Changing Facets of Nuclear Structure - Proceedings of the 9th International Spring Seminar on Nuclear Physics, 2008
A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statis... more A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statistics of quantum chaos studies, and on the other a new approach based on time series analysis methods. We emphasize the energy and isospin dependence of nuclear chaoticity, based on shell-model energy spectra fluctuations in Ca, Sc and Ti isotopes, which are analyzed using
In the last decade, there has been an increasing interest in the analysis of energy level spectra... more In the last decade, there has been an increasing interest in the analysis of energy level spectra and wave functions of nuclei, particles, atoms and other quantum many-body systems by means of statistical methods and random matrix ensembles. The concept of quantum chaos plays a central role for understanding the universal properties of the energy spectrum of quantum systems. Since these properties concern the whole spectrum, statistical methods become an essential tool. Besides random matrix theory, new theoretical developments making use of information theory, time series analysis, and the merging of thermodynamics and the semiclassical approximation are emphasized. Applications of these methods to quantum systems, especially to atomic nuclei, are reviewed. We focus on recent developments like the study of ''imperfect spectra'' to estimate the degree of symmetry breaking or the fraction of missing levels, the existence of chaos remnants in nuclear masses, the onset of chaos in nuclei, and advances in the comprehension of the Hamiltonian structure in many-body systems. Finally, some applications of statistical spectroscopy methods generated by many-body chaos and two-body random matrix ensembles are described, with emphasis on Gamow-Teller strength sums and beta decay rates for stellar evolution and supernovae.
Key Topics in Nuclear Structure - Proceedings of the 8th International Spring Seminar on Nuclear Physics, 2005
Many complex systems in nature and in human society exhibit time fluctuations characterized by a ... more Many complex systems in nature and in human society exhibit time fluctuations characterized by a power spectrum which is a power function of the frequency f. We show that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum behavior of such a signal for paradigmatic quantum systems suggests the following conjecture: The energy spectra of chaotic quantum systems are characterized by 1/f noise.
Spectral distribution method and exact shell-model predictions for the strength sums of different... more Spectral distribution method and exact shell-model predictions for the strength sums of different transition operators are compared in detail for the J=0, T−Tz=0 states of 46V and 50Sc using the full pf shell. Good agreement of both models is observed in the high level density region of the energy spectrum, where chaotic motion is dominant, and larger discrepancies are observed
Length-dependent oscillations in the dc conductance of laser-driven quantum wires. DF Martinez 1 ... more Length-dependent oscillations in the dc conductance of laser-driven quantum wires. DF Martinez 1 , RA Molina 2 , and Bambi Hu 1 1 Department of Physics, Center for Nonlinear Studies, and The Beijing-Hong Kong-Singapore ...
A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statis... more A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statistics of quantum chaos studies, and on the other a new approach based on time series analysis methods. The study of shell-model spectra in the pf shell shows that nuclear chaos is strongly isopin dependent and increases with excitation energy. On the other hand, it is found that chaotic quantum systems exhibit /f noise and regular systems exhibit 1/f2 behaviour. It is shown that the time series approach can be used to calculate quite accurately the fraction of missing levels and the existence of mixed symmetries in experimental level spectra.
We generalize the definition of localization length to disordered systems driven by a timeperiodi... more We generalize the definition of localization length to disordered systems driven by a timeperiodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.
We study a method to determine the residual conductance of a correlated system by means of the gr... more We study a method to determine the residual conductance of a correlated system by means of the ground-state properties of a large ring composed of the system itself and a long non-interacting lead. The transmission probability through the interacting region and thus its residual conductance is deduced from the persistent current induced by a flux threading the ring. Density Matrix Renormalization Group techniques are employed to obtain numerical results for one-dimensional systems of interacting spinless fermions. As the flux dependence of the persistent current for such a system demonstrates, the interacting system coupled to an infinite non-interacting lead behaves as a non-interacting scatterer, but with an interaction dependent elastic transmission coefficient. The scaling to large lead sizes is discussed in detail as it constitutes a crucial step in determining the conductance. Furthermore, the method, which so far had been used at half filling, is extended to arbitrary filling and also applied to disordered interacting systems, where it is found that repulsive interaction can favor transport.
