Luis Benet - Academia.edu (original) (raw)
Papers by Luis Benet
Monthly Notices of the Royal Astronomical Society, 2011
In this paper, we modify Laskar's simplified model of planetary evolution and accretion [J. Laska... more In this paper, we modify Laskar's simplified model of planetary evolution and accretion [J. Laskar, Phys. Rev. Lett, vol 84, p 3240 (2000)] to account for the full conservation of the total angular momentum of the system, and extend it to incorporate an accretion probability that depends on the mass and relative velocity of the colliding particles. We present statistical results for the mass and eccentricity of the planets formed, in terms of their semi-major axes, for a large number of realisations of different versions of the model. In particular, we find that by combining the mass-dependent accretion probability and the velocity-selection mechanism, the planets formed display a systematic occurrence at specific locations. By introducing properly scaled variables, our results are universal with respect to the total angular momentum of the system, the mass of the planetesimal disc, and the mass of the central star.
Revista Mexicana de Ciencias Geológicas
In this paper we review some open questions in the context of the structure observed in narrow pl... more In this paper we review some open questions in the context of the structure observed in narrow planetary rings, and summarize some recent results of our work directed to answer them. Using the scattering approach to narrow rings we have succeeded to reproduce some of their structural properties in a qualitative sense, using unrealistic toy models as examples. We obtain narrow rings which are non-circular and display sharp edges. In addition, these rings may have multiple components which may entangle in a complicated dynamically evolving way forming a braided structure, or may display strongly azimuthal dependent features such as arcs. The appearance of these structural properties can be understood in terms of the underlying phase space.
Revista Mexicana de Fisica
Estudiamos la formación de planetas en un modelo sencillo de acreción planetaria , que incluye ad... more Estudiamos la formación de planetas en un modelo sencillo de acreción planetaria , que incluye además restricciones físicas en la acreción y un proto-Júpiter inmerso en el disco protoplanetario. Los efectos locales en tiempos cortos aumentan la migración del Júpiter y generan distribuciones más anchas de la excentricidad. Estos procesos de tres cuerpos podrían explicar las altas excentricidades observadas en los planetas exosolares.
Revista Mexicana de Ciencias Geológicas
In this paper we review some open questions in the context of the structure observed in narrow pl... more In this paper we review some open questions in the context of the structure observed in narrow planetary rings, and summarize some recent results of our work directed to answer them. Using the scattering approach to narrow rings we have succeeded to reproduce some of their structural properties in a qualitative sense, using unrealistic toy models as examples. We obtain narrow rings which are non-circular and display sharp edges. In addition, these rings may have multiple components which may entangle in a complicated dynamically evolving way forming a braided structure, or may display strongly azimuthal dependent features such as arcs. The appearance of these structural properties can be understood in terms of the underlying phase space.
The k-body Gaussian Embedded Ensemble of Random Matrices is considered for N bosons distributed o... more The k-body Gaussian Embedded Ensemble of Random Matrices is considered for N bosons distributed on two single-particle levels. When k = N , the ensemble is equivalent to the Gaussian Orthogonal Ensemble (GOE), and when k = 2 it corresponds to the Two-body Random Ensemble (TBRE) for bosons. It is shown that the energy spectrum leads to a rank function which is of the form of a discrete generalized beta distribution. The same distribution is obtained assuming N non-interacting quasiparticles that obey the fractional exclusion statistics introduced by Haldane two decades ago.
In 2006, Showalter and Lissauer announced the discovery of the mu-ring around Uranus and a accomp... more In 2006, Showalter and Lissauer announced the discovery of the mu-ring around Uranus and a accompanying small moon Mab (Showalter and Lissauer, 2006). They derived the orbital position of Mab from both Voyager flyby (1986) and HST (2003-2006) data and showed that it is poorly understood. The observed positions were compared against an orbital model that includes gravitational flattening of
A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relax... more A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relaxation (thermalization), a phase memory of the way the strongly interacting many-body system was excited remains. In this contribution we analyze a low energy evaporating proton data in nucleon induced reactions at ≃62 MeV incident energy with 197 Au, 208 Pb, 209 Bi and nat U. Our analysis demonstrates that the thermalized non-equilibrated matter survives a cascade of several evaporating particles. Thus the experiments show that the effect of the anomalously slow phase relaxation, with upper limits of the phase relaxation widths in the range 1-10 −4 eV, is stable with respect to the multi-step evaporating cascade from the thermalized compound nuclei. We also briefly mention manifestations and implications of the thermalized non-equilibrated matter for some other fields.
