arXiv subjects

Iwo Bialynicki-Birula

Publications and source records attributed to Iwo Bialynicki-Birula.

67 records · Page 4Linked to original sources

arXiv2004

Harmonic oscillator in a rotating trap: Complete solution in 3D

Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case, for an arbitrary orientation of the rotation axis, there are two regions of instability with different characteristics. The analysis of the quantum-mechanical problem is made simple due to a direct connection between the classical mode vectors and the quantum-mechanical wave functions. This connection is obtained via the matrix Riccati equation that governs the time evolution of squeezed states of the harmonic oscillator. It is also shown that the inclusion of gravity leads to a resonant behavior -- the particles are expelled from the trap.

quant-ph↗

arXiv2004

Particle beams guided by electromagnetic vortices: New solutions of the Lorentz, Schrödinger, Klein-Gordon, and Dirac equations

It is shown that electromagnetic vortices can act as beam guides for charged particles. The confinement in the transverse directions is due to the rotation of the electric and magnetic fields around the vortex line. Large class of exact solutions describing various types of relativistic beams formed by an electromagnetic wave with a simple vortex line is found both in the classical and in the quantum case. In the second case, the motion in the transverse direction is fully quantized. Particle trajectories trapped by a vortex are very similar to those in a helical undulator.

physics.class-ph↗

arXiv2003

Electromagnetic vortex lines riding atop null solutions of the Maxwell equations

New method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann-Silberstein vector $({\bm E} + i{\bm B})/\sqrt{2}$ is multiplied by a complex scalar function $ϕ$. Such a multiplication may lead to new solutions of the Maxwell equations only when the electromagnetic field is null, i.e. when both relativistic invariants vanish. In general, zeroes of the $ϕ$ function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.

physics.class-ph↗

arXiv2003

Vortex lines of the electromagnetic field

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schroedinger wave mechanics to Maxwell theory. It is shown that time evolution of vortex lines has universal features; in Maxwell theory it is very similar to that in Schroedinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of Maxwell equations with embedded vortex lines are given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.

physics.class-ph↗

arXiv2002

Center-of-mass motion in many-body theory of BEC

The method of generating a family of new solutions starting from any wave function satisfying the nonlinear Schrödinger equation in a harmonic potential proposed recently [ J. J. Garc\'ıa-Ripoll, V. M. Pérez-Garc\'ıa, and V. Vekslerchik, Phys. Rev. E {\bf 64}, 056602 (2001)] is extended to many-body theory of mutually interacting particles. Our method is based on a generalization of the displacement operator known in quantum optics and results in the separation of the center of mass motion from the internal dynamics of many-body systems. The center of mass motion is analyzed for an anisotropic rotating trap and a region of instability for intermediate rotational velocities is predicted.

quant-ph↗

arXiv2001

Motion of vortex lines in nonlinear wave mechanics

We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schroedinger equation with harmonic forces. We also argue that under certain conditions the influence of the contact nonlinearity on the motion of vortex lines is negligible. The present analysis adds new weight to our previous conjecture that the topological features of vortex dynamics are to a large extent universal.

quant-ph↗

arXiv2000

Time Evolution of Quantum Fractals

We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential and free particle. The box-counting dimension of the probability density $P_t(x)=|Ψ(x,t)|^2$ is shown not to change during the time evolution. We prove a universal relation $D_t=1+D_x/2$ linking the dimensions of space cross-sections $D_x$ and time cross-sections $D_t$ of the fractal quantum carpets.

quant-ph↗

arXiv2000

Squeezing of electromagnetic field in a cavity by electrons in Trojan states

The notion of the Trojan state of a Rydberg electron, introduced by I.Bialynicki-Birula, M.Kaliński, and J.H.Eberly (Phys. Rev. Lett. 73, 1777 (1994)) is extended to the case of the electromagnetic field quantized in acavity. The shape of the electronic wave packet describing the Trojan state is practically the same as in the previously studied externally driven system. The fluctuations of the quantized electromagnetic field around its classical value exhibit strong squeezing. The emergence of Trojan states in the cylindrically symmetrical system is attributed to spontaneous symmetry braking.

quant-ph↗

arXiv1999

Motion of vortex lines in quantum mechanics

Exact analytic solutions of the time dependent Schrodinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are identified. Vortex creation and annihilation and vortex interactions are illustrated in the special cases of the free motion, the motion in the harmonic potential, and in the constant magnetic field. Similar analysis of the vortex motions is carried out also for a relativistic wave equation.

quant-ph↗

arXiv1998

Nonstandard introduction to squeezing of the electromagnetic field

This article contains a review of an alternative theory of squeezing, based entirely on the wave function description of the squeezed states. Quantum field theoretic approach is used to describe the squeezing of the electromagnetic field in its most complete form that takes into account temporal and spatial characteristics of the squeezed state. An analog of the Wigner function for the full electromagnetic field is introduced and expressed in terms of second order correlation functions. The field-theoretic approach enables one to study the propagation of the ``squeezing wave'' in space-time. A simple example of weak squeezing, that allows for all calculations to be done analytically, is discussed in detail.

quant-ph↗

arXiv1998

The Fermi accelerator in atom optics

We study the classical and quantum dynamics of a Fermi accelerator realized by an atom bouncing off a modulated atomic mirror. We find that in a window of the modulation amplitude dynamical localization occurs in both position and momentum. A recent experiment [A. Steane, P. Szriftgiser, P. Desbiolles, and J. Dalibard, Phys. Rev. Lett. {\bf 74}, 4972 (1995)] shows that this system can be implemented experimentally.

quant-ph↗

arXiv1993

Simple relativistic model of a finite-size particle

Soluble model of a relativistic particle describing a bag of matter with fixed radius held together in perfect balance by a self-consistent combination of three forces generated by electromagnetic and massive scalar and vector fields is presented. For realistic values of parameters the bag radius becomes that of a proton.

nucl-th↗

arXiv1993

Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata

A discretized time evolution of the wave function for a Dirac particle on a cubic lattice is represented by a very simple quantum cellular automaton. In each evolution step the updated value of the wave function at a given site depends only on the values at the nearest sites, the evolution is unitary and preserves chiral symmetry. Moreover, it is shown that the relationship between Dirac particles and cellular automata operating on two component objects on a lattice is indeed very close. Every local and unitary automaton on a cubic lattice, under some natural assumptions, leads in the continuum limit to the Weyl equation. The sum over histories is evaluated and its connection with path integrals and theories of fermions on a lattice is outlined.

hep-th↗