Iwo Białynicki-Birula - Academia.edu (original) (raw)

Uploads

Papers by Iwo Białynicki-Birula

AIP Conference Proceedings, 2007

Quantum mechanical uncertainty relations for the position and the momentum and for the angle and ... more Quantum mechanical uncertainty relations for the position and the momentum and for the angle and the angular momentum are expressed in the form of inequalities involving the Rényi entropies. These uncertainty relations hold not only for pure but also for mixed states. Analogous uncertainty relations are valid also for a pair of complementary observables (the analogs of x and p) in N-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Rényi entropies. The mathematical proofs of all the inequalities discussed in this paper can be found in Phys. Rev. A 74, No. 5 (2006); arXiv:quant-ph/0608116.

Classical and Quantum Gravity, 2015

The fluctuations of spacetime geometries at finite temperature are evaluated within the linearize... more The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The field configurations are described by the linearized Riemann-Weyl tensor without any reference to the metric. The probability distribution of various configurations is described by the Wigner functional of the gravitational field. It has a foam-like structure; dominant configurations are those with large changes of geometry at nearby points. In the high-temperature limit one obtains the Bolzmann distribution that enables one to identify the expression for the total energy of the gravitational field. The appearance of the same expression for the total energy when the gravitational field is treated as a collection of gravitons and as the high-temperature limit of the Wigner functional proves the consistency of the whole procedure. Striking differences are found between the fluctuations of the electromagnetic field and the gravitational field; among them is the divergence in the gravitational case of the probability distribution at zero temperature. This divergence is of the "infrared type" because it occurs in integrals over the wave vector at small k.

New Journal of Physics, 2014

It is pointed out that there exists an unambiguous definition of locality that enables one to dis... more It is pointed out that there exists an unambiguous definition of locality that enables one to distinguish local and nonlocal quantities. Observables of both types coexist in quantum optics but one must be very careful when attempting to measure them. A nonlocal observable which formally depends on the spatial position r cannot be locally measured without disturbing the measurements of this observable at all other positions.

Lecture Notes in Mathematics, 1985

ABSTRACT

Physical Review A, 1979

It is proved that the superradiant phase transition cannot occur in a general system of atoms or ... more It is proved that the superradiant phase transition cannot occur in a general system of atoms or molecules if only charges (not intrinsic magnetic moments) of the particles interact with a finite number of radiation modes in the dipole approximation.

A free quantum particle in two dimensions with vanishing angular momentum (s-wave) in the form of... more A free quantum particle in two dimensions with vanishing angular momentum (s-wave) in the form of a ring-shaped wave packet feels an attractive force towards the center of the ring, leading first to an implosion followed by an explosion.

Acta Physica Polonica Series B

ABSTRACT

Exact analytical solutions are presented for the time evolution of the density of pairs produced ... more Exact analytical solutions are presented for the time evolution of the density of pairs produced in the QED vacuum by a uniform electric field that is adiabatically switched on starting at minus infinity. Pair production is described by the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44, 1825 (1991)]. The explicit solution is obtained by an extension of the method of the spinorial decomposition to deal with a time-varying electric field. The main result of this work is that the pair density is an analytic function of the field strength; it can be expanded into a convergent power series. Therefore, the essential singularity present in the Schwinger formula is to be attributed to the infinitely long duration of the process of pair creation by a time-independent field.

Previous work [I. Bialynicki-Birula, Phys. Rev. Lett. {\bf 93}, 20402 (2004)] is extended to cove... more Previous work [I. Bialynicki-Birula, Phys. Rev. Lett. {\bf 93}, 20402 (2004)] is extended to cover more realistic examples of electromagnetic waves, viz. the Bessel beams. It is shown that electrons may be guided by a Bessel beam with nonvanishing orbital angular momentum. The mechanism for trapping the electrons near the electromagnetic vortex line of such a wave field is the

Nonlinear Waves: Classical and Quantum Aspects

We study the influence of the nonlinearity in the Schrödinger equation on the motion of quantum p... more We study the influence of the nonlinearity in the Schrödinger equation on the motion of quantum particles in a harmonic trap. In order to obtain exact analytic solutions, we have chosen the logarithmic nonlinearity. The unexpected result of our study is the existence in the presence of nonlinearity of two or even three coexisting Gaussian solutions.

Physical Review D, 2014

The changes in the cosmic microwave background (CMB) spectrum seen as an increase of temperature ... more The changes in the cosmic microwave background (CMB) spectrum seen as an increase of temperature due to a strong magnetic field are determined and their influence on the polarization of the radiation is exhibited. The effect is due to the coupling of the CMB photons to the magnetic field in the QED vacuum via the interaction with virtual pairs. In spite of the fact that the distortion of the CMB spectrum for magnetic fields that exist in the vicinity of magnetars is quite large, this effect is very difficult to detect at present because the required angular resolutions is not yet available.

The Angular Momentum of Light

The Angular Momentum of Light

Physical Review D, 1987

We show that the change of the phase of the wave function of a free relativistic spinning particl... more We show that the change of the phase of the wave function of a free relativistic spinning particle under the action of the Poincaré group is described by a certain universal connection in momentum space. This connection determines the parallel transport of the spin during the motion of the particle through external fields. In the special case of photons we

Physical Review A, 1976

A new formula for induced transition amplitudes in intense photon beams is derived which relates ... more A new formula for induced transition amplitudes in intense photon beams is derived which relates the photon-number description to the coherent-field description. According to this formula transition amplitudes describing processes in which m photons axe added to the intense one-mode beam or subtracted from that beam are equal to the Fourier coefficients of the corresponding amplitude in the external field, expanded with respect to the phase of the classical field. The same formula is used to study the expectation values of dynamical variables in n-photon states leading to the conclusion that for large n such states are very much like classical statistical states with a given amplitude and evenly distributed phase.

