arXiv subjects

K. Andrzejewski

Publications and source records attributed to K. Andrzejewski.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics of spinning particles in pp-wave spacetimes

In this work, we study the dynamics of a spinning particle in pp-wave spacetimes; in particular, plane gravitational waves and impulsive shockwaves. We present a step-by-step procedure that reduces the original problem to the dynamics of the transverse coordinates, in direct analogy with geodesic motion. To achieve this, we use an appropriate spin supplementary condition, Hamiltonian formulations (including a non-minimal one), and constants of motion associated with conformal Killing fields.

gr-qc↗

arXiv2025

Group-theoretical analysis of quantum complexity: the oscillator group case

Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our approach is based on the observation that the whole problem refers to the structure of the underlying group. The questions concerning the complexity of particular unitaries are solved by lifting the abstract structure to the operator level by considering the relevant unitary representation. For the class of right-invariant metrics obeying natural invariance condition we solve the geodesic equations on oscillator group. The solution is given explicitly in terms of elementary functions. Imposing the boundary conditions yield a transcendental equation and the length of the geodesic is given in terms of the solutions to the latter. Since the unitary irreducible representations of oscillator group are classified this allows us to compute, at least in principle, the complexity of any unitary operator belonging to the representation.

quant-ph↗

arXiv2025

The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes

We study the area and volume laws for entanglement of free quantum scalar fields. In addition to the entropy, we use the notion of the capacity of entanglement, which measures entropy fluctuations. We consider flat spacetimes as well as the curved ones relevant for cosmology. Moreover, we put special emphasis on quench phenomena and different geometries of the entangling surfaces. First, we show that, in the Minkowski spacetime, the capacity of entanglement, like entropy, exhibits the area law for two kinds of geometries of the entangling surfaces: the sphere and strip. Moreover, we show that the ratio of both quantities takes the same values for both surfaces. Next, we turn our attention to quenches. Namely, we analyse the dynamics of capacity; in particular, contribution of the volume and surface terms. Moreover, we compare these results with theoretical predictions resulting from the quasiparticles model. In the second part, we consider the above issues for the FLRW spaces; especially, for de Sitter space as well as a metric modeling the transition to radiation-dominated era. Finally, we analyse the abrupt quenches in de Sitter space.

hep-th↗

arXiv2024

Revisiting the dynamics of a charged spinning body in curved spacetime

We analyse the motion of the spinning body (in the pole-dipole approximation) in the gravitational and electromagnetic fields described by the Mathisson-Papapetrou-Dixon-Souriau equations. First, we define a novel spin condition for the body with the magnetic dipole moment proportional to spin, which generalizes the one proposed by Ohashi-Kyrian-Semer\'ak for gravity. As a result, we get the whole family of charged spinning particle models in the curved spacetime with remarkably simple dynamics (momentum and velocity are parallel). Applying the reparametrization procedure, for a specific dipole moment, we obtain equations of motion with constant mass and gyromagnetic factor. Next, we show that these equations follow from an effective Hamiltonian formalism, previously interpreted as a classical model of the charged Dirac particle.

gr-qc↗

arXiv2023

Evolution of capacity of entanglement and modular entropy in harmonic chains and scalar fields

We examine the temporal evolution of the modular entropy and capacity (in particular, the fluctuation of the entanglement entropy) for systems of time-dependent oscillators coupled by a (time-dependent) parameter. Such models, through the discretization procedure, fit into field theory problems arising from quench phenomena or non-static spacetimes. First, we compare the dynamics of the modular and Renyi entropies and derive the form of the modular capacity for the single time-dependent oscillator as well as chains with bipartite decompositions. In the latter case we analyse distinguished periodicities during the evolution and the role of various boundary conditions. Next, we focus on the dynamics of the capacity (fluctuation) of entanglement. We compare the results obtained with the predictions of quasiparticles models; in particular, we obtain a theoretical value of the initial slope of the capacity for abrupt quenches. We study also continuous protocols with the frequency that vanishes at plus (and minus) infinity, including a model in which the frequency tends to the Dirac delta. All the above issues are discussed with the emphasis on the analytical methods.

hep-th↗

arXiv2022

Dynamics of entropy and information of time-dependent quantum systems: exact results

Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied. First, we show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic fields, the increase of the entropy and dynamics of the Fisher information can be directly described and related. To illustrate these results we have considered several examples for which all the relations take the elementary form. Moreover, we show that the integrals of (geodesic) motion associated with some conformal Killing vectors lead to the Ermakov-Lewis invariants for the considered electromagnetic fields. Next, we explicitly work out the dynamics of the entanglement entropy of the oscillators coupled by a continuous time-dependent parameter as well as we analyse some aspects of quantum-classical transition (in particular decoherence). Finally, we study in some detail the behavior of quantum quenches (in the presence of the critical points) for the case of mutually non-interacting non-relativistic fermions in a harmonic trap.

quant-ph↗

arXiv2021

Global propagation of massive quantum fields in the plane gravitational waves and electromagnetic backgrounds

The behavior of massive quantum fields in the general plane wave spacetime and external, non-plane, electromagnetic waves is studied. The asymptotic conditions, the "in" ("out") states and the cross sections are analysed. It is observed that, despite of the singularities encountered, the global form of these states can be obtained: at the singular points the Dirac delta-like behavior emerges and there is a discrete change of phase of the wave function after passing through each singular point. The relations between these phase corrections and local charts are discussed. Some examples of waves of infinite range (including the circularly polarized ones) are presented for which the explicit form of solutions can be obtained. All these results concern both the scalar as well as spin one-half fields; in the latter case the change of the spin polarization after the general sandwich wave has passed is studied.

