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B. Georgeot

Publications and source records attributed to B. Georgeot.

At least 37 records · Page 2Linked to original sources
arXiv2010

Spectral properties of the Google matrix of the World Wide Web and other directed networks

We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure in the vicinity of the maximal eigenvalue for Google damping parameter $α$ equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to another, reflecting specific properties of the networks. We also determine specific properties of eigenstates of the Google matrix, including the PageRank. The fidelity of the PageRank is proposed as a new characterization of its stability.

cs.IR↗
arXiv2009

Entanglement and localization of wavefunctions

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.

quant-ph↗
arXiv2009

Asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars

The asteroseismology of rapidly rotating pulsating stars is hindered by our poor knowledge of the effect of the rotation on the oscillation properties. Here we present an asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars. We study the Hamiltonian dynamics of acoustic rays in uniformly rotating polytropic stars and show that the phase space structure has a mixed character, regions of chaotic trajectories coexisting with stable structures like island chains or invariant tori. In order to interpret the ray dynamics in terms of acoustic mode properties, we then use tools and concepts developed in the context of quantum physics. Accordingly, the high-frequency acoustic spectrum is a superposition of frequency subsets associated with dynamically independent phase space regions. The sub-spectra associated with stable structures are regular and can be modelled through EBK quantization methods while those associated with chaotic regions are irregular but with generic statistical properties. The results of this asymptotic analysis are successfully confronted with the properties of numerically computed high-frequency acoustic modes. The implications for the asteroseismology of rapidly rotating stars are discussed.

astro-ph.SR↗
arXiv2008

Quantum computation of multifractal exponents through the quantum wavelet transform

We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum algorithms for multifractal exponents with a polynomial gain compared to classical simulations. Numerical results indicate that a rough estimate of fractality could be obtained exponentially fast. Our findings are relevant e.g. for quantum simulations of multifractal quantum maps and of the Anderson model at the metal-insulator transition.

quant-ph↗
arXiv2008

Chaotic dynamics of a Bose-Einstein condensate coupled to a qubit

We study numerically the coupling between a qubit and a Bose-Einstein condensate (BEC) moving in a kicked optical lattice, using Gross-Pitaevskii equation. In the regime where the BEC size is smaller than the lattice period, the chaotic dynamics of the BEC is effectively controlled by the qubit state. The feedback effects of the nonlinear chaotic BEC dynamics preserve the coherence and purity of the qubit in the regime of strong BEC nonlinearity. This gives an example of an exponentially sensitive control over a macroscopic state by internal qubit states. At weak nonlinearity quantum chaos leads to rapid dynamical decoherence of the qubit. The realization of such coupled systems is within reach of current experimental techniques.

cond-mat.stat-mech↗
arXiv2008

Time reversal of Bose-Einstein condensates

Using Gross-Pitaevskii equation, we study the time reversibility of Bose-Einstein condensates (BEC) in kicked optical lattices, showing that inside the regime of quantum chaos the dynamics can be inverted from explosion to collapse. The accuracy of time reversal decreases with the increase of atom interactions inside BEC, until it is completely lost. Surprisingly, quantum chaos helps to restore time reversibility. These predictions can be tested with existing experimental setups.

cond-mat.stat-mech↗
arXiv2008

Wave chaos in rapidly rotating stars

Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens new perspectives for rapidly rotating star seismology and also provides a new and potentially observable manifestation of wave chaos in a large scale natural system.

astro-ph↗
arXiv2008

Quantum computing of semiclassical formulas

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.

quant-ph↗
arXiv2007

Loschmidt cooling by time reversal of atomic matter waves

We propose an experimental scheme which allows to realize approximate time reversal of matter waves for ultracold atoms in the regime of quantum chaos. We show that a significant fraction of the atoms return back to their original state, being at the same time cooled down by several orders of magnitude. We give a theoretical description of this effect supported by extensive numerical simulations. The proposed scheme can be implemented with existing experimental setups.

cond-mat.stat-mech↗
arXiv2007

Multifractality and intermediate statistics in quantum maps

We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical computations and provide analytical arguments showing that the generalized fractal dimensions are directly related to the parameter of the underlying classical map, and thus to other properties such as spectral statistics. Our results could be relevant for Anderson and quantum Hall transitions, where wave functions also show multifractality.

nlin.CD↗
arXiv2007

Entanglement of localized states

We derive exact expressions for the mean value of Meyer-Wallach entanglement Q for localized random vectors drawn from various ensembles corresponding to different physical situations. For vectors localized on a randomly chosen subset of the basis, tends for large system sizes to a constant which depends on the participation ratio, whereas for vectors localized on adjacent basis states it goes to zero as a constant over the number of qubits. Applications to many-body systems and Anderson localization are discussed.

quant-ph↗
arXiv2005

Intermediate quantum maps for quantum computation

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production, and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically, and yields pseudorandom operators with original properties, enabling for example to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.

quant-ph↗
arXiv2005

Quantum computing of delocalization in small-world networks

We study a quantum small-world network with disorder and show that the system exhibits a delocalization transition. A quantum algorithm is built up which simulates the evolution operator of the model in a polynomial number of gates for exponential number of vertices in the network. The total computational gain is shown to depend on the parameters of the network and a larger than quadratic speed-up can be reached. We also investigate the robustness of the algorithm in presence of imperfections.

quant-ph↗
arXiv2004

Quantum computation and analysis of Wigner and Husimi functions: toward a quantum image treatment

We study the efficiency of quantum algorithms which aim at obtaining phase space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions, and compared with the classical computation. Different procedures to extract more efficiently information from the final wave function of these algorithms are studied, including coarse-grained measurements, amplitude amplification and measure of wavelet-transformed wave function. The algorithms are analyzed and numerically tested on a complex quantum system showing different behavior depending on parameters, namely the kicked rotator. The results for the Wigner function show in particular that the use of the quantum wavelet transform gives a polynomial gain over classical computation. For the Husimi distribution, the gain is much larger than for the Wigner function, and is bigger with the help of amplitude amplification and wavelet transforms. We also apply the same set of techniques to the analysis of real images. The results show that the use of the quantum wavelet transform allows to lower dramatically the number of measurements needed, but at the cost of a large loss of information.

quant-ph↗
arXiv2004

Quantum Computing of Poincare Recurrences and Periodic Orbits

Quantum algorithms are built enabling to find Poincaré recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of systems. Quadratic gain can be achieved for a larger set of dynamical systems. The simplest cases can be implemented with small number of qubits.

quant-ph↗
arXiv2003

Quantum Computing of Quantum Chaos in the Kicked Rotator Model

We investigate a quantum algorithm which simulates efficiently the quantum kicked rotator model, a system which displays rich physical properties, and enables to study problems of quantum chaos, atomic physics and localization of electrons in solids. The effects of errors in gate operations are tested on this algorithm in numerical simulations with up to 20 qubits. In this way various physical quantities are investigated. Some of them, such as second moment of probability distribution and tunneling transitions through invariant curves are shown to be particularly sensitive to errors. However, investigations of the fidelity and Wigner and Husimi distributions show that these physical quantities are robust in presence of imperfections. This implies that the algorithm can simulate the dynamics of quantum chaos in presence of a moderate amount of noise.

quant-ph↗
arXiv2002

Strange attractor simulated on a quantum computer

We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature.

quant-ph↗