P. F. O'Mahony
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
P. F. O'Mahony has a total of 15 co-authors. Here are the top co-authors by number of shared publications:
- F. Mota-Furtado
Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
7 shared publications G. Alber
Abteilung für Quantenphysik, Universität Ulm, D-89069 Ulm, Germany
2 shared publicationsM. Rigo
Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 OEX, United Kingdom
2 shared publicationsW. Ihra
Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
2 shared publicationsA. Hamido
1 shared publication- Alexander Galstyan
Institute of Condensed Matter and Nanosciences, Université Catholique de Louvain, 2 Chemin du Cyclotron, Box L7.01.07, B-1348 Louvain-la-Neuve, Belgium
1 shared publication
Latest Publications
- 3 August 2016
- Published by American Physical Society (APS) in Physical Review A
- Vol. 94 (2) , 029901
Erratum: Reformulation of the strong-field approximation for light-matter interactions [Phys. Rev. A93, 023422 (2016)]
DOI:https://doi.org/10.1103/PhysRevA.94.029901
- 3 August 2016
- Published by American Physical Society (APS) in Physical Review A
- Vol. 94 (2) , 029901
Erratum: Reformulation of the strong-field approximation for light-matter interactions [Phys. Rev. A93, 023422 (2016)]
DOI:https://doi.org/10.1103/PhysRevA.94.029901
- 2 April 2007
- Published by American Physical Society (APS) in Physical Review E
- Vol. 75 (4) , 041102
Exact propagator for generalized Ornstein-Uhlenbeck processes
A closed form expression for the propagator is derived, in terms of modified Bessel functions, for the Fokker-Planck equation for a physically important generalization of the Ornstein-Uhlenbeck process where the diffusion constant is a function of the momentum. The closed form is found for the general case where and leads to the standard Gaussian form for . The propagator for the specific case is used to derive analytic expressions for probability distributions and correlation coefficients. An exact expression is found for the constant of proportionality for the anomalous diffusion of the mean-square displacement of a particle at short times.- 2 April 2007
- Published by American Physical Society (APS) in Physical Review E
- Vol. 75 (4) , 041102
Exact propagator for generalized Ornstein-Uhlenbeck processes
A closed form expression for the propagator is derived, in terms of modified Bessel functions, for the Fokker-Planck equation for a physically important generalization of the Ornstein-Uhlenbeck process where the diffusion constant is a function of the momentum. The closed form is found for the general case where and leads to the standard Gaussian form for . The propagator for the specific case is used to derive analytic expressions for probability distributions and correlation coefficients. An exact expression is found for the constant of proportionality for the anomalous diffusion of the mean-square displacement of a particle at short times.- 13 October 2006
- Published by American Physical Society (APS) in Physical Review A
- Vol. 74 (4) , 044102
Eigenfunctions and matrix elements for a class of eigenvalue problems with staggered ladder spectra
We present an alternate solution to an eigenvalue problem which arises in the study of the Fokker-Planck equation for generalized Ornstein-Uhlenbeck processes. We obtain the staggered ladder spectra found previously but in addition we obtain the normalized eigenfunctions in terms of associated Laguerre polynomials. The representation of the eigenfunctions in this form greatly simplifies the evaluation of matrix elements required in calculating ensemble averages and correlation coefficients for various observables. The solution to the eigenvalue problem is given in the generic and general cases.
- 13 October 2006
- Published by American Physical Society (APS) in Physical Review A
- Vol. 74 (4) , 044102
Eigenfunctions and matrix elements for a class of eigenvalue problems with staggered ladder spectra
We present an alternate solution to an eigenvalue problem which arises in the study of the Fokker-Planck equation for generalized Ornstein-Uhlenbeck processes. We obtain the staggered ladder spectra found previously but in addition we obtain the normalized eigenfunctions in terms of associated Laguerre polynomials. The representation of the eigenfunctions in this form greatly simplifies the evaluation of matrix elements required in calculating ensemble averages and correlation coefficients for various observables. The solution to the eigenvalue problem is given in the generic and general cases.
- 1 July 1998
- Published by American Physical Society (APS) in Physical Review A
- Vol. 58 (1) , 478-487
Measurement-induced quantum fluctuations and bistability of a relativistic electron in a Penning trap
A detailed quantum-mechanical description of an electron in a Penning trap is developed in which nonlinear relativistic effects as well as stochastic effects arising from radiative damping and the continuous measurement of the electronic motion are taken into account. A master equation is derived that describes the influence of these environmental effects on the bistable dynamics of the electron. Manifestations of measurement-induced fluctuations on the bistable dynamics of individual continuous measurement processes are investigated with the help of the quantum state diffusion model.
- 1 July 1998
- Published by American Physical Society (APS) in Physical Review A
- Vol. 58 (1) , 478-487
Measurement-induced quantum fluctuations and bistability of a relativistic electron in a Penning trap
A detailed quantum-mechanical description of an electron in a Penning trap is developed in which nonlinear relativistic effects as well as stochastic effects arising from radiative damping and the continuous measurement of the electronic motion are taken into account. A master equation is derived that describes the influence of these environmental effects on the bistable dynamics of the electron. Manifestations of measurement-induced fluctuations on the bistable dynamics of individual continuous measurement processes are investigated with the help of the quantum state diffusion model.
