arXiv subjects

R. Pincak

Publications and source records attributed to R. Pincak.

At least 19 recordsLinked to original sources

arXiv2021

The "emerging" reality from "hidden" spaces

The main purpose of this paper is to show and introduce some new interpretative aspects of the concept of "emergent space" as geometric/topological approach in the cosmological field. We will present some possible applications of this theory, among which the possibility of considering a non-orientable wormhole. Finally, in Subsection 2.3, we give a topological interpretation, using this new approach, to M-Theory and String Theory in $10$ dimensions. Further we present some conclusions which this new interpretation suggests, and also some remarks considering a unifying approach between strings and dark matter. The approach shown in the paper considers that reality, as it appears to us, can be the "emerging" part of a more complex hidden structure.

physics.gen-ph↗

arXiv2017

Boundary conditions and Green function approach of the spin-orbit interaction in the graphitic nanocone

The boundary effects affecting the Hamiltonian for the nanocone with curvatureinduced spin orbit coupling were considered and the corresponding electronic structure was calculated. These boundary effects include the spin orbit coupling, the electron mass acquisition and the Coulomb interaction. Different numbers of the pentagonal defects in the tip were considered. The Green function approach into the second order was used for getting more precise results in the case of the spin orbit coupling.

cond-mat.mes-hall↗

arXiv2016

Electronic Properties of Bilayer Fullerene Onions

The HOMO-LUMO gaps of the bilayer fullerene onions were investigated. For this purpose, the HOMO and LUMO energies were calculated for the isolated fullerenes using the parametrization of the tight binding method with the Harrison-Goodwin modification. Next, the difference of the Fermi levels of the outer and inner shell was calculated by considering the hybridization of the orbitals on the base of the geometric parameters. The results were obtained by the combination of these calculations.

cond-mat.mes-hall↗

arXiv2016

Analogies in electronic properties of graphene wormhole and perturbed nanocylinder

The electronic properties of the wormhole and the perturbed nanocylinder will be investigated using two different methods: the continuum gauge field-theory model which deals with the contin- uum approximation of the surface and the Haydock recursion method which transforms the surface into simplier structure and deals with the nearest-neighbor interactions. Furthermore, the changes of the electronic properties will be investigated for the case of enclosing the appropriate structure and possible substitutes for the encloser will be derived. Finally, possible character of the electron flux will be derived from the model based on the multiwalled nanotubes.

cond-mat.mes-hall↗

arXiv2015

Calculation of the electronic structure near the tip of a graphitic nanocone

In the earlier works, the electronic structure of the graphitic nanocone for the long distance from the tip was investigated. Here, we investigate the behaviour of the given nanostructure near the tip where in our approach hybridizations of pi-orbitals need to be included. In this case, the curvature dependence of pi-orbital energy has to be imposed into the model. For this purpose, we use an approximation valid for small values of the corresponding parameters. We consider different numbers of the pentagonal defects in the tip. This localization of the electrons on the nanocone tip could be used as a real application in the electron microscopes.

cond-mat.mes-hall↗

arXiv2015

Electronic structure of disordered graphene with Green's function approach

The Green functions play a big role in the calculation of the local density of states of the carbon nanostructures. We investigate their nature for the variously oriented and disclinated graphene-like surface. Next, we investigate the case of a small perturbation generated by two heptagonal defects and from the character of the local density of states in the border sites of these defects we derive their minimal and maximal distance on the perturbed cylindrical surface. For this purpose, we transform the given surface into a chain using the Haydock recursion method. We will suppose only the nearest-neighbor interactions between the atom orbitals, in other words, the calculations suppose the short-range potential.

cond-mat.mes-hall↗

arXiv2015

Spin-orbit interaction in the graphitic nanocone

The Hamiltonian for nanocones with curvature induced spin orbit coupling have been derived. The effect of curvature induced spin orbit coupling on the electronic properties of graphitic nanocones is considered. Energy spectra for different numbers of the pentagonal defects in the tip of the nanocones are calculated. It was shown that the spin orbit interaction considerably affects the local density of states of the graphitic nanocone. This influence depends on the number of defects present at the tip of the nanocone. This property could be applied in atomic force microscopy for the construction of the probing tip.