High-energy interactions of cosmic rays with Earth atmosphere and the resulting extensive air sho... more High-energy interactions of cosmic rays with Earth atmosphere and the resulting extensive air showers have been simulated by means of the CORSIKA Monte Carlo code. Statistical fluctuations of the two-dimensional secondary Cerenkov photon density distributions at ground level produced by GeV cosmic c rays and protons are studied by means of principal components analysis (PCA). This provides a decreasing sequence of covariance matrix eigenvalues that may be fitted to an analytical expression allowing to distinguish among different primary cosmic rays. A very efficient discrimination method of gamma ray induced showers from proton simulated extensive air showers is proposed as a result of this analysis. A cutting parameter is calculated, and the efficiency of the cutting procedure for c-proton separation is evaluated under experimental conditions.
The energy spectrum fluctuations of quantum systems can be formally considered as a discrete time... more The energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum of such signal gives rise to 1/f noise in chaotic systems, whereas integrable systems present 1/f 2 noise. This statistic is very useful for the analysis of two kinds of imperfect spectra: those with missing levels whose number and position are unknown, and those in which all the quantum numbers cannot be determined and levels of different symmetries are mixed. The power spectrum analysis provides an estimation of the number of symmetries and the fraction of mixing and missing levels.
Fermionic atoms in two different hyperfine states confined in optical lattices show strong commen... more Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave (ADW) ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.
Cold fermionic atoms with three different hyperfine states with SU(3) symmetry confined in onedim... more Cold fermionic atoms with three different hyperfine states with SU(3) symmetry confined in onedimensional optical lattices show color-charge separation, generalizing the conventional spin charge separation for interacting SU(2) fermions in one dimension. Through time-dependent DMRG simulations, we explore the features of this phenomenon for a generalized SU(3) Hubbard Hamiltonian. In our numerical simulations of finite size systems, we observe different velocities of the charge and color degrees of freedom when a Gaussian wave packet or a charge (color) density response to a local perturbation is evolved. The differences between attractive and repulsive interactions are explored and we note that neither a small anisotropy of the interaction, breaking the SU(3) symmetry, nor the filling impedes the basic observation of these effects.
We study the linewidth of the surface plasmon resonance in the optical absorption spectrum of met... more We study the linewidth of the surface plasmon resonance in the optical absorption spectrum of metallic nanoparticles, when the decay into electron-hole pairs is the dominant channel. Within a semiclassical approach, we find that the electron-hole density-density correlation oscillates as a function of the size of the particles, leading to oscillations of the linewidth. This result is confirmed numerically for alkali and noble metal particles. While the linewidth can increase strongly, the oscillations persist when the particles are embedded in a matrix.
We study the localization properties of disordered semiconductor superlattices driven by ac-field... more We study the localization properties of disordered semiconductor superlattices driven by ac-fields. The localization length of the electrons in the superlattice increases when the frequency of the driving field is smaller than the miniband width. We show that there is an optimal value of the amplitude of the driving field for which the localization length of the system is maximal. This maximum localization length increases with the inverse of the driving frequency.
Using a model of spinless fermions in a lattice with nearest neighbor and next-nearest neighbor i... more Using a model of spinless fermions in a lattice with nearest neighbor and next-nearest neighbor interaction we show that the entropy of the reduced two site density matrix (the bond entropy) can be used as an extremely accurate and easy to calculate numerical indicator for the critical parameters of the quantum phase transition when the basic ordering pattern has a two-site periodicity. The actual behavior of the bond entropy depends on the particular characteristics of the transition under study. For the Kosterlitz-Thouless type phase transition from a Luttinger liquid phase to a charge density wave state the bond entropy has a local maximum while in the transition from the Luttinger liquid to the phase separated state the derivative of the bond entropy has a divergence due to the cancelation of the third eigenvalue of the two-site reduced density matrix.
