Paolo Bellomo - Academia.edu (original) (raw)
Papers by Paolo Bellomo
Journal of physics, Jun 19, 1998
We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduc... more We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasiclassically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit.
The Journal of Physical Chemistry A, 1997
The Journal of Chemical Physics, 1997
Zero-electron-kinetic-energy photoelectron spectroscopy (“ZEKE-PES”) is based on the pulsed field... more Zero-electron-kinetic-energy photoelectron spectroscopy (“ZEKE-PES”) is based on the pulsed field ionization of long lived Rydberg states (ZEKE states); it is generally accepted that ZEKE states have large angular momentum l, which quenches electron-core interactions, but how they acquire it remains a matter of dispute. We show that {nl}→{nl′} ion-Rydberg collisions are a viable and prominent mechanism for the excitation of large-l Rydberg states. We elucidate the dynamics by an exactly solvable classical model which provides a transparent and intuitive picture of the excitation of high-l states. By a geometric interpretation of the dynamics we are able to predict for which values of the impact parameter and reduced velocity of the incoming ion a change of the angular momentum of the state becomes possible. We pay particular attention to the influence of the quantum defect, δl, on the {nl}→{nl′} cross section and demonstrate that, for small initial angular momenta, δl is itself a major contributor to the ...
International Journal of Bifurcation and Chaos, 1995
We study the spectral statistics of three triangular quantum billiards. We show that for an ergod... more We study the spectral statistics of three triangular quantum billiards. We show that for an ergodic billiard the nearest neighbor spacings distribution in the low energy regime is strongly influenced by a neighboring integrable domain (equilateral triangle). With increasing energy we observe a transition towards a more chaotic-like pattern. We also show that for all three triangles the properties of the spectral distributions depend heavily on the energy range considered. This is specially true for the spectral rigidity, because of its essentially local character. The features of the distributions do not depend strongly on the genus of classical billiards.
Physical Review A, 1999
We predict and confirm numerically the existence of localized Rydberg wave packets that travel on... more We predict and confirm numerically the existence of localized Rydberg wave packets that travel on classical elliptical trajectories with negligible spreading. These wave packets are supported by a resonant circularly polarized microwave field, and we study them by a semiclassical action-angle representation.
We study the dispersion of the “temporally stable ” coherent states for the hydrogen atom introdu... more We study the dispersion of the “temporally stable ” coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasiclassically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit. PACS numbers: 03.65.Ca, 32.80.Rm, 33.80.Rv – To appear in J. Phys. A 1. Temporally stable coherent states for the hydrogen atom In recent years accurate experimental results have generated renewed interest [1– 13] in a long standing problem of quantum physics, which was addressed, albeit unsuccessfully, already in 1926 by Schrödinger himself [14]: that is the problem of constructing localized, non-spreading wave packets in the hydrogen atom which travel along the classical trajectories (Keple...
J Phys a Math Gen, 1998
We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduc... more We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasiclassically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit.
Thesis Georgia Institute of Technology Source Dai B 58 06 P 3100 Dec 1997 225 Pages, Dec 1, 1997
Physical Review E - PHYS REV E, 1994
In this paper we discover a generic structure in the eigenfunctions of quantum billiards, namely,... more In this paper we discover a generic structure in the eigenfunctions of quantum billiards, namely, scarring by families of stable periodic orbits in a nonchaotic system. Our study is conducted on two different triangular billiards, one an ergodic system and the other a ``pseudointegrable'' billiard. Surprisingly, we detect scars in regions which contain no periodic orbits. The periodic orbits responsible for scarring reside in a ``neighboring'' triangle. Such orbits show a more complex phase space structure than the ``bouncing ball'' trajectories of the stadium billiard. While diffuse nodal structure is usually the antithesis of scarring, we show that in some eigenstates it is supported by extensive families of stable periodic orbits.
