No abstract

We regularise the 3d λφ 4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent rôle. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m 2 and λ. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c = 1-model in string theory. This observation enables a conjecture about the thermodynamic limit.

We explore a new way to simulate quantum field theory, without introducing a spatial lattice. As a pilot study we apply this method to the 3d λ φ 4 model. The regularisation consists of a fuzzy sphere with radius R for the two spatial directions, plus a discrete Euclidean time. The fuzzy sphere approximates the algebra of functions of the sphere with a matrix algebra, and the scalar field is represented by a Hermitian N × N matrix at each time site. We evaluate the phase diagram, where we find a disordered phase and an ordered regime, which splits into phases of uniform and non-uniform order. We discuss the behaviour of the model in different limits of large N and R, which lead to a commutative or to a non-commutative λ φ 4 model in flat space.

We present a manifestly Spin(5) invariant construction of squashed fuzzy CP 3 as a fuzzy S 2 bundle over fuzzy S 4 . We develop the necessary projectors and exhibit the squashing in terms of the radii of the S 2 and S 4 . Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative S 4 .

Se analiza la estabilidad de algoritmos específicos de control cuántico a través de la si­mulación. Se estudian sistemas cuánticos de dos niveles manipulados por campos reso­nantes externos. Nos enfocamos en aquellos protocolos que requieren secuencias grandes de pulsos externos. Se prueba que estas técnicas son susceptibles de errores de acarreo. Inspirados por la metodología de tratamiento de señales, se consideran efectos de ruidos en implementaciones prácticas de algoritmos cuánticos para un qubit. Los resultados en­contrados están en concordancia con datos experimentales reportados.