AIP Conference Proceedings, 2007

Quantum mechanical uncertainty relations for the position and the momentum and for the angle and ... more Quantum mechanical uncertainty relations for the position and the momentum and for the angle and the angular momentum are expressed in the form of inequalities involving the Rényi entropies. These uncertainty relations hold not only for pure but also for mixed states. Analogous uncertainty relations are valid also for a pair of complementary observables (the analogs of x and p) in N-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Rényi entropies. The mathematical proofs of all the inequalities discussed in this paper can be found in Phys. Rev. A 74, No. 5 (2006); arXiv:quant-ph/0608116.

Classical and Quantum Gravity, 2015

The fluctuations of spacetime geometries at finite temperature are evaluated within the linearize... more The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The field configurations are described by the linearized Riemann-Weyl tensor without any reference to the metric. The probability distribution of various configurations is described by the Wigner functional of the gravitational field. It has a foam-like structure; dominant configurations are those with large changes of geometry at nearby points. In the high-temperature limit one obtains the Bolzmann distribution that enables one to identify the expression for the total energy of the gravitational field. The appearance of the same expression for the total energy when the gravitational field is treated as a collection of gravitons and as the high-temperature limit of the Wigner functional proves the consistency of the whole procedure. Striking differences are found between the fluctuations of the electromagnetic field and the gravitational field; among them is the divergence in the gravitational case of the probability distribution at zero temperature. This divergence is of the "infrared type" because it occurs in integrals over the wave vector at small k.

New Journal of Physics, 2014

It is pointed out that there exists an unambiguous definition of locality that enables one to dis... more It is pointed out that there exists an unambiguous definition of locality that enables one to distinguish local and nonlocal quantities. Observables of both types coexist in quantum optics but one must be very careful when attempting to measure them. A nonlocal observable which formally depends on the spatial position r cannot be locally measured without disturbing the measurements of this observable at all other positions.

Lecture Notes in Mathematics, 1985

ABSTRACT

Physical Review A, 1979

It is proved that the superradiant phase transition cannot occur in a general system of atoms or ... more It is proved that the superradiant phase transition cannot occur in a general system of atoms or molecules if only charges (not intrinsic magnetic moments) of the particles interact with a finite number of radiation modes in the dipole approximation.

A free quantum particle in two dimensions with vanishing angular momentum (s-wave) in the form of... more A free quantum particle in two dimensions with vanishing angular momentum (s-wave) in the form of a ring-shaped wave packet feels an attractive force towards the center of the ring, leading first to an implosion followed by an explosion.

Acta Physica Polonica Series B

ABSTRACT

Exact analytical solutions are presented for the time evolution of the density of pairs produced ... more Exact analytical solutions are presented for the time evolution of the density of pairs produced in the QED vacuum by a uniform electric field that is adiabatically switched on starting at minus infinity. Pair production is described by the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44, 1825 (1991)]. The explicit solution is obtained by an extension of the method of the spinorial decomposition to deal with a time-varying electric field. The main result of this work is that the pair density is an analytic function of the field strength; it can be expanded into a convergent power series. Therefore, the essential singularity present in the Schwinger formula is to be attributed to the infinitely long duration of the process of pair creation by a time-independent field.

Previous work [I. Bialynicki-Birula, Phys. Rev. Lett. {\bf 93}, 20402 (2004)] is extended to cove... more Previous work [I. Bialynicki-Birula, Phys. Rev. Lett. {\bf 93}, 20402 (2004)] is extended to cover more realistic examples of electromagnetic waves, viz. the Bessel beams. It is shown that electrons may be guided by a Bessel beam with nonvanishing orbital angular momentum. The mechanism for trapping the electrons near the electromagnetic vortex line of such a wave field is the

Nonlinear Waves: Classical and Quantum Aspects

We study the influence of the nonlinearity in the Schrödinger equation on the motion of quantum p... more We study the influence of the nonlinearity in the Schrödinger equation on the motion of quantum particles in a harmonic trap. In order to obtain exact analytic solutions, we have chosen the logarithmic nonlinearity. The unexpected result of our study is the existence in the presence of nonlinearity of two or even three coexisting Gaussian solutions.

Physical Review D, 2014

The changes in the cosmic microwave background (CMB) spectrum seen as an increase of temperature ... more The changes in the cosmic microwave background (CMB) spectrum seen as an increase of temperature due to a strong magnetic field are determined and their influence on the polarization of the radiation is exhibited. The effect is due to the coupling of the CMB photons to the magnetic field in the QED vacuum via the interaction with virtual pairs. In spite of the fact that the distortion of the CMB spectrum for magnetic fields that exist in the vicinity of magnetars is quite large, this effect is very difficult to detect at present because the required angular resolutions is not yet available.

The Angular Momentum of Light

The Angular Momentum of Light

Physical Review D, 1987

We show that the change of the phase of the wave function of a free relativistic spinning particl... more We show that the change of the phase of the wave function of a free relativistic spinning particle under the action of the Poincaré group is described by a certain universal connection in momentum space. This connection determines the parallel transport of the spin during the motion of the particle through external fields. In the special case of photons we

Physical Review A, 1976

A new formula for induced transition amplitudes in intense photon beams is derived which relates ... more A new formula for induced transition amplitudes in intense photon beams is derived which relates the photon-number description to the coherent-field description. According to this formula transition amplitudes describing processes in which m photons axe added to the intense one-mode beam or subtracted from that beam are equal to the Fourier coefficients of the corresponding amplitude in the external field, expanded with respect to the phase of the classical field. The same formula is used to study the expectation values of dynamical variables in n-photon states leading to the conclusion that for large n such states are very much like classical statistical states with a given amplitude and evenly distributed phase.