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| Author(s): |
Andrey Gomes Martins
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Física (IF/SBI) |
| Defense date: | 2006-08-11 |
| Examining board members: |
Paulo Teotonio Sobrinho;
Eliezer Batista;
Maria Carolina Nemes;
Adilson Jose da Silva;
Daniel Augusto Turolla Vanzella
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| Advisor: | Paulo Teotonio Sobrinho |
| Abstract | |
We study the nonrelativistic Quantum Mechanics of physical systems characterized F(Q) X \"A IND.\"teta\"\"(R X \"S POT.1\"), by the presence of an extra degree of freedom which does not commute with the time coordinate. In the language of Noncommutative Geometry, we deal with systems described by an algebra of the form F(Q) X \"A IND.\"teta\"\"(R X \"S POT.1\"),, where F(Q) is the algebra of functions over the usual con¯guration space \"Q\" e \"A IND.\"teta\"\"(R X\"S POT.1\") is a deformation of F(R X \"S POT.1\"), known as noncommutative cylinder. From a geometric viewpoint, the generators of the noncommutative cylinder correspond to the time coordinate and to an extra compact spatial coordinate, just like in Kaluza-Klein theories. We show that because of the noncommutativity between the time coordinate and the extra degree of freedom, the time evolution of systems described by F(Q) X \"A_t(R X S 1) is discretized. We develop the scattering theory for such systems, and verify the presence of a new e®ect: transitions from an in state with energy \"E IND.\"alfa\"\" and an out state with energy \"E IND.\"beta\"\" (diferente de \"E IND.\"alfa\"\") are now allowed, in contrast to the usual case. In fact, transitions take place whenever \"E IND.\"beta\" -\" E IND.\"alfa\" = 2\"pi\"/\"teta\"n,, with n \'PERTENCE A\'. The consequences of this result are investigated in the case of a one-dimensional delta barrier. Our analysis is based on the Born approximation for the transition matrix. (AU) | |