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P. Kosinski

Publications and source records attributed to P. Kosinski.

At least 19 recordsLinked to original sources
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

A generalized Noether theorem for scaling symmetry

The recently discovered conserved quantity associated with Kepler rescaling is generalised by an extension of Noether's theorem which involves the classical action integral as an additional term. For a free particle the familiar Schroedinger dilations are recovered. A general pattern arises for homogeneous potentials. The associated conserved quantity allows us to derive the virial theorem. The relation to the Bargmann framework is explained and illustrated by exact plane gravitational waves.

math-ph↗
arXiv2014

Killing tensors and canonical geometry

The systematic derivation of constants of the motion, based on Killing tensors and the gauge covariant approach, is outlined. Quantum dots are shown to support second-, third- and fourth-rank Killing tensors.

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↗
arXiv2012

Newton-Hooke type symmetry of anisotropic oscillators

The rotation-less Newton--Hooke - type symmetry found recently in the Hill problem and instrumental for explaining the center-of-mass decomposition is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton-Hooke symmetry is recovered in the isotropic case. Star escape from a Galaxy is studied as application.

hep-th↗
arXiv2012

Note on lattice spin in graphene and "spin from isospin" phenomenon

It is well-known that the dynamics of low energy electron in graphene honeycomb lattice near the K/K' points can be described, in tight-binding approximation, by 2+1 massless Dirac equation. Graphene's spin equivalent, "pseudospin", arises from the degeneracy introduced by the honeycomb lattice's two inequivalent atomic sites per unit cell. Mecklenburg and Regan (Phys. Rev. Lett. 106 (2011), 116803) have shown that, contrary to the common view, the pseudospin has all attributes of real angular momentum. In some circumstances, the internal symmetries can produce an important contribution to angular momentum. This phenomenon has been known for many years in particle physics and called "spin from isospin". We show that similar mechanism works in the case of lattice pseudospin.

cond-mat.mes-hall↗
arXiv2012

Nonlinear realizations, the orbit method and Kohn's theorem

The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart lift.

hep-th↗
arXiv2012

QED2+1 in graphene: symmetries of Dirac equation in 2+1 dimensions

It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism of quantum electrodynamics in 2+1 dimensions (QED2+1) which provides the opportunity to verify the high energy physics phenomena in the condensed matter system. We study the symmetry properties of 2+1-dimensional Dirac equation, both in the non-interacting case and in the case with constant uniform magnetic field included in the model. The maximal symmetry group of the massless Dirac equation is considered by putting it in the Jordan block form and determining the algebra of operators leaving invariant the subspace of solutions. It is shown that the resulting symmetry operators expressed in terms of Dirac matrices cannot be described exclusively in terms of gamma matrices (and their products) entering the corresponding Dirac equation. It is a consequence of the reducibility of the considered representation in contrast to the 3+1-dimensional case. Symmetry algebra is demonstrated to be a direct sum of two gl(2,C) algebras plus an eight-dimensional abelian ideal. Since the matrix structure which determines the rotational symmetry has all required properties of the spin algebra, the pseudospin related to the sublattices (M. Mecklenburg and B. C. Regan, Phys. Rev. Lett. 106, 116803 (2011)) gains the character of the real angular momentum, although the degrees of freedom connected with the electron's spin are not included in the model. This seems to be graphene's analogue of the phenomenon called "spin from isospin" in high energy physics.

cond-mat.mtrl-sci↗
arXiv2011

Nonrelativistic counterparts of twistors and the realizations of Galilean conformal algebra

Using the notion of Galilean conformal algebra (GCA) in arbitrary space dimension d, we introduce for d=3 quantized nonrelativistic counterpart of twistors as the spinorial representation of O(2,1){\oplus}SO(3) which is the maximal semisimple subalgebra of three-dimensional GCA. The GC-covariant quantization of such nonrelativistic spinors, which shall be called also Galilean twistors, is presented. We consider for d=3 the general spinorial matrix realizations of GCA, which are further promoted to quantum-mechanical operator representations, expressed as bilinears in quantized Galilean twistors components. For arbitrary Hermitian quantum-mechanical Galilean twistor realizations we obtain the result that the representations of GCA with positive-definite Hamiltonian do not exist. For non-positive H we construct for N{\geq}2 the Hermitian Galilean N-twistor realizations of GCA; for N=2 such realization is provided explicitly.

hep-th↗
arXiv2010

Comment on "Tunable Band Gaps in Bilayer Graphene-BN Heterostructures"

We study the electronic properties of h-BN/graphene/h-BN ABC-stacked trilayer systems using tight binding and DFT methods. We comment on the recent work of Ramasubramaniam et al. (arxiv:1011.2489) whose results seem to be in disagreement with our recent calculations. Detailed analysis reaffirms our previous conclusions.

cond-mat.mtrl-sci↗
arXiv2010

Reversible modifications of linear dispersion - graphene between boron nitride monolayers

Electronic properties of the graphene layer sandwiched between two hexagonal boron nitride sheets have been studied using the first-principles calculations and the minimal tight-binding model. It is shown that for the ABC-stacked structure in the absence of external field the bands are linear in the vicinity of the Dirac points as in the case of single-layer graphene. For certain atomic configuration, the electric field effect allows opening of a band gap of over 230 meV. We believe that this mechanism of energy gap tuning could significantly improve the characteristics of graphene-based field-effect transistors and pave the way for future electronic applications.

cond-mat.mtrl-sci↗
arXiv2007

Note on charge interaction in NQED

The interaction of charges in NQED is discussed. It is shown that the relativistic correction have the same form as in the commutative case provided the Weyl ordering rule is used.

hep-th↗