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Journal of Physics Conference Series

Quantum interference vs. quantum chaos in the nuclear shell model

Gerardo Fernández, Edna M. Hernández, Mathieu Hautefeuille, Emmanuel Landa, Irving O. Morales, Víctor Velázquez, Rubén Fossión, Carlos Ernesto Vargas, Alejandro Frank

Published Jan 22, 2015• 2 citations
Publisher

Abstract

In this paper we study the complexity of the nuclear states in terms of a two body quadupole-quadrupole interaction. Energy distributions and eigenvectors composition exhibit a visible interference pattern which is dependent on the intensity of the interaction. In analogy with optics, the visibility of the interference is related to the purity of the states, therefore, we show that the fluctuations associated with quantum chaos have as their origin the remaining quantum coherence with a visibility magnitude close to 5%.

DOI
10.1088/1742-6596/578/1/012014

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In this paper we study the complexity of the nuclear states in terms of a two body quadupole-quadrupole interaction. Energy distributions and eigenvectors composition exhibit a visible interference pattern which is dependent on the intensity of the interaction. In analogy with optics, the visibility of the interference is related to the purity of the states, therefore, we show that the fluctuations associated with quantum chaos have as their origin the remaining quantum coherence with a visibility magnitude close to 5%.
The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Shell model calculations with the Wildenthal interaction are performed in the J−TJ-TJ−T scheme for 12 particles in the sdsdsd-shell. The local level statistics are in perfect agreement with the GOE predictions. The analysis of the amplitudes of the eigenvectors in the shell model basis with the aid of the informational entropy and moments of the distribution function shows evidence for local chaos with a localization length reaching 90\% of the total dimension in the middle of the spectrum. The degree of chaoticity is sensitive to the the strength of the residual interaction as compared to the single particle energy spacing.
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of the interference pattern. One might naively expect that a particle ensemble suffers a greater loss of quantum coherence by interacting with an increasingly randomized distribution of shifts. As we shall see, this is not always true. Decoherence is an interesting phenomenon and a topic that attracts widespread attention [1]. However, it is not easy to give a quantitative definition of decoherence [2]. All attempts at defining it always depend on the experimental configuration and on the authors ’ taste. An interesting related quantity is the
An algorithm for calculating the level density for a given shell-model Hamiltonian without diagonalzation of a huge matrix is presented and explained. The level density is expressed in terms of the moments (traces) of the Hamiltonian over the restricted orbital space. The underlying physics is that of quantum chaos and intrinsic thermalization in closed systems of interacting particles. We show the examples of the approach and briefly discuss the dependence of the level density on the interaction parameters.
In quantum information and communication two fundamental nonclassical features that one exploits in harnessing the true power of composite quantum systems are the interference and quantum correlations. We show how a concept akin to interference can be connected to entanglement and quantum correlation. In particular, we prove that the difference in the squared visibility for the density operator before and after a complete measurement, averaged over all unitary evolutions, is related to the quantum correlation measure based on the measurement disturbance. For pure and mixed bipartite states the unitary average of the squared visibility is related to the entanglement measure. This may provide a method to detect entanglement and quantum correlation with quantum interference setups. Furthermore, we prove that for a fixed purity of the subsystem state, there is a complementarity relation between the linear entanglement of formation and the measurement disturbance. This brings out a quantitative difference between two kinds of quantum correlations and suggests that the origins of these two can be different.