Papers by Tomasz Radozycki
Molecular Physics, Sep 1, 2016
The probability density distributions for the ground states of certain model systems in quantum m... more The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by incorporating into them the Heisenberg uncertainty relation between position and momentum. Even the crude form of this incorporation makes the agreement between classical and quantum distributions unexpectedly good, except for the small area, where classical momenta are large. It is demonstrated that the slight improvement of this form, makes the classical distribution very similar to the quantum one in the whole space. The obtained results are much better than those from the WKB method. The paper is devoted to ground states, but the method applies to excited states too.
Physical Review A, Sep 1, 1993
We investigate multiphoton ejection probability of strongly bound electrons in relativistically i... more We investigate multiphoton ejection probability of strongly bound electrons in relativistically intense laser fields. A solvable model of a Klein-Gordon electron bound in a finite-range separable potential and interacting with a circularly polarized plane-wave field is used for the analysis. For binding energies of the order of several keV the rates of electron ejection for m=100 eV are found to be significant at relativistic intensities but are extremely small for m=10 eV. For lower binding energies spectra are obtained for the available COz laser frequency (m=0. 117 eV) and Nd laser frequency (~=1.169 eV) Numerical results show the stabilization efFect for both relativistic and nonrelativistic intensities and subthreshold frequencies.
Physical review, Jan 11, 2021
A simple analytical way of creating superpositions of Bessel-Gaussian light beams with knotted no... more A simple analytical way of creating superpositions of Bessel-Gaussian light beams with knotted nodal lines is proposed. It is based on the equivalence between the paraxial wave equation and the two-dimensional Schrödinger equation for a free particle. The 2D Schrödinger propagator is expressed in terms of Bessel functions, which allows to obtain directly superpositions of beams with a desired topology of nodal lines. Four types of knots are constructed in the explicit way: the unknot, the Hopf link, the Borromean rings and the trefoil. It is also shown, using the example of the figure-eight knot, that more complex structures require larger number of constituent beams as well as high precision both from the numerical and the experimental side. A tiny change of beam's intensity can lead to the knot "switching".
Physical review, Jun 2, 2016
The motion of a neutral atom endowed with a magnetic moment interacting with the magnetic field i... more The motion of a neutral atom endowed with a magnetic moment interacting with the magnetic field is determined from the Ehrenfest-like equations of motion. These equations for the average values of the translational and spin degrees of freedom are derived from the Schrödinger-Pauli wave equation and they form a set of nine coupled nonlinear evolution equations. The numerical and analytic solutions of these equations are obtained for the combination of the rotating magnetic field of a wave carrying orbital angular momentum and a static magnetic field. The running wave traps the atom only in the transverse direction while the standing wave traps the atom also in the direction of the beam.
Acta Physica Polonica A, Dec 1, 2001
W e ex tend our pre viou s analysi s of the motion of vortex lines in wave me chanics to the case... more W e ex tend our pre viou s analysi s of the motion of vortex lines in wave me chanics to the case of more ela borate vortex patterns and to a rotatin g harmonic trap .
Journal of Modern Optics, Jan 23, 2020
It is shown, within classical mechanics, that the field of an electromagnetic vortex is capable o... more It is shown, within classical mechanics, that the field of an electromagnetic vortex is capable of capturing and guiding neutral molecules endowed with a permanent electric dipole moment (PEDM). Similarly as in the case of the magnetic field applied to elementary particles or atoms, this effect turns out to be very delicate because of the small values of PEDM observed in real molecules. They amount to 2 × 10 5 efm (electron charge × fermi) or less, which requires the use of very strong electric fields. It has also been observed that there exists a threshold in field strength above which the particles are ejected from the trap. Trajectories of guided particles are usually quite chaotic, which is a consequence of non-linearity of the equations of motion. With a very special and precise adjustment of parameters, a regular (i.e., circular, in the transverse plane) trajectory can be obtained. The presence of an additional constant electric field pointing along the direction of the wave propagation might help to achieve the necessary tuning and realize such trajectories.
Acta Physica Polonica B, 2013
This paper addresses the singular 1-soliton solution of the K(m, n) equation that is being consid... more This paper addresses the singular 1-soliton solution of the K(m, n) equation that is being considered with generalized evolution. The ansatz method will be used to extract the singular 1-soliton solution of this equation. A couple of constraint conditions will fall out in order for the singular soliton solutions to exist. Subsequently, the special cases of this equation will be studied. They are the KdV and the mKdV equations where the extended (G /G)-expansion method will be employed to extract a few nonlinear wave solutions.