Pramana, 1995
A new scheme for computing the eigenvalues and eigenstates of the Laplacian with Dirichlet bounda... more A new scheme for computing the eigenvalues and eigenstates of the Laplacian with Dirichlet boundary conditions on arbitrary triangular domains is presented. Its reliability is tested by comparing numerical results with analytical ones whenever possible. The computation of eigenvalues shows a good agreement with analytical results. The procedure is shown to give accurate results also in the case of eigenfunctions computation. Finally, the sensitivity of our scheme to the geometry of the domain is discussed and the algorithm is shown to detect small changes in the shape of the domain.
Physical Review Letters, 1995
A Comment on the Letter by Francesco Benvenuto, Guilio Casata and D. L. Shepelyansky, Phys. Rev. ... more A Comment on the Letter by Francesco Benvenuto, Guilio Casata and D. L. Shepelyansky, Phys. Rev. Lett. 72, 1818 (1994).
Physical Review A, 1998
The complex processes leading to the collisional population of ultra-long-lived Rydberg states wi... more The complex processes leading to the collisional population of ultra-long-lived Rydberg states with very high angular momentum can be explained surprisingly well using classical mechanics. In this paper, we explain the reason behind this striking agreement between classical theory and experiment by showing that the classical and quantum dynamics of Rydberg electrons in weak, slowly varying external fields agree beyond the mandates of Ehrenfest's theorem. In particular, we show that the expectation values of angular momentum and Runge-Lenz vectors in hydrogenic eigenstates obey exactly the same perturbative equations of motion as the time averages of the corresponding classical variables. By time averaging the quantum dynamics over a Kepler period, we extend this special quantum-classical equivalence to Rydberg wave packets relatively well localized in energy. Finally, the perturbative equations hold well also for external fields beyond the Inglis-Teller limit, and in the case of elliptic states, which yield the appropriate quasiclassical initial conditions, the matching with classical mechanics is complete. ͓S1050-2947͑98͒05111-7͔
Physical Review A, 1999
Majumdar and Sharatchandra recently proposed a set of ''coherent states'' for the hydrogen atom ͓... more Majumdar and Sharatchandra recently proposed a set of ''coherent states'' for the hydrogen atom ͓Phys. Rev. A 56, R3322 ͑1997͔͒. These states satisfy some of the typical properties of coherent states, such as, for example, continuity in the parameters. The time evolution of these states is given by the classical evolution of the angle variables, and the expectation values of the quantum observables behave quasiclassically. However, those authors also claimed that, although one does not obtain exactly the same state after a Kepler period, the gross features of their wave packets do not change. We show that this is not correct, and that these wave packets do not remain localized on the classical variables, but spread rapidly over the Keplerian orbit. The localization properties of these states do not improve in the limit of large quantum numbers.
![Research paper thumbnail of Erratum: “Coherent stabilization of zero-electron-kinetic-energy states” [J. Chem Phys. 110, 7658 (1999)]](https://attachments.academia-assets.com/81955248/thumbnails/1.jpg)
](The Journal of Chemical Physics, 1999
The Journal of Chemical Physics, 1998
We present a comprehensive classical model of large-scale angular momentum transfer in alkali Ryd... more We present a comprehensive classical model of large-scale angular momentum transfer in alkali Rydberg atoms by collisions with ions near or below the matching velocity, at which the speed of the colliding ion equals the classical, average speed of the Rydberg electron. We model the atomic quantum defect by perturbative methods, and obtain excellent agreement with experiments measuring the total collision cross section and the collisional population of individual high-l states. At the matching velocity, or right below it, the final distribution of angular momenta is peaked along the direction of the ionic beam, which indicates that the population of the ml sublevels is not uniform. We apply our model to intrashell {n,l}→{n,l′} transitions induced by ion-Rydberg collisions under zero-electron-kinetic-energy photoelectron spectroscopy (ZEKE-PES) conditions, and demonstrate that the excitation of ultra-long-lived Rydberg states via ion-Rydberg collisions is a two-step mechanism: First, a collision quenches th...