cond-mat.mes-hall↗

arXiv2015

The chiral massive fermions in the graphitic wormhole

The graphitic wormhole is in the focus of physical interest because of its interesting properties which can remotely resemble the concept of the space wormhole. Apart from the usual applications of the carbon nanostructures like the electronic computer devices, it seems to be a good material for the accumulation of the electric charge and different kinds of molecules, e.g. the hydrogen molecules, which enables using this material for the storage of the new kinds of fuel. Here, we present the geometric and electronic structure and calculate the zero modes of this material and its possibly significant derivate, the perturbed wormhole. Next, the influence of some additional factors on the electronic structure like the changes of the Fermi velocity close to the wormhole bridge as well as the spin-orbit interaction will be investigated. On this basis, we predict the massive chiral fermions in the connecting wormhole nanotube.

cond-mat.mes-hall↗

arXiv2013

D-Brane solutions under market panic

The relativistic quantum mechanic approach is used to develop a stock market dynamics. The relativistic is conceptional here as the meaning of big external volatility or volatility shock on a financial market. We used a differential geometry approach with the parallel transport of the prices to obtain a direct shift of the stock price movement. The prices are represented here as electrons with different spin orientation. Up and down orientations of the spin particle are likened here as an increase or a decrease of stock prices. The paralel transport of stock prices is enriched about Riemann curvature which describes some arbitrage opportunities in the market. To solve the stock-price dynamics, we used the Dirac equation for bispinors on the spherical brane-world. We found that when a spherical brane is abbreviated to the disk on the equator, we converge to the ideal behaviour of financial market where Black Scholes as well as semi-classical equations are sufficient. Full spherical brane-world scenarios can descibe a non-equilibrium market behaviour were all arbitrage opportunities as well as transaction costs are take into account.

q-fin.GN↗

arXiv2012

Edge states of graphene bilayer strip

The electronic structure of the zig-zag bilayer strip is analyzed. The electronic spectra of the bilayer strip is computed. The dependence of the edge state band flatness on the bilayer width is found. The density of states at the Fermi level is analytically computed. It is shown that it has the singularity which depends on the width of the bilayer strip. There is also asymmetry in the density of states below and above the Fermi energy.

cond-mat.mtrl-sci↗

arXiv2011

Electronic properties of disclinated nanostructured cylinder

The electronic structure of nanocylinder without and with a small perturbation is investigated with the help of calculation of the local density of states. A continuum gauge field-theory model is used for this purpose. In this model, Dirac equation is solved on a curved surface. The local density of states is calculated from its solution. The case of 2 heptagonal defects is considered. This paper is an extension of our previous work [1] where one heptagonal and one pentagonal defects in hexagonal graphene network were compared. The metallization for the perturbed cylinder structure is found.

cond-mat.mtrl-sci↗

arXiv2011

Quantum non-equilibrium approach for fast electron transport in open systems: photosynthetic reaction centers

Creation of electron or exciton by external fields in a system with initially statistically independent unrelaxed vibrational modes leads to an initial condition term. The contribution of this term in the time convolution generalized master equation approach is studied in second order of the perturbation theory in the path integral formalism. The developed approach, applied for analysis of dynamics in the photosynthetic reaction center, exhibits the key role of the initial condition terms at the primary stage of electron transfer.

physics.bio-ph↗

arXiv2011

Electronic Structure of Disclinated Graphene in an Uniform Magnetic Field

The electronic structure in the vicinity of the 1-heptagonal and 1-pentagonal defects in the carbon graphene plane is investigated. Using a continuum gauge field-theory model the local density of states around the Fermi energy is calculated for both cases. In this model, the disclination is represented by an SO(2) gauge vortex and corresponding metric follows from the elasticity properties of the graphene membrane. To enhance the interval of energies, a self-consistent perturbation scheme is used. The Landau states are investigated and compared with the predicted values.