We study the complex eigenvalues of the Wishart model defined for nonsymmetric correlation matric... more We study the complex eigenvalues of the Wishart model defined for nonsymmetric correlation matrices. The model is defined for two statistically equivalent but different Gaussian real matrices, as C = ABt /T , where Bt is the transpose of B and both matrices A and B are of dimension N × T . We consider actual correlations between the matrices so that on the ensemble average C does not vanish. We derive a loop equation for the spectral density of C in the large N and T limit where the ratio N/T is finite. The actual correlations changes the complex eigenvalues of C, and hence their domain from the results known for the vanishing C or for the uncorrelated A and B. Using the loop equation we derive a result for the contour describing the domain of the bulk of the eigenvalues of C. If the nonvanishing-correlation matrix is diagonal with the same element c = 0, the contour is no longer a circle centered at origin but a shifted ellipse. In this case, the loop equation is analytically solva...
Annalen der Physik, 2015
The quantum efficiency in the transfer of an initial excitation in disordered finite networks, mo... more The quantum efficiency in the transfer of an initial excitation in disordered finite networks, modeled by the k-body embedded Gaussian ensembles of random matrices, is studied for bosons and fermions. The influence of the presence or absence of time-reversal symmetry and centrosymmetry/centrohermiticity are addressed. For bosons and fermions, the best efficiencies of the realizations of the ensemble are dramatically enhanced when centrosymmetry (centrohermiticity) is imposed. For few bosons distributed in two single-particle levels this permits perfect state transfer for almost all realizations when one-particle interactions are considered. For fermionic systems the enhancement is found to be maximal for cases when all but one single particle levels are occupied.
We compare the influence of perturbations of classically regular respectively chaotic Hamiltonian... more We compare the influence of perturbations of classically regular respectively chaotic Hamiltonians on their eigenfunctions. A generic measure of the perturbation strength is given by the average spreading width, which semiclassically is a phase-space integral. Thus, contrary to common assumption, the spreading width cannot be an indicator of regularity or chaos. The distribution of expansion coefficients of perturbed eigenfunctions in terms of unperturbed ones is markedly different for the two cases and may serve as a quantum signature of chaos referring to states rather than to spectra.
Quantum-classical correspondence for the shape of eigenfunctions, local spectral density of state... more Quantum-classical correspondence for the shape of eigenfunctions, local spectral density of states and occupation number distribution is studied in a chaotic model of two coupled quartic oscillators. In particular, it is shown that both classical quantities and quantum spectra determine global properties of occupation numbers and inverse participation ratio.
We construct an ensemble of second-quantized Hamiltonians with two bosonic degrees of freedom, wh... more We construct an ensemble of second-quantized Hamiltonians with two bosonic degrees of freedom, whose members display with probability one Gaussian orthogonal ensemble (GOE) or Gaussian unitary ensemble (GUE) statistics. Nevertheless, these Hamiltonians have a second integral of motion, namely, the boson number, and thus are integrable. To construct this ensemble we use some "reverse engineering" starting from the fact that n bosons in a two-level system with random interactions have an integrable classical limit by the old Heisenberg association of boson operators to actions and angles. By choosing an n-body random interaction and degenerate levels we end up with GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.
We address the occurrence of narrow planetary rings under the interaction with shepherds. Our app... more We address the occurrence of narrow planetary rings under the interaction with shepherds. Our approach is based on a Hamiltonian framework of non-interacting particles where open motion (escape) takes place, and includes the quasi-periodic perturbations of the shepherd's Kepler motion with small and zero eccentricity. We concentrate in the phase-space structure and establish connections with properties like the eccentricity, sharp edges and narrowness of the ring. Within our scattering approach, the organizing centers necessary for the occurrence of the rings are stable periodic orbits, or more generally, stable tori. In the case of eccentric motion of the shepherd, the rings are narrower and display a gap which defines different components of the ring.