We determine the lifetime of the surface plasmon in metallic nanoparticles under various conditio... more We determine the lifetime of the surface plasmon in metallic nanoparticles under various conditions, concentrating on the Landau damping, which is the dominant mechanism for intermediate-size particles. Besides the main contribution to the lifetime, which smoothly increases with the size of the particle, our semiclassical evaluation yields an additional oscillating component. For the case of noble metal particles embedded in a dielectric medium, it is crucial to consider the details of the electronic confinement; we show that in this case the lifetime is determined by the shape of the self-consistent potential near the surface. Strong enough perturbations may lead to the second collective excitation of the electronic system. We study its lifetime, which is limited by two decay channels: Landau damping and ionization. We determine the size dependence of both contributions and show that the second collective excitation remains as a well-defined resonance.
Cold Fermionic atoms with three different hyperfine states confined in optical lattices show pron... more Cold Fermionic atoms with three different hyperfine states confined in optical lattices show pronounced Atomic Density Waves (ADWs). These ADWs are pinned due to the confining potential that traps the atoms in the optical lattice and can be considered a crystal of strongly bound trions. We show that the crystalline phase is incompressible and robust against SU(3) symmetry breaking interaction. We also show that it is generic in the presence of the trap due to its incompressible characteristics. A simulation of the time evolution of the fermionic gas after the trapping potential is switch off shows that the formation of the trionic crystal is marked by a freezing of the dynamics in the lattice.
We show that tunneling and localization properties of interacting ultracold atoms in an optical l... more We show that tunneling and localization properties of interacting ultracold atoms in an optical lattice can be controlled by adiabatically turning on a fast oscillatory force even in the presence of disorder. Our calculations are based on the exact solution of the time-dependent Schrödinger equation, using the Floquet formalism. Implications of our findings for larger systems and the possibility of controlling the phase diagram of disordered-interacting bosonic systems are discussed.
Changing Facets of Nuclear Structure - Proceedings of the 9th International Spring Seminar on Nuclear Physics, 2008
A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statis... more A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statistics of quantum chaos studies, and on the other a new approach based on time series analysis methods. We emphasize the energy and isospin dependence of nuclear chaoticity, based on shell-model energy spectra fluctuations in Ca, Sc and Ti isotopes, which are analyzed using
In the last decade, there has been an increasing interest in the analysis of energy level spectra... more In the last decade, there has been an increasing interest in the analysis of energy level spectra and wave functions of nuclei, particles, atoms and other quantum many-body systems by means of statistical methods and random matrix ensembles. The concept of quantum chaos plays a central role for understanding the universal properties of the energy spectrum of quantum systems. Since these properties concern the whole spectrum, statistical methods become an essential tool. Besides random matrix theory, new theoretical developments making use of information theory, time series analysis, and the merging of thermodynamics and the semiclassical approximation are emphasized. Applications of these methods to quantum systems, especially to atomic nuclei, are reviewed. We focus on recent developments like the study of ''imperfect spectra'' to estimate the degree of symmetry breaking or the fraction of missing levels, the existence of chaos remnants in nuclear masses, the onset of chaos in nuclei, and advances in the comprehension of the Hamiltonian structure in many-body systems. Finally, some applications of statistical spectroscopy methods generated by many-body chaos and two-body random matrix ensembles are described, with emphasis on Gamow-Teller strength sums and beta decay rates for stellar evolution and supernovae.
Key Topics in Nuclear Structure - Proceedings of the 8th International Spring Seminar on Nuclear Physics, 2005
Many complex systems in nature and in human society exhibit time fluctuations characterized by a ... more Many complex systems in nature and in human society exhibit time fluctuations characterized by a power spectrum which is a power function of the frequency f. We show that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum behavior of such a signal for paradigmatic quantum systems suggests the following conjecture: The energy spectra of chaotic quantum systems are characterized by 1/f noise.