- 1 June 1997
- Published by American Physical Society (APS) in Physical Review A
- Vol. 55 (6) , 4263-4268
Three-particle breakup near threshold when the Wannier exponent diverges
Wannier theory predicts an infinite threshold exponent for the breakup of three charged particles if two of the particles have equal charges and the ratio of the charge of one of these to the charge of the third particle has the value (-4). We show that the Wannier picture of ridge propagation remains valid and that the threshold law changes to the form σ∝exp(-κ/). The classical and quantum results differ, which is in contrast to the generic Wannier case. We show that the classical limit of the threshold law explains the threshold behavior obtained numerically by classical trajectory calculations.- 1 June 1997
- Published by American Physical Society (APS) in Physical Review A
- Vol. 55 (6) , 4263-4268
Three-particle breakup near threshold when the Wannier exponent diverges
Wannier theory predicts an infinite threshold exponent for the breakup of three charged particles if two of the particles have equal charges and the ratio of the charge of one of these to the charge of the third particle has the value (-4). We show that the Wannier picture of ridge propagation remains valid and that the threshold law changes to the form σ∝exp(-κ/). The classical and quantum results differ, which is in contrast to the generic Wannier case. We show that the classical limit of the threshold law explains the threshold behavior obtained numerically by classical trajectory calculations.- 1 May 1997
- Published by American Physical Society (APS) in Physical Review A
- Vol. 55 (5) , 3724-3729
Rydberg wave packets in parallel electric and magnetic fields
The magnitude of the time autocorrelation function M between states excited by two Gaussian laser pulses is calculated for both hydrogen and rubidium atoms in parallel electric and magnetic fields. M is determined by a full quantum-mechanical calculation but the peaks are identified with the periods of the shortest periodic orbits of the corresponding classical system. Qualitative agreement is obtained with experimental results, however, discrepancies are found in the relative heights of the peaks.
- 1 May 1997
- Published by American Physical Society (APS) in Physical Review A
- Vol. 55 (5) , 3724-3729
Rydberg wave packets in parallel electric and magnetic fields
The magnitude of the time autocorrelation function M between states excited by two Gaussian laser pulses is calculated for both hydrogen and rubidium atoms in parallel electric and magnetic fields. M is determined by a full quantum-mechanical calculation but the peaks are identified with the periods of the shortest periodic orbits of the corresponding classical system. Qualitative agreement is obtained with experimental results, however, discrepancies are found in the relative heights of the peaks.
- 1 April 1997
- Published by American Physical Society (APS) in Physical Review A
- Vol. 55 (4) , 3250-3253
Threshold law for the triplet state for electron-impact ionization in the Temkin-Poet model
We derive the analytical threshold behavior for the triplet cross section for electron-impact ionization in the Temkin-Poet model. The analytical results indicate that the most recent numerical calculations may fail to reproduce the correct threshold behavior in an energy regime below about E=0.1 a.u. We also present an analytical expression for the energy distribution of the two electrons near threshold.
- 1 April 1997
- Published by American Physical Society (APS) in Physical Review A
- Vol. 55 (4) , 3250-3253
Threshold law for the triplet state for electron-impact ionization in the Temkin-Poet model
We derive the analytical threshold behavior for the triplet cross section for electron-impact ionization in the Temkin-Poet model. The analytical results indicate that the most recent numerical calculations may fail to reproduce the correct threshold behavior in an energy regime below about E=0.1 a.u. We also present an analytical expression for the energy distribution of the two electrons near threshold.
- 1 March 1997
- Published by American Physical Society (APS) in Physical Review A
- Vol. 55 (3) , 1665-1673
Quantum-state diffusion model and the driven damped nonlinear oscillator
We consider a driven damped anharmonic oscillator that classically leads to a bistable steady state and to hysteresis. The quantum counterpart for this system has an exact analytical solution in the steady state that does not display any bistability or hysteresis. We use quantum-state diffusion theory to describe this system and to provide a new perspective on the lack of hysteresis in the quantum regime so as to study in detail the quantum to classical transition. The analysis is also relevant to measurements of a single periodically driven electron in a Penning trap where hysteresis has been observed.
- 1 March 1997
- Published by American Physical Society (APS) in Physical Review A
- Vol. 55 (3) , 1665-1673
Quantum-state diffusion model and the driven damped nonlinear oscillator
We consider a driven damped anharmonic oscillator that classically leads to a bistable steady state and to hysteresis. The quantum counterpart for this system has an exact analytical solution in the steady state that does not display any bistability or hysteresis. We use quantum-state diffusion theory to describe this system and to provide a new perspective on the lack of hysteresis in the quantum regime so as to study in detail the quantum to classical transition. The analysis is also relevant to measurements of a single periodically driven electron in a Penning trap where hysteresis has been observed.