We study the effect of phase relaxation on coherent superpositions of rotating clockwise and anti... more We study the effect of phase relaxation on coherent superpositions of rotating clockwise and anticlockwise wave packets in the regime of strongly overlapping resonances of the intermediate complex. Such highly excited deformed complexes may be created in binary collisions of heavy ions, molecules and atomic clusters. It is shown that phase relaxation leads to a reduction of the interference fringes, thus mimicking the effect of decoherence. This reduction is crucial for the determination of the phase-relaxation width from the data on the excitation function oscillations in heavy-ion collisions and bimolecular chemical reactions. The difference between the effects of phase relaxation and decoherence is discussed.
We study coherent superpositions of clockwise and anti-clockwise rotating intermediate complexes ... more We study coherent superpositions of clockwise and anti-clockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the H+D2 chemical reaction. Thus we demonstrate the quantum-classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment.
Progress and Challenges in Dynamical Systems, 2013
In this paper we discuss a simple model for the confinement of Saturn's F ring and present some p... more In this paper we discuss a simple model for the confinement of Saturn's F ring and present some preliminary numerical results. The model involves the gravitational interaction of independent test particles with Saturn, including its second zonal harmonic, the shepherd moons Prometheus and Pandora, and Titan, the largest of Saturn's satellites. We perform accurate long-time integrations (3.2 × 10 6 revolutions of Prometheus) to check if the particle has escaped or remains trapped in the region between the shepherds. A particle escapes if its orbit crosses the region between the shepherds, or if it displays a physical collisions (lies with Hill's region) with them. We find a wide region of initial conditions of the test particle that remain confined. We carry out a frequency analysis and use the ratio of the standard deviation over the average main frequencies as stability index. This indicator separates clearly the set of trapped initial conditions of the test particles, displaying some localised structures for the most stable ones. Retaining only those particles which are more stable according to our indicator, we obtain a narrow elliptic ring displaying sharp edges which agrees with the nominal location of Saturn's F ring.
Physical Review E, 2014
We study complex eigenvalues of the Wishart model for nonsymmetric correlation matrices. The mode... more We study complex eigenvalues of the Wishart model for nonsymmetric correlation matrices. The model is defined for two statistically equivalent but different Gaussian real matrices, as C = AB t /T , where B t is the transpose of B and both matrices A and B are of dimensions N × T . If A and B are uncorrelated, or equivalently if C vanishes on average, it is known that at large matrix dimension the domain of the eigenvalues of C is a circle centered-at-origin and the eigenvalue density depends only on the radial distances. We consider actual correlation in A and B and derive a result for the contour describing the domain of the bulk of the eigenvalues of C in the limit of large N and T where the ratio N/T is finite. In particular, we show that the eigenvalue domain is sensitive to the correlations. For example, when C is diagonal on average with the same element c = 0, the contour is no longer a circle centered at origin but a shifted ellipse. In this case we explicitly derive a result for the spectral density which again depends only on the radial distances. For more general cases, we show that the contour depends on the symmetric and antisymmetric parts of the correlation matrix resulting from the ensemble-averaged C. If the correlation matrix is normal, then the contour depends only on its spectrum. We also provide numerics to justify our analytics.
We study the fidelity decay of the k-body embedded ensembles of random matrices for bosons distri... more We study the fidelity decay of the k-body embedded ensembles of random matrices for bosons distributed over two single-particle states. Fidelity is defined in terms of a reference Hamiltonian, which is a purely diagonal matrix consisting of a fixed one-body term and includes the diagonal of the perturbing k-body embedded ensemble matrix, and the perturbed Hamiltonian which includes the residual off-diagonal elements of the k-body interaction. This choice mimics the typical mean-field basis used in many calculations. We study separately the cases k = 2 and 3. We compute the ensemble-averaged fidelity decay as well as the fidelity of typical members with respect to an initial random state. Average fidelity displays a revival at the Heisenberg time, t = t H = 1, and a freeze in the fidelity decay, during which periodic revivals of period t H are observed. We obtain the relevant scaling properties with respect to the number of bosons and the strength of the perturbation. For certain members of the ensemble, we find that the period of the revivals during the freeze of fidelity occurs at fractional times of t H . These fractional periodic revivals are related to the dominance of specific k-body terms in the perturbation.
