Show simple item record

dc.contributor.advisorDemir, Durmuş Ali
dc.contributor.authorSargın, Ozan
dc.date.accessioned2014-11-17T13:58:33Z
dc.date.available2014-11-17T13:58:33Z
dc.date.issued2014
dc.identifier.urihttp://hdl.handle.net/11147/4173
dc.descriptionThesis (Master)--Izmir Institute of Technology, Physics, Izmir, 2014en_US
dc.descriptionIncludes bibliographical references (leaves 47-51)en_US
dc.descriptionText in English; Abstract: Turkish and Englishen_US
dc.descriptionviii, 57 leavesen_US
dc.description.abstractPolymer quantization is a non-standard and exotic representation of the canonical commutation relations which is introduced in the context of loop quantum gravity to investigate the low energy limit of this non-perturbative quantization of gravity. It is one of the representations of the Weyl-Heisenberg algebra which is inequivalent to the standard Schr¨odinger representation. Since this representation is inequivalent to Schr¨odinger mechanics, by Stone-von Neuman uniqueness theorem there should not be a one to one correspondence between the operators of the two representations. It turns out that, one can not define the position and momentum operators simultaneously in this construction. In this work, we use the standard position operator and a second operator which is the analog of ^p. To define an operator similar to the momentum operator ^p, one needs to use a regularization length scale which can not be removed and stays as a free parameter in the theory. This free parameter is interpreted to descend from the fundamental discreteness of space in loop quantum gravity. As another application of the polymer quantization scheme, in this work we investigate the one dimensional quantum mechanical tunneling phenomenon from the perspective of polymer representation of a non-relativistic point particle, derive the transmission and reflection coefficients and show that they add up to one which is the requirement of probability conservation. Since any tunneling phenomenon inevitably evokes a tunneling time we attempt an analytical calculation of tunneling times by defining an operator well suited in discrete spatial geometry. We expand our time expression in a Maclaurin series around zero polymer length scale and arrive at results which hint at appearance of the Quantum Zeno Effect in polymer framework. Quantum Zeno effect is the inhibition of a quantum system from making a transition from an initial state to a final state. And in summary, as a result of our work we can say that discretization of space leads to the Quantum Zeno effect.en_US
dc.language.isoengen_US
dc.publisherIzmir Institute of Technologyen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectQuantum Zeno effecten_US
dc.subjectPolymer quantizationen_US
dc.subject.lcshTunneling (Physics)en_US
dc.titleTunneling in polymer quantization and quantum zeno effecten_US
dc.title.alternativePolimer kuantizasyonunda tünelleme ve kauntum zeno etkisien_US
dc.typemasterThesisen_US
dc.contributor.authorIDTR160242en_US
dc.contributor.departmentIzmir Institute of Technology. Physicsen_US
dc.relation.publicationcategoryTezen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record