cond-mat.mes-hall↗

arXiv2011

From the currency rate quotations onto strings and brane world scenarios

In the paper, we study numerically the projections of the real exchange rate dynamics onto the string-like topology. Our approach is inspired by the contemporary movements in the string theory. The string map of data is defined here by the boundary conditions, characteristic length, real valued and the method of redistribution of information. As a practical matter, this map represents the detrending and data standardization procedure. We introduced maps onto 1-end-point and 2-end-point open strings that satisfy the Dirichlet and Neumann boundary conditions. The questions of the choice of extra-dimensions, symmetries, duality and ways to the partial compactification are discussed. Subsequently, we pass to higher dimensional and more complex objects. The 2D-Brane was suggested which incorporated bid-ask spreads. Polarization by the spread was considered which admitted analyzing arbitrage opportunities on the market where transaction costs are taken into account. The model of the rotating string which naturally yields calculation of angular momentum is suitable for tracking of several currency pairs. The systematic way which allows one suggest more structured maps suitable for a simultaneous study of several currency pairs was analyzed by means of the Gâteaux generalized differential calculus. The effect of the string and brane maps on test data was studied by comparing their mean statistical characteristics. The study revealed notable differences between topologies. We review the dependence on the characteristic string length, mean fluctuations and properties of the intra-string statistics. The study explores the coupling of the string amplitude and volatility.

q-fin.ST↗

arXiv2010

Electronic properties of disclinated flexible membrane beyond the inextensional limit: Application to graphene

Gauge-theory approach to describe Dirac fermions on a disclinated flexible membrane beyond the inextensional limit is formulated. The elastic membrane is considered as an embedding of 2D surface into R^3. The disclination is incorporated through an SO(2) gauge vortex located at the origin, which results in a metric with a conical singularity. A smoothing of the conical singularity is accounted for by replacing a disclinated rigid plane membrane with a hyperboloid of near-zero curvature pierced at the tip by the SO(2) vortex. The embedding parameters are chosen to match the solution to the von Karman equations. A homogeneous part of that solution is shown to stabilize the theory. The modification of the Landau states and density of electronic states of the graphene membrane due to elasticity is discussed.

cond-mat.mes-hall↗

arXiv2009

Electronic properties of double-layer carbon nanotubes

The electronic spectra for double-wall zigzag and armchair nanotubes are found. The influence of nanotube curvatures on the electronic spectra is also calculated. Our finding that the outer shell is hole doped by the inner shell is in the difference between Fermi levels of individual shells which originate from the different hybridization of pi-orbital. The shift and rotation of the inner nanotube with respect to the outer nanotube are investigated. We found stable semimetal characteristics of the armchair DWNTs in regard of the shift and rotation of the inner nanotube. We predict the shift of k_F towards the bigger wave vectors with decreasing of the radius of the armchair nanotube.

cond-mat.mtrl-sci↗

arXiv2007

Electronic pathway in the photosynthetic reaction centers and some mutation of RC's

The reaction center of Chloroflexus aurantiacus and Rhodobacter sphaeroides mutation of RC`s was investigated. To describe the kinetic of the Chloroflexus aurantiacus RC's we use incoherent model of electron transfer. It was shown that the asymmetry in electronic coupling must be included to explain the experiments. For the description of Rhodobacter sphaeroides H(M182)L mutation we used partially coherent as incoherent models of electron transfer. These two models are discussed with regard to the observed electron transfer kinetics. It can be concluded that partially coherent model is more adequate. We predict some new electron pathways for describing the kinetic of RC's and some mutation.

cond-mat.soft↗

arXiv2007

Spheroidal geometry approach to fullerene molecules

Graphite is an example of a layered material that can be bent to form fullerenes which promise important applications in electronic nanodevices. The spheroidal geometry of a slightly elliptically deformed sphere was used as a possible approach to fullerenes. We assumed that for a small deformation the eccentricity of the spheroid is smaller than one. We are interested here in the big elliptically deformed fullerenes.The low-lying electronic levels are described by the Dirac equation in (2+1) dimensions. We show how a small deformation of spherical geometry evokes a shift of the electronic spectra compared to the sphere. The flux of a monopole field was included inside the surface to describe the fullerenes. Both the electronic spectrum of spherical and the shift of spheroidal fullerenes were derived.

cond-mat.mtrl-sci↗