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More then 35 approaches to the Dirac equation derivation are presented. The various physical principles and mathematical methods are used. A review of well-known and not enough known contributions to the problem is given, the unexpected and unconventional derivations are presented as well. Three original approaches to the problem suggested by the author are considered as well. They are (i) the generalization of H. Sallhofer derivation, (ii) the obtaining of the massless Dirac equation from the Maxwell equations in maximally symmetrical form, (iii) the derivation of the Dirac equation with nonzero mass from the relativistic canonical quantum mechanics of the fermion-antifermion spin s=1/2 doublet. Today we are able to demonstrate new features of our derivations given in original papers. In some sense the important role of the Dirac equation in contemporary theoretical physics is demonstrated. A criterion for the usefulness of one or another derivation of the Dirac equation has been established, Comment: 31 pages

We present a new category of quantum Lissajous states for a 2DHO having commensurate angular frequencies. The states result from the projection of ordinary coherent states onto a degenerate subspace of the 2DHO. In this way, new, non-classical quantum mechanically stationary states arise from the classical but non-stationary coherent states. The connection to Lissajous figures is that our states all have probability densities that are localized along the corresponding classical Lissajous figures. We further emphasize the important interplay between the probability current density and the emergence of quantum interference in the states we examine. In doing so, we are able to present a consistent discussion of a class of states known as vortex states., Comment: 76 pages

We investigate the phenomenology leading to the non-conservation of energy of the continuous spontaneous localization (CSL) model from the viewpoint of non-equilibrium thermodynamics, and use such framework to assess the equilibration process entailed by the dissipative formulation of the model (dCSL). As a paradigmatic situation currently addressed in frontier experiments aimed at investigating possible collapse theories, we consider a one-dimensional mechanical oscillator in a thermal state. We perform our analysis in the phase space of the oscillator, where the entropy production rate, a non-equilibrium quantity used to characterize irreversibility, can be conveniently analyzed. We show that the CSL model violates Clausius law, as it exhibits a negative entropy production rate, while the dCSL model reaches equilibrium consistently only under certain dynamical conditions, thus allowing us to identify the values -- in the parameter space -- where the latter mechanism can be faithfully used to describe a thermodynamically consistent phenomenon., Comment: 9 pages, 8 figures

A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident charged particle with a complex of charged particles (for example, in the collision of electrons with atoms). For the wave function, an integral equation is constructed for an arbitrary value of the orbital momentum of relative motion. By solving this equation, an exact integral representation for the $K$-matrix of the problem is obtained in terms of the wave function. This representation is used to analyze the behavior of the $K$-matrix at low energies and to obtain comprehensive information on its threshold behavior for various values of the dipole momentum. The resulting solution is applied to study the behavior of the scattering cross sections in the electron, positron and antiproton system., Comment: 15 pages, 2 figures

Concurrent natural time scales related to relaxation, recombination, trapping, and drifting processes rule the semiconductor heterostructures' response to external drives when charge carrier fluxes are induced. This paper highlights the role of stoichiometry not only for the quantitative tuning of the electron-hole dynamics but also for significant qualitative contrasts of time-resolved optical responses during the operation of resonant tunneling devices. Therefore, similar device architectures and different compositions have been compared to elucidate the correlation among structural parameters, radiative recombination processes, and electron-hole pair and minority carrier relaxation mechanisms. When these ingredients intermix with the electronic structure in Sb-based tunneling devices, it is proven possible to assess various time scales according to the intensity of the current flux, contrary to what has been observed in As-based tunneling devices with similar design and transport characteristics. These time scales are strongly affected not only by the filling process in the $\Gamma$ and L states in Sb-based double-barrier quantum wells but also by the small separation between these states, compared to similar heterostructures based on As., Comment: 11 pages, 6 figures, submitted to the Physical Review Applied journal

We investigate the energy relaxation segmentation in a resonant tunneling heterostructures by assessing the optical and transport dynamics of non-equilibrium charge carriers. The electrical and optical properties are analyzed using electronic transport measurements combined with electro- and photoluminescence spectroscopies in continuous-wave mode. The radiative recombination is mainly governed by the creation of heavy holes \textit{via} impact ionization processes. Our results suggest hot electrons and holes populations form independent non-equilibrium systems that do not thermalize among them and with the lattice. Consequently, the carriers effective temperature changes independently at different regions of the heterostructure, with a population distribution for holes colder than for electrons., Comment: This version of the manuscript was submitted to the Journal of the Physical Chemistry C. The revised published version can be found at https://pubs.acs.org/doi/10.1021/acs.jpcc.1c02173

