arXiv subjects

Piotr Milczarski

Publications and source records attributed to Piotr Milczarski.

5 recordsLinked to original sources

arXiv2015

New Method for Public Key Distribution Based on Social Networks

The security of communication in everyday life becomes very important. On the other hand, all existing encryption protocols require from user additional knowledge end resources. In this paper we discuss the problem of public key distribution between interested parties. We propose to use a popular social media as a channel to publish public keys. This way of key distribution allows also easily connect owner of the key with real person institution (what is not always easy). Recognizing that the mobile devices become the main tool of communication, we present description of mobile application that uses proposed security methods.

cs.CR↗

arXiv2000

Borel Summable Solutions to 1D Schrödinger Equation

It is shown that so called fundamental solutions the semiclassical expansions of which have been established earlier to be Borel summable to the solutions themselves appear also to be the unique solutions to the 1D Schrödinger equation having this property. Namely, it is shown in this paper that for the polynomial potentials the Borel function defined by the fundamental solutions can be considered as the canonical one. The latter means that any Borel summable solution can be obtained by the Borel transformation of this unique canonical Borel function multiplied by some $\hbar$-dependent and Borel summable constant. This justify the exceptional role the fundamental solutions play in 1D quantum mechanics and completes the relevant semiclassical theory relied on the Borel resummation technique and developed in our other papers.

quant-ph↗

arXiv1998

Exactness of Conventional and Supersymmetric JWKB Formulae and Glo bal Symmetries of Stokes Graphs

It has been shown that the cases of the JWKB formulae in 1--dim QM quantizing the energy levels exactly are results of essentially one global symmetry of both potentials and their corresponding Stokes graphs. Namely, this is the invariance of the latter on translations in the complex plain of the space variable i.e. the potentials and the Stokes graphs have to be periodic. A proliferation of turning points in the basic period strips (parallelograms) is another limitation for the exactness of the JWKB formulae. A systematic analyses of a single-well class of potentials satisfying suitable conditions has been performed. Only ten potentials (with one or two real parameters) quantized exactly by the JWKB formulae have been found all of them coinciding (or being equivalent to) with the well-known ones found previously. It was shown also that the exactness of the supersymmetric JWKB formulae is a consequence of the corresponding exactness of the conventional ones and vice versa. Because of the latter two exactly JWKB quantized potentials have been additionally established. These results show that the exact SUSY JWKB formulae choose the Comtet at al form of them independently of whether the supersymmetry is broken or not. A close relation between the shape invariance property of potentials considered and their meromorphic structure on the x-plane is also demonstrated.

quant-ph↗

arXiv1998

Change of Variable as Borel Resummation of Semiclassical Series

It is shown that a change of variable in 1-dim Schroedinger equation applied to the Borel summable fundamental solutions [Giller] is equivalent to Borel resummation of the fundamental solutions multiplied by suitably chosen $\hbar$-dependent constant. This explains why change of variable can improve JWKB formulae [Giller, Milczarski]. It is shown also that a change of variable alone cannot provide us with the exact JWKB formulae.

quant-ph↗

arXiv1997

Rectangular Well as Perturbation

We discuss a finite rectangular well as a perturbation for the infinite one with a depth $λ^2$ of the former as a perturbation parameter. In particular we consider a behaviour of energy levels in the well as functions of complex $λ$. It is found that all the levels of the same parity are defined on infinitely sheeted Riemann surfaces which topological structures are described in details. These structures differ considerably from those found in models investigated earlier. It is shown that perturbation series for all the levels converge what is in contrast with the known results of Bender and Wu. The last property is shown to hold also for the finite rectangular well with Dirac delta barier as a perturbation considered earlier by Ushveridze.

quant-ph↗