The Journal of Chemical Physics, 1998
Recent experiments by Jones, Fu, and Gallagher [J. Chem. Phys. 106, 3578 (1997)] designed to mimi... more Recent experiments by Jones, Fu, and Gallagher [J. Chem. Phys. 106, 3578 (1997)] designed to mimic collisional effects on the lifetimes of ZEKE Rydberg states find that, in a circularly polarized microwave field, autoionization lifetimes of atomic Rydberg states exceed those in a linearly polarized field. Surprisingly, however, the lifetimes not only do not display the expected n5 scaling but are essentially independent of n for most of the states prepared in the experiment. Similar observations were made by Vrakking and Lee [J. Chem. Phys. 102, 8818 (1995)] in studies of NO Rydberg states. We present a classical model that predicts n-independent behavior of autoionization lifetimes over essentially the same range of n-values as in the experiments of Jones, Fu, and Gallagher. The origin of this behavior is traced to the particular combinations of field strengths and frequency used in the experiment.
The Journal of Chemical Physics, 1999
The accuracy of zero-electron-kinetic-energy ͑ZEKE͒ photoelectron spectroscopy rests on the ultra... more The accuracy of zero-electron-kinetic-energy ͑ZEKE͒ photoelectron spectroscopy rests on the ultralong lifetimes of the high-n, high-l Rydberg states that are responsible for the ZEKE signal. However, a few-photon process cannot excite electrons directly from the low-l ground state to the high-l ZEKE manifold. In this paper we show that using the dynamics of Rydberg Stark states in slowly time dependent external fields it is possible to control coherently the angular momentum of Rydberg electrons, and therefore also their lifetime. We derive explicitly two different schemes based on simple, short electric dc pulses, which populate precisely those high-l, long-lived Rydberg states that are necessary for accurate ZEKE experiments. The high-l states that we construct are also Stark eigenstates, therefore a moderate dc external field can eventually enforce cylindrical symmetry and lock the ZEKE electrons in the stable, long-lived high-l manifold.
Journal of physics, Jun 19, 1998
We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduc... more We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasiclassically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit.
The Journal of Physical Chemistry A, 1997
The Journal of Chemical Physics, 1997
Zero-electron-kinetic-energy photoelectron spectroscopy (“ZEKE-PES”) is based on the pulsed field... more Zero-electron-kinetic-energy photoelectron spectroscopy (“ZEKE-PES”) is based on the pulsed field ionization of long lived Rydberg states (ZEKE states); it is generally accepted that ZEKE states have large angular momentum l, which quenches electron-core interactions, but how they acquire it remains a matter of dispute. We show that {nl}→{nl′} ion-Rydberg collisions are a viable and prominent mechanism for the excitation of large-l Rydberg states. We elucidate the dynamics by an exactly solvable classical model which provides a transparent and intuitive picture of the excitation of high-l states. By a geometric interpretation of the dynamics we are able to predict for which values of the impact parameter and reduced velocity of the incoming ion a change of the angular momentum of the state becomes possible. We pay particular attention to the influence of the quantum defect, δl, on the {nl}→{nl′} cross section and demonstrate that, for small initial angular momenta, δl is itself a major contributor to the ...
International Journal of Bifurcation and Chaos, 1995
We study the spectral statistics of three triangular quantum billiards. We show that for an ergod... more We study the spectral statistics of three triangular quantum billiards. We show that for an ergodic billiard the nearest neighbor spacings distribution in the low energy regime is strongly influenced by a neighboring integrable domain (equilateral triangle). With increasing energy we observe a transition towards a more chaotic-like pattern. We also show that for all three triangles the properties of the spectral distributions depend heavily on the energy range considered. This is specially true for the spectral rigidity, because of its essentially local character. The features of the distributions do not depend strongly on the genus of classical billiards.