Monthly Notices of the Royal Astronomical Society, 2011
In this paper, we modify Laskar's simplified model of planetary evolution and accretion [J. Laska... more In this paper, we modify Laskar's simplified model of planetary evolution and accretion [J. Laskar, Phys. Rev. Lett, vol 84, p 3240 (2000)] to account for the full conservation of the total angular momentum of the system, and extend it to incorporate an accretion probability that depends on the mass and relative velocity of the colliding particles. We present statistical results for the mass and eccentricity of the planets formed, in terms of their semi-major axes, for a large number of realisations of different versions of the model. In particular, we find that by combining the mass-dependent accretion probability and the velocity-selection mechanism, the planets formed display a systematic occurrence at specific locations. By introducing properly scaled variables, our results are universal with respect to the total angular momentum of the system, the mass of the planetesimal disc, and the mass of the central star.
Revista Mexicana de Ciencias Geológicas
In this paper we review some open questions in the context of the structure observed in narrow pl... more In this paper we review some open questions in the context of the structure observed in narrow planetary rings, and summarize some recent results of our work directed to answer them. Using the scattering approach to narrow rings we have succeeded to reproduce some of their structural properties in a qualitative sense, using unrealistic toy models as examples. We obtain narrow rings which are non-circular and display sharp edges. In addition, these rings may have multiple components which may entangle in a complicated dynamically evolving way forming a braided structure, or may display strongly azimuthal dependent features such as arcs. The appearance of these structural properties can be understood in terms of the underlying phase space.
Revista Mexicana de Fisica
Estudiamos la formación de planetas en un modelo sencillo de acreción planetaria , que incluye ad... more Estudiamos la formación de planetas en un modelo sencillo de acreción planetaria , que incluye además restricciones físicas en la acreción y un proto-Júpiter inmerso en el disco protoplanetario. Los efectos locales en tiempos cortos aumentan la migración del Júpiter y generan distribuciones más anchas de la excentricidad. Estos procesos de tres cuerpos podrían explicar las altas excentricidades observadas en los planetas exosolares.
Revista Mexicana de Ciencias Geológicas
In this paper we review some open questions in the context of the structure observed in narrow pl... more In this paper we review some open questions in the context of the structure observed in narrow planetary rings, and summarize some recent results of our work directed to answer them. Using the scattering approach to narrow rings we have succeeded to reproduce some of their structural properties in a qualitative sense, using unrealistic toy models as examples. We obtain narrow rings which are non-circular and display sharp edges. In addition, these rings may have multiple components which may entangle in a complicated dynamically evolving way forming a braided structure, or may display strongly azimuthal dependent features such as arcs. The appearance of these structural properties can be understood in terms of the underlying phase space.
The k-body Gaussian Embedded Ensemble of Random Matrices is considered for N bosons distributed o... more The k-body Gaussian Embedded Ensemble of Random Matrices is considered for N bosons distributed on two single-particle levels. When k = N , the ensemble is equivalent to the Gaussian Orthogonal Ensemble (GOE), and when k = 2 it corresponds to the Two-body Random Ensemble (TBRE) for bosons. It is shown that the energy spectrum leads to a rank function which is of the form of a discrete generalized beta distribution. The same distribution is obtained assuming N non-interacting quasiparticles that obey the fractional exclusion statistics introduced by Haldane two decades ago.
In 2006, Showalter and Lissauer announced the discovery of the mu-ring around Uranus and a accomp... more In 2006, Showalter and Lissauer announced the discovery of the mu-ring around Uranus and a accompanying small moon Mab (Showalter and Lissauer, 2006). They derived the orbital position of Mab from both Voyager flyby (1986) and HST (2003-2006) data and showed that it is poorly understood. The observed positions were compared against an orbital model that includes gravitational flattening of
A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relax... more A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relaxation (thermalization), a phase memory of the way the strongly interacting many-body system was excited remains. In this contribution we analyze a low energy evaporating proton data in nucleon induced reactions at ≃62 MeV incident energy with 197 Au, 208 Pb, 209 Bi and nat U. Our analysis demonstrates that the thermalized non-equilibrated matter survives a cascade of several evaporating particles. Thus the experiments show that the effect of the anomalously slow phase relaxation, with upper limits of the phase relaxation widths in the range 1-10 −4 eV, is stable with respect to the multi-step evaporating cascade from the thermalized compound nuclei. We also briefly mention manifestations and implications of the thermalized non-equilibrated matter for some other fields.
