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Author  |
Andrianopoli, L.; Merino, N.; Nadal, F.; Trigiante, M. |
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Title |
General properties of the expansion methods of Lie algebras |
Type |
Journal Article |
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Year |
2013 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
46 |
Issue |
36 |
Pages |
365204 - 33pp |
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Abstract |
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also means that a new physical theory can be obtained from a known one. One of the procedures that allow us to do so is called expansion of Lie algebras, and has been recently used in different physical applications-particularly in gauge theories of gravity. Here we report on further developments of this method, required to understand in a deeper way their consequences in physical theories. We have found theorems related to the preservation of some properties of the algebras under expansions that can be used as criteria and, more specifically, as necessary conditions to know if two arbitrary Lie algebras can be related by some expansion mechanism. Formal aspects, such as the Cartan decomposition of the expanded algebras, are also discussed. Finally, an instructive example that allows us to check explicitly all our theoretical results is also provided. |
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Address |
[Andrianopoli, L.; Nadal, F.; Trigiante, M.] Politecn Torino, Dipartimento Sci Applicata & Tecnol DISAT, I-10129 Turin, Italy, Email: nelson.merino@ucv.cl |
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Iop Publishing Ltd |
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English |
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1751-8113 |
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Notes |
WOS:000323421800008 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1560 |
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Author |
Arnault, P.; Macquet, A.; Angles-Castillo, A.; Marquez-Martin, I.; Pina-Canelles, V.; Perez, A.; Di Molfetta, G.; Arrighi, P.; Debbasch, F. |
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Title |
Quantum simulation of quantum relativistic diffusion via quantum walks |
Type |
Journal Article |
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Year |
2020 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
53 |
Issue |
20 |
Pages |
205303 - 39pp |
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Keywords |
noisy quantum walks; noisy quantum systems; decoherence; Lindblad equation; quantum simulation; relativistic diffusions; telegraph equation |
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Abstract |
Two models are first presented, of a one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: the diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position. |
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Address |
[Arnault, Pablo; Angles-Castillo, Andreu; Marquez-Martin, Ivan; Pina-Canelles, Vicente; Perez, Armando; Di Molfetta, Giuseppe] Univ Valencia, Dept Fis Teor, Dr Moliner 50, Burjassot 46100, Spain, Email: pablo.arnault@ic.uv.es |
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Publisher |
Iop Publishing Ltd |
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English |
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ISSN |
1751-8113 |
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Conference |
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Notes |
WOS:000531359000001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4390 |
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Author |
Botella-Soler, V.; Castelo, J.M.; Oteo, J.A.; Ros, J. |
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Title |
Bifurcations in the Lozi map |
Type |
Journal Article |
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Year |
2011 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
44 |
Issue |
30 |
Pages |
305101 - 14pp |
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Abstract |
We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period. |
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Address |
[Botella-Soler, V; Ros, J] Univ Valencia, CSIC, Dept Fis Teor, E-46100 Valencia, Spain, Email: vicente.botella@uv.es |
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Publisher |
Iop Publishing Ltd |
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English |
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ISSN |
1751-8113 |
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Notes |
WOS:000292386000006 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
679 |
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Author |
Botella-Soler, V.; Oteo, J.A.; Ros, J.; Glendinning, P. |
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Title |
Lyapunov exponent and topological entropy plateaus in piecewise linear maps |
Type |
Journal Article |
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Year |
2013 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
46 |
Issue |
12 |
Pages |
125101 - 26pp |
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Keywords |
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Abstract |
We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory. |
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Address |
[Botella-Soler, V.] IST Austria, A-3400 Klosterneuburg, Austria, Email: vbsoler@ist.ac.at; |
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Publisher |
Iop Publishing Ltd |
Place of Publication |
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Language |
English |
Summary Language |
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Original Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1751-8113 |
ISBN |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000316058200010 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1353 |
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Author |
Caroca, R.; Kondrashuk, I.; Merino, N.; Nadal, F. |
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Title |
Bianchi spaces and their three-dimensional isometries as S-expansions of two-dimensional isometries |
Type |
Journal Article |
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Year |
2013 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
46 |
Issue |
22 |
Pages |
225201 - 24pp |
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Keywords |
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Abstract |
In this paper we show that certain three-dimensional isometry algebras, specifically those of type I, II, III and V (according to Bianchi's classification), can be obtained as expansions of the isometries in two dimensions. In particular, we use the so-called S-expansionmethod, which makes use of the finite Abelian semigroups, because it is the most general procedure known until now. Also, it is explicitly shown why it is impossible to obtain the algebras of type IV, VI-IX as expansions from the isometry algebras in two dimensions. All the results are checked with computer programs. This procedure shows that the problem of how to relate, by an expansion, two Lie algebras of different dimensions can be entirely solved. In particular, the procedure can be generalized to higher dimensions, which could be useful for diverse physical applications, as we discuss in our conclusions. |
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Address |
Univ Catolica Santisima, Dept Matemat & Fis Aplicadas, Concepcion, Chile, Email: nelson.merino@ucv.cl |
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Corporate Author |
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Thesis |
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Publisher |
Iop Publishing Ltd |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1751-8113 |
ISBN |
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Medium |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000319044900004 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1457 |
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