Physical Review A, 1999
We predict and confirm numerically the existence of localized Rydberg wave packets that travel on... more We predict and confirm numerically the existence of localized Rydberg wave packets that travel on classical elliptical trajectories with negligible spreading. These wave packets are supported by a resonant circularly polarized microwave field, and we study them by a semiclassical action-angle representation.
We study the dispersion of the “temporally stable ” coherent states for the hydrogen atom introdu... more We study the dispersion of the “temporally stable ” coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasiclassically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit. PACS numbers: 03.65.Ca, 32.80.Rm, 33.80.Rv – To appear in J. Phys. A 1. Temporally stable coherent states for the hydrogen atom In recent years accurate experimental results have generated renewed interest [1– 13] in a long standing problem of quantum physics, which was addressed, albeit unsuccessfully, already in 1926 by Schrödinger himself [14]: that is the problem of constructing localized, non-spreading wave packets in the hydrogen atom which travel along the classical trajectories (Keple...
J Phys a Math Gen, 1998
We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduc... more We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasiclassically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit.
Thesis Georgia Institute of Technology Source Dai B 58 06 P 3100 Dec 1997 225 Pages, Dec 1, 1997
Physical Review E - PHYS REV E, 1994
In this paper we discover a generic structure in the eigenfunctions of quantum billiards, namely,... more In this paper we discover a generic structure in the eigenfunctions of quantum billiards, namely, scarring by families of stable periodic orbits in a nonchaotic system. Our study is conducted on two different triangular billiards, one an ergodic system and the other a ``pseudointegrable'' billiard. Surprisingly, we detect scars in regions which contain no periodic orbits. The periodic orbits responsible for scarring reside in a ``neighboring'' triangle. Such orbits show a more complex phase space structure than the ``bouncing ball'' trajectories of the stadium billiard. While diffuse nodal structure is usually the antithesis of scarring, we show that in some eigenstates it is supported by extensive families of stable periodic orbits.
Pramana, 1995
A new scheme for computing the eigenvalues and eigenstates of the Laplacian with Dirichlet bounda... more A new scheme for computing the eigenvalues and eigenstates of the Laplacian with Dirichlet boundary conditions on arbitrary triangular domains is presented. Its reliability is tested by comparing numerical results with analytical ones whenever possible. The computation of eigenvalues shows a good agreement with analytical results. The procedure is shown to give accurate results also in the case of eigenfunctions computation. Finally, the sensitivity of our scheme to the geometry of the domain is discussed and the algorithm is shown to detect small changes in the shape of the domain.
Physical Review Letters, 1995
A Comment on the Letter by Francesco Benvenuto, Guilio Casata and D. L. Shepelyansky, Phys. Rev. ... more A Comment on the Letter by Francesco Benvenuto, Guilio Casata and D. L. Shepelyansky, Phys. Rev. Lett. 72, 1818 (1994).
Physical Review A, 1998
The complex processes leading to the collisional population of ultra-long-lived Rydberg states wi... more The complex processes leading to the collisional population of ultra-long-lived Rydberg states with very high angular momentum can be explained surprisingly well using classical mechanics. In this paper, we explain the reason behind this striking agreement between classical theory and experiment by showing that the classical and quantum dynamics of Rydberg electrons in weak, slowly varying external fields agree beyond the mandates of Ehrenfest's theorem. In particular, we show that the expectation values of angular momentum and Runge-Lenz vectors in hydrogenic eigenstates obey exactly the same perturbative equations of motion as the time averages of the corresponding classical variables. By time averaging the quantum dynamics over a Kepler period, we extend this special quantum-classical equivalence to Rydberg wave packets relatively well localized in energy. Finally, the perturbative equations hold well also for external fields beyond the Inglis-Teller limit, and in the case of elliptic states, which yield the appropriate quasiclassical initial conditions, the matching with classical mechanics is complete. ͓S1050-2947͑98͒05111-7͔
Physical Review A, 1999
Majumdar and Sharatchandra recently proposed a set of ''coherent states'' for the hydrogen atom ͓... more Majumdar and Sharatchandra recently proposed a set of ''coherent states'' for the hydrogen atom ͓Phys. Rev. A 56, R3322 ͑1997͔͒. These states satisfy some of the typical properties of coherent states, such as, for example, continuity in the parameters. The time evolution of these states is given by the classical evolution of the angle variables, and the expectation values of the quantum observables behave quasiclassically. However, those authors also claimed that, although one does not obtain exactly the same state after a Kepler period, the gross features of their wave packets do not change. We show that this is not correct, and that these wave packets do not remain localized on the classical variables, but spread rapidly over the Keplerian orbit. The localization properties of these states do not improve in the limit of large quantum numbers.