gr-qc↗

arXiv2020

Conformal symmetries and integrals of the motion in pp waves with external electromagnetic fields

The integrals of the motion associated with conformal Killing vectors of a curved space-time with an additional electromagnetic background are studied for massive particles. They involve a new term which might be non-local. The difficulty disappears for pp-waves, for which explicit, local conserved charges are found. Alternatively, the mass can be taken into account by "distorting" the conformal Killing vectors. The relation of these non-point symmetries to the charges is analysed both in the Lagrangian and Hamiltonian approaches, as well as in the framework of Eisenhart-Duval lift.

gr-qc↗

arXiv2019

From polarized gravitational waves to analytically solvable electromagnetic beams

Using the correspondence between solutions of gravitational and gauge theories (the so-called classical double copy conjecture) some electromagnetic fields with vortices are constructed, for which the Lorentz force equations are analytically solvable. The starting point is a certain class of plane gravitational waves exhibiting the conformal symmetry. The notion of the Niederer transformation, crucial for the solvability, is analysed in the case of the Lorentz force equation on the curved spacetimes as well as its derivation by means of integrals of motion (associated with conformal generators preserving these vortices) is presented. Furthermore, some models discussed recently in the context of the intense laser beams are constructed from their gravitational counterparts, with the special emphasis put on the focusing property, and new solvable examples are presented.

hep-th↗

arXiv2019

The covariance of chiral fermions theory

The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles.

hep-th↗

arXiv2019

Niederer's transformation, time-dependent oscillators and polarized gravitational waves

It is noted that the Niederer transformation can be used to find the explicit relation between time-dependent linear oscillators, including the most interesting case when one of them is harmonic. A geometric interpretation of this correspondence is provided by certain subclasses of pp-waves; in particular the ones strictly related to the proper conformal transformations. This observation allows us to show that the pulses of plane gravitational wave exhibiting the maximal conformal symmetry are analytically solvable. Particularly interesting is the circularly polarized family for which some aspects (such as the classical cross section, velocity memory effect and impulsive limit) are discussed in more detail. The role of the additional integrals of motion, associated with the conformal generators, is clarified by means of Ermakov-Lewis invariants. Possible applications to the description of interaction of electromagnetic beams with matter are also indicated.

gr-qc↗

arXiv2018

Memory effect, conformal symmetry and gravitational plane waves

We discuss in some detail the interaction of classical particles, including the scattering and memory effect, with a pulse of gravitational plane wave. The key point is the conformal symmetry of gravitational plane waves. In particular, we obtain, in the limit of short pulse, some results for impulsive gravitational waves. Furthermore, in the general case, we give certain conditions which allow us to completely describe the interaction in terms of the singular Baldwin-Jeffery-Rosen coordinates.

gr-qc↗

arXiv2015

Nonlocal dynamics and infinite non-relativistic conformal symmetries

We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite dimensional symmetry algebra, containing the Virasoro algebra, which can be considered as a generalization of the non-relativistic conformal symmetries to the infinite order. Moreover, this nonlocal extension resembles to some extent the string model and on the quantum level it leads to the centrally extended Virasoro algebra.

hep-th↗

arXiv2015

Generalized Niederer's transformation for quantum Pais-Uhlenbeck oscillator

We extend, to the quantum domain, the results obtained in [Nucl. Phys. B 885 (2014) 150] and [Phys. Lett. B 738 (2014) 405] concerning the Niederer's transformation for the Pais-Uhlenbeck oscillator. Namely, the quantum counterpart (an unitary operator) of the transformation which maps the free higher derivatives theory into the Pais-Uhlenbeck oscillator is constructed. Some consequences of this transformation are discussed.

hep-th↗

arXiv2015

Quantum conformal mechanics

The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its universal covering). The coordinate representation is defined as the basis diagonalizing the special conformal generator K. It is indicated how the resulting theory emerges from the canonical/geometric quantization of the Hamiltonian dynamics on the relevant coadjoint orbits.

hep-th↗

arXiv2014

Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator

The study of the symmetry of Pais-Uhlenbeck oscillator initiated in [Nucl. Phys. B 885 (2014) 150] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton-Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory) is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.

hep-th↗

arXiv2014

Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator

Dynamical systems invariant under the action of the l-conformal Newton-Hooke algebras are constructed by the method of nonlinear realizations. The relevant first order Lagrangians together with the corresponding Hamiltonians are found. The relation to the Galajinsky and Masterov [Phys. Lett. B 723 (2013) 190] approach as well as the higher derivatives formulation is discussed. The generalized Niederer's transformation are presented which relate the systems under consideration to those invariant under the action of the l-conformal Galilei algebra [Nucl. Phys. B 876 (2013) 309]. As a nice application of these results an analogue of Niederer's transformation, on the Hamiltonian level, for the Pais-Uhlenbeck oscillator is constructed.

hep-th↗

arXiv2013

Free Particle Wave Function and Niederer's Transformation

The solutions to the free Schroedinger equation discussed by P. Strange (arXiv: 1309.6753) and A. Aiello (arXiv: 1309.7899) are analyzed. It is shown that their properties can be explained with the help of Niederer's transformation.

quant-ph↗