Spectral distribution method and exact shell-model predictions for the strength sums of different... more Spectral distribution method and exact shell-model predictions for the strength sums of different transition operators are compared in detail for the J=0, T−Tz=0 states of 46V and 50Sc using the full pf shell. Good agreement of both models is observed in the high level density region of the energy spectrum, where chaotic motion is dominant, and larger discrepancies are observed
Length-dependent oscillations in the dc conductance of laser-driven quantum wires. DF Martinez 1 ... more Length-dependent oscillations in the dc conductance of laser-driven quantum wires. DF Martinez 1 , RA Molina 2 , and Bambi Hu 1 1 Department of Physics, Center for Nonlinear Studies, and The Beijing-Hong Kong-Singapore ...
A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statis... more A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statistics of quantum chaos studies, and on the other a new approach based on time series analysis methods. The study of shell-model spectra in the pf shell shows that nuclear chaos is strongly isopin dependent and increases with excitation energy. On the other hand, it is found that chaotic quantum systems exhibit /f noise and regular systems exhibit 1/f2 behaviour. It is shown that the time series approach can be used to calculate quite accurately the fraction of missing levels and the existence of mixed symmetries in experimental level spectra.
We generalize the definition of localization length to disordered systems driven by a timeperiodi... more We generalize the definition of localization length to disordered systems driven by a timeperiodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.
We study a method to determine the residual conductance of a correlated system by means of the gr... more We study a method to determine the residual conductance of a correlated system by means of the ground-state properties of a large ring composed of the system itself and a long non-interacting lead. The transmission probability through the interacting region and thus its residual conductance is deduced from the persistent current induced by a flux threading the ring. Density Matrix Renormalization Group techniques are employed to obtain numerical results for one-dimensional systems of interacting spinless fermions. As the flux dependence of the persistent current for such a system demonstrates, the interacting system coupled to an infinite non-interacting lead behaves as a non-interacting scatterer, but with an interaction dependent elastic transmission coefficient. The scaling to large lead sizes is discussed in detail as it constitutes a crucial step in determining the conductance. Furthermore, the method, which so far had been used at half filling, is extended to arbitrary filling and also applied to disordered interacting systems, where it is found that repulsive interaction can favor transport.
High-energy interactions of cosmic rays with Earth atmosphere and the resulting extensive air sho... more High-energy interactions of cosmic rays with Earth atmosphere and the resulting extensive air showers have been simulated by means of the CORSIKA Monte Carlo code. Statistical fluctuations of the two-dimensional secondary Cerenkov photon density distributions at ground level produced by GeV cosmic c rays and protons are studied by means of principal components analysis (PCA). This provides a decreasing sequence of covariance matrix eigenvalues that may be fitted to an analytical expression allowing to distinguish among different primary cosmic rays. A very efficient discrimination method of gamma ray induced showers from proton simulated extensive air showers is proposed as a result of this analysis. A cutting parameter is calculated, and the efficiency of the cutting procedure for c-proton separation is evaluated under experimental conditions.
The energy spectrum fluctuations of quantum systems can be formally considered as a discrete time... more The energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum of such signal gives rise to 1/f noise in chaotic systems, whereas integrable systems present 1/f 2 noise. This statistic is very useful for the analysis of two kinds of imperfect spectra: those with missing levels whose number and position are unknown, and those in which all the quantum numbers cannot be determined and levels of different symmetries are mixed. The power spectrum analysis provides an estimation of the number of symmetries and the fraction of mixing and missing levels.
Fermionic atoms in two different hyperfine states confined in optical lattices show strong commen... more Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave (ADW) ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.
Cold fermionic atoms with three different hyperfine states with SU(3) symmetry confined in onedim... more Cold fermionic atoms with three different hyperfine states with SU(3) symmetry confined in onedimensional optical lattices show color-charge separation, generalizing the conventional spin charge separation for interacting SU(2) fermions in one dimension. Through time-dependent DMRG simulations, we explore the features of this phenomenon for a generalized SU(3) Hubbard Hamiltonian. In our numerical simulations of finite size systems, we observe different velocities of the charge and color degrees of freedom when a Gaussian wave packet or a charge (color) density response to a local perturbation is evolved. The differences between attractive and repulsive interactions are explored and we note that neither a small anisotropy of the interaction, breaking the SU(3) symmetry, nor the filling impedes the basic observation of these effects.