We study the complex eigenvalues of the Wishart model defined for nonsymmetric correlation matric... more We study the complex eigenvalues of the Wishart model defined for nonsymmetric correlation matrices. The model is defined for two statistically equivalent but different Gaussian real matrices, as C = ABt /T , where Bt is the transpose of B and both matrices A and B are of dimension N × T . We consider actual correlations between the matrices so that on the ensemble average C does not vanish. We derive a loop equation for the spectral density of C in the large N and T limit where the ratio N/T is finite. The actual correlations changes the complex eigenvalues of C, and hence their domain from the results known for the vanishing C or for the uncorrelated A and B. Using the loop equation we derive a result for the contour describing the domain of the bulk of the eigenvalues of C. If the nonvanishing-correlation matrix is diagonal with the same element c = 0, the contour is no longer a circle centered at origin but a shifted ellipse. In this case, the loop equation is analytically solva...
Annalen der Physik, 2015
The quantum efficiency in the transfer of an initial excitation in disordered finite networks, mo... more The quantum efficiency in the transfer of an initial excitation in disordered finite networks, modeled by the k-body embedded Gaussian ensembles of random matrices, is studied for bosons and fermions. The influence of the presence or absence of time-reversal symmetry and centrosymmetry/centrohermiticity are addressed. For bosons and fermions, the best efficiencies of the realizations of the ensemble are dramatically enhanced when centrosymmetry (centrohermiticity) is imposed. For few bosons distributed in two single-particle levels this permits perfect state transfer for almost all realizations when one-particle interactions are considered. For fermionic systems the enhancement is found to be maximal for cases when all but one single particle levels are occupied.
We compare the influence of perturbations of classically regular respectively chaotic Hamiltonian... more We compare the influence of perturbations of classically regular respectively chaotic Hamiltonians on their eigenfunctions. A generic measure of the perturbation strength is given by the average spreading width, which semiclassically is a phase-space integral. Thus, contrary to common assumption, the spreading width cannot be an indicator of regularity or chaos. The distribution of expansion coefficients of perturbed eigenfunctions in terms of unperturbed ones is markedly different for the two cases and may serve as a quantum signature of chaos referring to states rather than to spectra.
Quantum-classical correspondence for the shape of eigenfunctions, local spectral density of state... more Quantum-classical correspondence for the shape of eigenfunctions, local spectral density of states and occupation number distribution is studied in a chaotic model of two coupled quartic oscillators. In particular, it is shown that both classical quantities and quantum spectra determine global properties of occupation numbers and inverse participation ratio.
We construct an ensemble of second-quantized Hamiltonians with two bosonic degrees of freedom, wh... more We construct an ensemble of second-quantized Hamiltonians with two bosonic degrees of freedom, whose members display with probability one Gaussian orthogonal ensemble (GOE) or Gaussian unitary ensemble (GUE) statistics. Nevertheless, these Hamiltonians have a second integral of motion, namely, the boson number, and thus are integrable. To construct this ensemble we use some "reverse engineering" starting from the fact that n bosons in a two-level system with random interactions have an integrable classical limit by the old Heisenberg association of boson operators to actions and angles. By choosing an n-body random interaction and degenerate levels we end up with GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.
We address the occurrence of narrow planetary rings under the interaction with shepherds. Our app... more We address the occurrence of narrow planetary rings under the interaction with shepherds. Our approach is based on a Hamiltonian framework of non-interacting particles where open motion (escape) takes place, and includes the quasi-periodic perturbations of the shepherd's Kepler motion with small and zero eccentricity. We concentrate in the phase-space structure and establish connections with properties like the eccentricity, sharp edges and narrowness of the ring. Within our scattering approach, the organizing centers necessary for the occurrence of the rings are stable periodic orbits, or more generally, stable tori. In the case of eccentric motion of the shepherd, the rings are narrower and display a gap which defines different components of the ring.