The Journal of Chemical Physics, 1999
The Journal of Chemical Physics, 1998
We present a comprehensive classical model of large-scale angular momentum transfer in alkali Ryd... more We present a comprehensive classical model of large-scale angular momentum transfer in alkali Rydberg atoms by collisions with ions near or below the matching velocity, at which the speed of the colliding ion equals the classical, average speed of the Rydberg electron. We model the atomic quantum defect by perturbative methods, and obtain excellent agreement with experiments measuring the total collision cross section and the collisional population of individual high-l states. At the matching velocity, or right below it, the final distribution of angular momenta is peaked along the direction of the ionic beam, which indicates that the population of the ml sublevels is not uniform. We apply our model to intrashell {n,l}→{n,l′} transitions induced by ion-Rydberg collisions under zero-electron-kinetic-energy photoelectron spectroscopy (ZEKE-PES) conditions, and demonstrate that the excitation of ultra-long-lived Rydberg states via ion-Rydberg collisions is a two-step mechanism: First, a collision quenches th...
The Journal of Chemical Physics, 1998
Recent experiments by Jones, Fu, and Gallagher [J. Chem. Phys. 106, 3578 (1997)] designed to mimi... more Recent experiments by Jones, Fu, and Gallagher [J. Chem. Phys. 106, 3578 (1997)] designed to mimic collisional effects on the lifetimes of ZEKE Rydberg states find that, in a circularly polarized microwave field, autoionization lifetimes of atomic Rydberg states exceed those in a linearly polarized field. Surprisingly, however, the lifetimes not only do not display the expected n5 scaling but are essentially independent of n for most of the states prepared in the experiment. Similar observations were made by Vrakking and Lee [J. Chem. Phys. 102, 8818 (1995)] in studies of NO Rydberg states. We present a classical model that predicts n-independent behavior of autoionization lifetimes over essentially the same range of n-values as in the experiments of Jones, Fu, and Gallagher. The origin of this behavior is traced to the particular combinations of field strengths and frequency used in the experiment.
The Journal of Chemical Physics, 1999
The accuracy of zero-electron-kinetic-energy ͑ZEKE͒ photoelectron spectroscopy rests on the ultra... more The accuracy of zero-electron-kinetic-energy ͑ZEKE͒ photoelectron spectroscopy rests on the ultralong lifetimes of the high-n, high-l Rydberg states that are responsible for the ZEKE signal. However, a few-photon process cannot excite electrons directly from the low-l ground state to the high-l ZEKE manifold. In this paper we show that using the dynamics of Rydberg Stark states in slowly time dependent external fields it is possible to control coherently the angular momentum of Rydberg electrons, and therefore also their lifetime. We derive explicitly two different schemes based on simple, short electric dc pulses, which populate precisely those high-l, long-lived Rydberg states that are necessary for accurate ZEKE experiments. The high-l states that we construct are also Stark eigenstates, therefore a moderate dc external field can eventually enforce cylindrical symmetry and lock the ZEKE electrons in the stable, long-lived high-l manifold.