Journal of physics, Nov 7, 1990
Page 1. The properties of the electromagnetic field around the excited hydrogen atom-a quantum fi... more Page 1. The properties of the electromagnetic field around the excited hydrogen atom-a quantum field theory approach This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1990 J. Phys. A: Math. Gen. 23 4925 ...
arXiv (Cornell University), Mar 11, 2021
A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembe... more A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the prefactor all basic beams of cylindrical character can be easily obtained. This refers to Gaussian, Bessel-Gaussian, modified Bessel-Gaussian, Laguerre-Gaussian and Kummer-Gaussian (i.e., Hypergeometric-Gaussian) beams although potentially other beams can come into play as well. For instance a new type of a beam that can be derived in this way is described through the incomplete gamma function so it may be called a γ beam.
arXiv (Cornell University), Jul 10, 2008
The instanton-antiinstnton contributions to the qq bound state pole in the four-point Green funct... more The instanton-antiinstnton contributions to the qq bound state pole in the four-point Green function in the Schwinger Model are calculated. It is shown that these configurations, thanks to the cancellation of all unwanted terms, are responsible for the restoration of the perfect factorizability of the residue.
arXiv (Cornell University), Jun 2, 2017
The propagation of electromagnetic waves trapped within dielectric and magnetic layers is conside... more The propagation of electromagnetic waves trapped within dielectric and magnetic layers is considered. The description within the three-dimensional theory is compared with the simplified analysis in two dimensions. Two distinct media configurations with different topology are dealt with: a plane slab and a hollow cylinder. Choosing the appropriate values for the geometrical parameters (layer thickness, radius of the cylinder) and for the electromagnetic properties of the media one can trap exactly one mode corresponding to that obtained within the two-dimensional electromagnetism. However, the symmetry between electric and magnetic fields suggests, that the two versions of the simplified electromagnetism ought to be taken into account. Its usual form is incomplete to describe all modes. It is also found that there is a domain of optimal values of parameters for which the 2D model works relatively correctly. In the case of a cylindrical surface we observe, however, several differences which are attributed to the curvature of the layer, and which exclude the propagation of evanescent modes. The two-dimensional electrodynamics, whichever form used, turns out still too poor to describe the so called 'hybrid modes' excited in a real layer. The obtained results can be important for proper description of the propagating waves within thin layers for which 3D approach is not available due to mathematical complexity, and reducing the layer to a lower-dimensional structure seems the only possible option.
arXiv (Cornell University), May 30, 2014
The exact $q\bar{q}$ Bethe-Salpeter bound state amplitude is investigated in the space of relativ... more The exact $q\bar{q}$ Bethe-Salpeter bound state amplitude is investigated in the space of relative energy $E$ for fixed value of relative position. By means of approximate analysis it is shown to possess singularities in $E$ whenever one of the quarks reaches the energy threshold for the creation of certain number of Schwinger bosons. These results are afterwards confirmed by numerical plots.
arXiv (Cornell University), Jul 7, 2023
arXiv (Cornell University), Jul 7, 2023
European Physical Journal C, Sep 1, 2015
The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in t... more The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in the twodimensional massless quantum electrodynamics (the socalled Schwinger model) are considered. It is shown that while boosting a bound state (a 'meson') this amplitude is subject to approximate Lorentz contraction. The effect is exact for large separations of constituent particles ('quarks'), while for small distances the deviation is more significant. For this phenomenon to appear, the full function, i.e. with the inclusion of all instanton contributions, has to be considered. The amplitude in each separate topological sector does not exhibit such properties.
European Physical Journal C, Sep 1, 2014
The exact qq Bethe-Salpeter bound state amplitude is investigated in the space of relative energy... more The exact qq Bethe-Salpeter bound state amplitude is investigated in the space of relative energy E for a fixed value of the relative position. By means of an approximate analysis it is shown to possess singularities in E whenever one of the quarks reaches the energy threshold for the creation of a certain number of Schwinger bosons. These results are confirmed by plots of numerical results.
Physical review, Apr 26, 2013
The exact Bethe-Salpeter amplitude for the fermion-antifermion bound state in the Schwinger Model... more The exact Bethe-Salpeter amplitude for the fermion-antifermion bound state in the Schwinger Model is investigated. The dependence on the relative time and position in the center-of-mass frame in all contributing instanton sectors is analyzed. The same is accomplished for the relative energy and momentum variables. Several interesting properties of the amplitude are revealed. The explicit threshold structure is demonstrated.
Optics and Laser Technology, Mar 1, 2022
A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembe... more A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the prefactor all basic beams of cylindrical character can be easily obtained. This refers to Gaussian, Bessel-Gaussian, modified Bessel-Gaussian, Laguerre-Gaussian and Kummer-Gaussian (i.e., Hypergeometric-Gaussian) beams although potentially other beams can come into play as well. For instance a new type of a beam that can be derived in this way is described through the incomplete gamma function so it may be called a γ beam.
European Physical Journal C, 1999
Perturbation series for the electron propagator in the Schwinger Model is summed up in a direct w... more Perturbation series for the electron propagator in the Schwinger Model is summed up in a direct way by adding contributions coming from individual Feynman diagrams. The calculation shows the complete agreement between nonperturbative and perturbative approaches.
Physical Review A
Various superpositions of Bessel-Gaussian beams and modified Bessel Gaussian beams are considered... more Various superpositions of Bessel-Gaussian beams and modified Bessel Gaussian beams are considered. Two selected parameters characterizing these beams, with respect to which the superpositions are constructed, are the topological index n associated with the orbital angular momentum carried by the beam, and χ related to the dilation of the beam. It is shown that, from these modes, by choosing appropriate weighting factors, it is possible to create a number of well-and less-known solutions of the paraxial equation: Gaussian (shifted and non-shifted) beam, γ beam, Kummer-Gaussian beam, special hyperbolic Bessel-Gaussian beam, a certain special Laguerre-Gaussian beam, and generalized paraxial beams in hyperbolic and regular versions.
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Papers by Tomasz Radozycki