1,720,976 research outputs found
Relevance of classical chaos in quantum mechanics: the hydrogen atom in a microwave field
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Destruction of Anderson localization by nonlinearity in kicked rotator at different effective dimensions
Full text linkWe study numerically the frequency modulated kicked nonlinear rotator with effective dimension d = 1, 2, 3, 4. We follow the time evolution of the model up to 109 kicks and determine the exponent α of subdiffusive spreading which changes from 0.35 to 0.5 when the dimension changes from d = 1 to 4. All results are obtained in a regime of relatively strong Anderson localization well below the Anderson transition point existing for d = 3, 4. We explain that this variation of the exponent is different from the usual d− dimensional Anderson models with local nonlinearity where α drops with increasing d. We also argue that the renormalization arguments proposed by Cherroret N et al (arXiv:1401.1038) are not valid for this model and the Anderson model with local nonlinearity in d = 3.Fil: Ermann, Leonardo. Comisión Nacional de Energía Atómica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Shepelyansky, D. L.. Université de Toulouse; Franci
Statistical properties of eigenvalues for an operating quantum computer with static imperfections
No full textWe investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we discuss the quantum chaos border induced by static imperfections by analyzing the statistical properties of the quantum computer eigenvalues. For small imperfection strengths the level spacing statistics is close to the case of quasi-integrable systems while above the border it is described by the random matrix theory. We have found that the border drops exponentially with the number of qubits, both in the ergodic and quasi-integrable dynamical regimes of the map characterized by a complex phase space structure. On the contrary, the regime with integrable map dynamics remains more stable against static imperfections since in this case the border drops only algebraically with the number of qubits
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