We study the linewidth of the surface plasmon resonance in the optical absorption spectrum of met... more We study the linewidth of the surface plasmon resonance in the optical absorption spectrum of metallic nanoparticles, when the decay into electron-hole pairs is the dominant channel. Within a semiclassical approach, we find that the electron-hole density-density correlation oscillates as a function of the size of the particles, leading to oscillations of the linewidth. This result is confirmed numerically for alkali and noble metal particles. While the linewidth can increase strongly, the oscillations persist when the particles are embedded in a matrix.
We study the localization properties of disordered semiconductor superlattices driven by ac-field... more We study the localization properties of disordered semiconductor superlattices driven by ac-fields. The localization length of the electrons in the superlattice increases when the frequency of the driving field is smaller than the miniband width. We show that there is an optimal value of the amplitude of the driving field for which the localization length of the system is maximal. This maximum localization length increases with the inverse of the driving frequency.
Using a model of spinless fermions in a lattice with nearest neighbor and next-nearest neighbor i... more Using a model of spinless fermions in a lattice with nearest neighbor and next-nearest neighbor interaction we show that the entropy of the reduced two site density matrix (the bond entropy) can be used as an extremely accurate and easy to calculate numerical indicator for the critical parameters of the quantum phase transition when the basic ordering pattern has a two-site periodicity. The actual behavior of the bond entropy depends on the particular characteristics of the transition under study. For the Kosterlitz-Thouless type phase transition from a Luttinger liquid phase to a charge density wave state the bond entropy has a local maximum while in the transition from the Luttinger liquid to the phase separated state the derivative of the bond entropy has a divergence due to the cancelation of the third eigenvalue of the two-site reduced density matrix.
We determine the lifetime of the surface plasmon in metallic nanoparticles under various conditio... more We determine the lifetime of the surface plasmon in metallic nanoparticles under various conditions, concentrating on the Landau damping, which is the dominant mechanism for intermediate-size particles. Besides the main contribution to the lifetime, which smoothly increases with the size of the particle, our semiclassical evaluation yields an additional oscillating component. For the case of noble metal particles embedded in a dielectric medium, it is crucial to consider the details of the electronic confinement; we show that in this case the lifetime is determined by the shape of the self-consistent potential near the surface. Strong enough perturbations may lead to the second collective excitation of the electronic system. We study its lifetime, which is limited by two decay channels: Landau damping and ionization. We determine the size dependence of both contributions and show that the second collective excitation remains as a well-defined resonance.
Cold Fermionic atoms with three different hyperfine states confined in optical lattices show pron... more Cold Fermionic atoms with three different hyperfine states confined in optical lattices show pronounced Atomic Density Waves (ADWs). These ADWs are pinned due to the confining potential that traps the atoms in the optical lattice and can be considered a crystal of strongly bound trions. We show that the crystalline phase is incompressible and robust against SU(3) symmetry breaking interaction. We also show that it is generic in the presence of the trap due to its incompressible characteristics. A simulation of the time evolution of the fermionic gas after the trapping potential is switch off shows that the formation of the trionic crystal is marked by a freezing of the dynamics in the lattice.
We show that tunneling and localization properties of interacting ultracold atoms in an optical l... more We show that tunneling and localization properties of interacting ultracold atoms in an optical lattice can be controlled by adiabatically turning on a fast oscillatory force even in the presence of disorder. Our calculations are based on the exact solution of the time-dependent Schrödinger equation, using the Floquet formalism. Implications of our findings for larger systems and the possibility of controlling the phase diagram of disordered-interacting bosonic systems are discussed.
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Papers by Rafael Molina