Quantum Optics Effects in Quasi-One-Dimensional and Two-Dimensional Carbon Materials

Yerchuck, Dmitri; Dovlatova, Alla

doi:10.1021/jp205549b

Cited by 15 publications

(42 citation statements)

References 52 publications

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“…A number of rather complicated tasks in quantum physics can be solved by an application of a hypercomplex n-numbers' calculus. The apparatus of hypercomplex n-numbers was used successfully, for instance, by the calculation of optical properties of 1D carbon zigzag shaped nanotubes, taking into account the quantum nature of EM-field in the works [12,13].…”

Section: Connection Of Symmetry Of Quantum Systems With Algebra Of Comentioning

confidence: 99%

To Principles of Quantum Theory Construction

Yerchuck¹,

Dovlatova²,

Alexandrov³

2014

IJP

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New insight to the principles of the quantum theory construction is given. It is based on the symmetry study of main differential equations of mechanics and electrodynamics. It has been shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered within the frames of the number theory) determine the mathematical nature of the quantities, incoming in given equations. The substantial consequence of the given consideration is the proof of the main postulate of quantum mechanics, that is, the proof of the statement, that to any quantum mechanical quantity can be set up into the correspondence the Hermitian matrix. It is shown, that a non-abelian character of the multiplicative group of the quaternion ring leads to the nonapplicability of the quaternion calculus for the construction of new versions of quantum mechanics directly. The given conclusion seems to be actual, since there is a number of modern publications with the development of the quantum mechanics theory using the quaternions with the standard basis {e, i, j, k}. The correct way for the construction of new versions of quantum mechanics on the quaternion base is discussed in the paper presented. It is realized by means of the representation of the quaternions through the basis of the linear space of complex numbers over the field of real numbers, under the multiplicative group of which the equations of the dynamics of mechanical systems are invariant. At the same time the quaternion calculus is applicable in electrodynamics, at that the new versions of quantum electrodynamics can be constructed by an infinite number of the ways corresponding to an infinite number of the matrix representations of the standard quaternion basis {e, i, j, k}. The given conclusion is the consequence of the high symmetry of Maxwell equations.

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Section: Connection Of Symmetry Of Quantum Systems With Algebra Of Comentioning

confidence: 99%

To Principles of Quantum Theory Construction

Yerchuck¹,

Dovlatova²,

Alexandrov³

2014

IJP

Self Cite

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“…where S and A are symmetric and antisymmetric parts of Hermitian matrix. In the works [56], [57] was used the apparatus of hypercomplex n-numbers by calculation of the optical properties of 1D carbon zigzag shaped nanotubes, taking into account quantum nature of EM-field. Hypercomplex nnumbers were defined to be the elements of commutative ring Z n , being to be the direct sum of n fields C of complex numbers, n ∈ N , that is…”

Section: Algebraic Properties Of Em-fieldmentioning

confidence: 99%

“…Consequently, we come to conclusion, that the interaction between equivalent to oscillators "bosonic atoms" can be described within the frames of Fermi gas model in zero-th order approximation or in the frames of Fermi liquid model in the first order approximation. Mathematical description in zero-th order approximation will be similar to well known above mentioned SSH-model with some corrections, concerning two branch of quasiparticles, given in [57].…”

Section: Fermi-liquid Model Of Quantized Em-field Structurementioning

confidence: 99%

“…We have used the only necessary condition for extremum of the functions E(α k,s β k,s ). It was shown in [57], that for the SSH-model the sufficient conditions for the minimum are substantial, they change the role of both solutions. Sufficient conditions for the minimum of the functions E(α k,s β k,s ) can be obtained by standard way, which was used in [57].…”

Section: Fermi-liquid Model Of Quantized Em-field Structurementioning

confidence: 99%

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Classical and Quantum Electrodynamics Concept Based on Maxwell Equations’ Symmetry

