Tensor Representation of Spin States ; ; Baguette, Dorian et al in Physical Review Letters (2015), 114 We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most ... [more ▼] We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light. [less ▲] Detailed reference viewed: 32 (15 ULg)Tensor Representation of Spin States ; ; Baguette, Dorian et al in Physical Review Letters (2015), 114 We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most ... [more ▼] We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light. [less ▲] Detailed reference viewed: 32 (15 ULg)Tensor Representation of Spin States ; ; Baguette, Dorian et al in Physical Review Letters (2015), 114 We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most ... [more ▼] We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light. [less ▲] Detailed reference viewed: 32 (15 ULg); ; Baguette, Dorian et al in Physical Review Letters (2015), 114 Two Scenarios for Quantum Multifractality Breakdown Dubertrand, Rémy ; ; et al in Physical Review Letters (2014), 112 We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations ... [more ▼] We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications. [less ▲] Detailed reference viewed: 19 (8 ULg)The two scenarios for quantum multifractality breakdown ; ; et al Scientific conference (2014, June) Several types of physical systems are characterized by quantum wave func- tions with multifractal properties. In the quantum chaos field, they cor- respond to pseudointegrable systems, with properties ... [more ▼] Several types of physical systems are characterized by quantum wave func- tions with multifractal properties. In the quantum chaos field, they cor- respond to pseudointegrable systems, with properties intermediate between integrability and chaos. In condensed matter, they include electrons in a disordered potential at the Anderson metal-insulator transition. This multi- fractality leads to particular transport properties and appears in conjunction with specific types of spectral statistics. In parallel, progress in experimental techniques allows to observe finer and finer properties of the wavefunctions of quantum or wave systems, as well as to perform experiments with un- precedented control on the dynamics of the systems studied. In this context, this talk will discuss the robustness of multifractality in presence of footnote- size perturbations. We expose two scenarios for the breakdown of quantum multifractality under the effect of such perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three- dimensional Anderson model at the metal-insulator transition, and show that for different types of perturbation the destruction of multifractal properties always follows one of these two ways. Our results thus suggest that quantum multifractality breakdown is universal and obeys one of these two scenarios depending on the perturbation. We also discuss the experimental implica- tions. [less ▲] Detailed reference viewed: 35 (3 ULg)Robustness of quantum multifractality ; ; et al Scientific conference (2014, March) Several models where quantum wave functions display multifractal properties have been recently identified. In the quantum chaos field, they correspond to pseudointegrable systems, with properties ... [more ▼] Several models where quantum wave functions display multifractal properties have been recently identified. In the quantum chaos field, they correspond to pseudointegrable systems, with properties intermediate between integrability and chaos. In condensed matter, they include electrons in a disordered potential at the Anderson metal-insulator transition. These multifractality properties lead to particular transport properties and appear in conjunction with specific types of spectral statistics. In parallel, progress in experimental techniques allow to observe finer and finer properties of the wavefunctions of quantum or wave systems, as well as to perform experiments with unprecedented control on the dynamics of the systems studied. In this context, this talk will discuss the robustness of multifractality in presence of small perturbations. We identify two distinct processes of multifractality destruction according to the type of perturbation, and specify a range of parameters where multifractality could indeed be observed in physical systems in presence of imperfections. [less ▲] Detailed reference viewed: 31 (4 ULg)Multifractality of quantum wave functions ; ; et al Poster (2013, September) Detailed reference viewed: 25 (1 ULg)Multifractality of quantum wave functions Martin, John ; ; et al Poster (2013, March 19) We study the multifractality of individual wave packets in a periodically kicked system through a combination of numerical and analytical works. We consider a version of the mathematical Ruijsenaars ... [more ▼] We study the multifractality of individual wave packets in a periodically kicked system through a combination of numerical and analytical works. We consider a version of the mathematical Ruijsenaars-Schneider model and reinterpreted it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter [1]. We compare different methods to measure the multifractality of wave packets and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, which is different from the multifractality of eigenvectors but related to it, as is the rate of the decrease. Our results could guide the study of experimental situations where multifractality is present in quantum systems. [less ▲] Detailed reference viewed: 25 (4 ULg)Multifractality of quantum wave packets ; Martin, John ; et al in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2012), 86 We study a version of the mathematical Ruijsenaars-Schneider model and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can ... [more ▼] We study a version of the mathematical Ruijsenaars-Schneider model and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, which is different from the multifractality of eigenvectors but related to it, as is the rate of the decrease. Our results could guide the study of experimental situations where multifractality is present in quantum systems. [less ▲] Detailed reference viewed: 86 (3 ULg)Multiqubit symmetric states with a high geometric entanglement Martin, John ; ; et al Poster (2011, May 25) We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric ... [more ▼] We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement behaves asymptotically for large N. We show that much higher geometric entanglement with improved asymptotical behavior can be obtained in comparison with the highly entangled balanced Dicke states studied previously. We also derive an upper bound for the geometric measure of entanglement of symmetric states. The connection with the quantumness of a state is discussed. [less ▲] Detailed reference viewed: 42 (9 ULg)Multifractality in the kicked rotator Martin, John ; ; et al Poster (2010, July) Detailed reference viewed: 28 (9 ULg)Multifractality in quantum maps Martin, John ; ; et al Poster (2010, March) Detailed reference viewed: 11 (4 ULg)Multifractal wave functions of simple quantum maps Martin, John ; ; et al in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2010), 82 We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like ... [more ▼] We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting and wavelet methods). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, and absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects. [less ▲] Detailed reference viewed: 25 (7 ULg)Entanglement of random localized and multifractal states Martin, John ; ; Conference (2009, August) Detailed reference viewed: 6 (0 ULg)Entanglement and Localization of Wavefunctions ; ; Martin, John in Complex Phenomena in Nanoscale Systems, NATO Science for Peace and Security Series B: Physics and Biophysics, Volume . ISBN 978-90-481-3118-1. Springer Netherlands, 2009, p. 51 (2009) We review recent works that relate entanglement of random vectors to their localization properties. In particular, the linear entropy is related by a simple expression to the inverse participation ratio ... [more ▼] We review recent works that relate entanglement of random vectors to their localization properties. In particular, the linear entropy is related by a simple expression to the inverse participation ratio, while next orders of the entropy of entanglement contain information about e.g. the multifractal exponents. Numerical simulations show that these results can account for the entanglement present in wavefunctions of physical systems. [less ▲] Detailed reference viewed: 22 (0 ULg)Entanglement of localized states Martin, John ; ; Poster (2007, October) Detailed reference viewed: 4 (0 ULg)Entanglement of localized states Martin, John ; ; Conference (2007, June) Detailed reference viewed: 4 (1 ULg) |
||