detail.php
Line: 489
Function: pubMedGetRelatedKeyword
File: /var/www/html/index.php
Line: 316
Function: require_once
We discuss the derivation of the electrodynamics of superconductors coupled to the electromagnetic field from a Lorentz-invariant bosonic model of Cooper pairs. Our results are obtained at zero temperature where, according to the third law of thermodynamics, the entropy of the system is zero. In the nonrelativistic limit, we obtain a Galilei-invariant superconducting system, which differs with respect to the familiar Schrödinger-like one. From this point of view, there are similarities with the Pauli equation of fermions, which is derived from the Dirac equation in the nonrelativistic limit and has a spin-magnetic field term in contrast with the Schrödinger equation. One of the peculiar effects of our model is the decay of a static electric field inside a superconductor exactly with the London penetration length. In addition, our theory predicts a modified D'Alembert equation for the massive electromagnetic field also in the case of nonrelativistic superconducting matter. We emphasize the role of the Nambu-Goldstone phase field, which is crucial to obtain the collective modes of the superconducting matter field. In the special case of a nonrelativistic neutral superfluid, we find a gapless Bogoliubov-like spectrum, while for the charged superfluid we obtain a dispersion relation that is gapped by the plasma frequency.
Download full-text PDF |
Source |
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC10813907 | PMC |
http://dx.doi.org/10.3390/e26010069 | DOI Listing |
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