We study the effect of phase relaxation on coherent superpositions of rotating clockwise and anti... more We study the effect of phase relaxation on coherent superpositions of rotating clockwise and anticlockwise wave packets in the regime of strongly overlapping resonances of the intermediate complex. Such highly excited deformed complexes may be created in binary collisions of heavy ions, molecules and atomic clusters. It is shown that phase relaxation leads to a reduction of the interference fringes, thus mimicking the effect of decoherence. This reduction is crucial for the determination of the phase-relaxation width from the data on the excitation function oscillations in heavy-ion collisions and bimolecular chemical reactions. The difference between the effects of phase relaxation and decoherence is discussed.
We study coherent superpositions of clockwise and anti-clockwise rotating intermediate complexes ... more We study coherent superpositions of clockwise and anti-clockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the H+D2 chemical reaction. Thus we demonstrate the quantum-classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment.
Progress and Challenges in Dynamical Systems, 2013
In this paper we discuss a simple model for the confinement of Saturn's F ring and present some p... more In this paper we discuss a simple model for the confinement of Saturn's F ring and present some preliminary numerical results. The model involves the gravitational interaction of independent test particles with Saturn, including its second zonal harmonic, the shepherd moons Prometheus and Pandora, and Titan, the largest of Saturn's satellites. We perform accurate long-time integrations (3.2 × 10 6 revolutions of Prometheus) to check if the particle has escaped or remains trapped in the region between the shepherds. A particle escapes if its orbit crosses the region between the shepherds, or if it displays a physical collisions (lies with Hill's region) with them. We find a wide region of initial conditions of the test particle that remain confined. We carry out a frequency analysis and use the ratio of the standard deviation over the average main frequencies as stability index. This indicator separates clearly the set of trapped initial conditions of the test particles, displaying some localised structures for the most stable ones. Retaining only those particles which are more stable according to our indicator, we obtain a narrow elliptic ring displaying sharp edges which agrees with the nominal location of Saturn's F ring.
Physical Review E, 2014
We study complex eigenvalues of the Wishart model for nonsymmetric correlation matrices. The mode... more We study complex eigenvalues of the Wishart model for nonsymmetric correlation matrices. The model is defined for two statistically equivalent but different Gaussian real matrices, as C = AB t /T , where B t is the transpose of B and both matrices A and B are of dimensions N × T . If A and B are uncorrelated, or equivalently if C vanishes on average, it is known that at large matrix dimension the domain of the eigenvalues of C is a circle centered-at-origin and the eigenvalue density depends only on the radial distances. We consider actual correlation in A and B and derive a result for the contour describing the domain of the bulk of the eigenvalues of C in the limit of large N and T where the ratio N/T is finite. In particular, we show that the eigenvalue domain is sensitive to the correlations. For example, when C is diagonal on average with the same element c = 0, the contour is no longer a circle centered at origin but a shifted ellipse. In this case we explicitly derive a result for the spectral density which again depends only on the radial distances. For more general cases, we show that the contour depends on the symmetric and antisymmetric parts of the correlation matrix resulting from the ensemble-averaged C. If the correlation matrix is normal, then the contour depends only on its spectrum. We also provide numerics to justify our analytics.
We study the fidelity decay of the k-body embedded ensembles of random matrices for bosons distri... more We study the fidelity decay of the k-body embedded ensembles of random matrices for bosons distributed over two single-particle states. Fidelity is defined in terms of a reference Hamiltonian, which is a purely diagonal matrix consisting of a fixed one-body term and includes the diagonal of the perturbing k-body embedded ensemble matrix, and the perturbed Hamiltonian which includes the residual off-diagonal elements of the k-body interaction. This choice mimics the typical mean-field basis used in many calculations. We study separately the cases k = 2 and 3. We compute the ensemble-averaged fidelity decay as well as the fidelity of typical members with respect to an initial random state. Average fidelity displays a revival at the Heisenberg time, t = t H = 1, and a freeze in the fidelity decay, during which periodic revivals of period t H are observed. We obtain the relevant scaling properties with respect to the number of bosons and the strength of the perturbation. For certain members of the ensemble, we find that the period of the revivals during the freeze of fidelity occurs at fractional times of t H . These fractional periodic revivals are related to the dominance of specific k-body terms in the perturbation.