Yerchuck

2014

PSIJ

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The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. Tey are reviewed in the work presented. It is drawing the attention on the following aspects.EM-field has in general case quaternion structure, consisting of four independent field constituents, which differ from each other by the parities under space inversion and time reversal.Any complex relativistic field has the gauge invariant conserving quantity -two-component scalar or pseudoscalar value -complex charge.There exists physical conserving quantity, which is simultaneously invariant under both Rainich dual and additional hyperbolic dual symmetry transformation of Maxwell equations. It is spin in general case or spirality in the corresponding geometry. EM-field is described instead of unobservable vector and scalar potentials by observable electric field 4-vector-function with the components Eα( r, t) = {Ex( r, t), Ey( r, t), Ez( r, t), i cρe( r,t) λ } and (or in the case of free EM-field) by means of magnetic field 4-vector-function Hµ( r, t) = {Hx( r, t), Hy( r, t), Hz( r, t), i cρm( r,t) λ }, where icρe( r, t), icρm( r, t) are the j4( r, t)-component of 4current density, corresponding to contribution of electric and magnetic component of charge densities correspondingly, λ is conductivity, which for the case of EM-field propagation in vacuum is λv = 1 120π (Ohm) −1 . Generalized Maxwell equations for quaternion four-component EM-field are obtained. Invariants for EM-field, consisting of dually symmetric parts are found. The main postulate of quantum mechanics: "To any mechanical quantity can be set up in the correspondence the Hermitian matrix by quantization" was proved.Canonical Dirac quantization method was developed in two aspects. The first aspect is its application the only to observable quantities. The second aspect is the realization along with well known time-local quantization of space-local quantization and space-time-local quantization. It is also shown, that Coulomb field can be quantized in 1D and 2D systems.New model of photons is proposed. The photons in quantized EM-field are main excitations in oscillator structure of EM-field, which is equivalent to spin S = 1 "boson-atomic" 1D lattice structure, consisting of the "atoms" with zeroth rest mass. The photons of the first kind and of the second kind represent themselves respectively neutral chargeless spin 1/2 EM-solitons and charged spinless EM-solitons of Su-Schrieffer-Heeger family.

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“…In other words the lines, the appearance of which in stationary RS and IR measurements is determined by the formation and the propagation of quantum Rabi corpuscular-wave packets have been registered and/or identified in a number of quasionedimensional and two-dimensional carbon systems. Especially interesting that additionaql lines are observed the only in experiments, when the coherent state of the electronic system, interacting with an external EM-field is retained, and they disappear (in distincton from main usual lines) by the violation of the coherence, which was experimentally achieved by the adjustment of spectra registration conditions, corresponding to the stochastic regime [19]. It seems to be appropriate to draw the attention, that the transition to the stochastic behaviour is characteristic for quantum systems.…”

Section: Introductionmentioning

confidence: 99%

The Photon Concept and the Physics of Quantum Absorption Process

Yerchuck¹,

Yerchak²,

Dovlatova³

et al. 2015

BJAST

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The status of the photon in the modern physics was analysed. Within the frames of the Standard Model of particle physics the photon is considered to be the genuine elementary particle, being to be the messenger of the electromagnetic interaction to which are subject charged particles. In contrast, the experts in quantum electodynamics (in particular, in quantum optics) insist, that the description of an photon to be the particle is impossible. The given viewpoint was carefully analysed and its falseness was proved. The expression for a photon wave function is presented. So, the status of the photon in quantum electodynamics was restored. The physics of a quantum absorption process is analysed. It is argued in accordance with Dirac guess, that the photon revival takes place by its absorption. Being to be a soliton, it seems to be keeping safe after an energy absorption in a pinned state, possessing the only by spin. It is shown, that the time of the transfer of absorbing systems in an excited state is finite and moreover, that it can govern the stationary signal registered. The given result is significant for the all stationary spectroscopy, in which at present the transfer of absorbing systems in an excited state is considered to be instantaneous.

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Quantum Optics Effects in Quasi-One-Dimensional and Two-Dimensional Carbon Materials

Cited by 15 publications

References 52 publications

To Principles of Quantum Theory Construction

To Principles of Quantum Theory Construction

Classical and Quantum Electrodynamics Concept Based on Maxwell Equations’ Symmetry

The Photon Concept and the Physics of Quantum Absorption Process

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