Relativistic wave equation of motion without redundant components for the particle having spin 3/2 has been considered. In order to show the newness a comparison with the known equations for the spin s=3/2 field is given. Therefore, the brief review of the relativistic wave equations for the particle with spin s=3/2 is given. In our equation the wave function for the particle-antiparticle doublet has only 8 components. The consideration is carried out both at the level of relativistic quantum mechanics and at the level of local field theory. The extended Foldy--Wouthuysen transformation, which gives the operator link between these two levels is suggested., Comment: 14 pages

Extended gamma matrix Clifford--Dirac and SO(1,9) algebras in the terms of $8 \times 8$ matrices have been considered. The 256-dimensional gamma matrix representation of Clifford algebra for 8-component Dirac equation is suggested. Two isomorphic realizations $\textit{C}\ell^{\texttt{R}}$(0,8) and $\textit{C}\ell^{\texttt{R}}$(1,7) are considered. The corresponding gamma matrix representations of 45-dimensional SO(10) and SO(1,9) algebras, which contain standard and additional spin operators, are introduced as well. The SO(10), SO(1,9) and the corresponding $\textit{C}\ell^{\texttt{R}}$(0,8)$, \textit{C}\ell^{\texttt{R}}$(1,7) representations are determined as algebras over the field of real numbers. The suggested gamma matrix representations of the Lie algebras SO(10), SO(1,9) are constructed on the basis of the Clifford algebras $\textit{C}\ell^{\texttt{R}}$(0,8)$, \textit{C}\ell^{\texttt{R}}$(1,7) representations. Comparison with the corresponded algebras in the space of standard 4-component Dirac spinors is demonstrated. The proposed mathematical objects allow generalization of our results, obtained earlier for the standard Dirac equation, for equations of higher spin and, especially, for equations, describing particles with spin 3/2. The maximal 84-dimensional pure matrix algebra of invariance of the 8-component Dirac equation in the Foldy--Wouthuysen representation is found. The corresponding symmetry of the Dirac equation in ordinary representation is found as well. The possible generalizations of considered Lie algebras to the arbitrary dimensional SO(n) and SO(m,n) are discussed briefly., Comment: 22 pages. arXiv admin note: substantial text overlap with arXiv:0908.3106; text overlap with arXiv:1906.07018

We construct several quantum gauge theories in 4 dimensional space time, including both Abelian and non Abelian gauge groups, with the Abelian gauge fields coupled to zero mass matter fields. The construction occurs in a fixed finite Euclidean spatial domain. The construction begins with the doubly cutoff bare field theory (with a finite space time volume and a mesh based ultraviolet cutoff) constructed in a separate paper. We use a limited range of renormalized perturbation theory, just sufficient to cancel all the divergences. We demonstrate convergence of the ultraviolet limit and of the renormalized perturbation theory, when summed to all orders. We construct the fully renormalized Lagrangian and Schwinger functions., Comment: 8 pages

Standard Quantum Limit (SQL) of a classical mechanical force detection results from quantum back action impinged by the meter on a probe mechanical transducer perturbed by the force of interest. In this paper we introduce a technique of continuous \vy{broadband} back action avoiding measurements for the case of a resonant signal force acting on a linear mechanical oscillator supporting one of mirrors of an optical Michelson-Sagnac Interferometer (MSI). The interferometer with the movable mirror is an opto-mechanical transducer able to support polychromatic probe field. The method involves a dichromatic optical probe resonant with the MSI modes and having frequency separation equal to the mechanical frequency. We show that analyzing each of the harmonics of the probe reflected from the mechanical system separately and postprocessing the measurement results allows excluding the back action in a broad frequency band and measuring the force with sensitivity better than SQL., Comment: 12 pages, 3 figures

The purpose of this article is to derive a Markovian approximation of the reduced time dynamics of observables for the Pauli-Fierz Hamiltonian with a precise control of the error terms. In that aim, we define a Lindblad operator associated to the corresponding quantum master equation. In a particular case, this allows to study the transition probability matrix.

The issue of irreversibility in a universe with time-reversal-symmetric laws is a central problem in physics. % , and, in particular, to statistical mechanics, information theory and quantum thermodynamics. In this letter, we discuss for the first time how irreversibility can emerge within the recently proposed constructor theory framework. Here irreversibility is expressed as the requirement that a task is possible, while its inverse is not. In particular, we demonstrate that this irreversibility is compatible with quantum theory's time reversal symmetric laws, by exploiting a specific model, based on the universal quantum homogeniser, realised experimentally with high-quality single-photon qubits., Comment: 6 pages, 4 figures

The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by the 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are found. Two different bosonic realizations of this algebra are found as well. All generators of the above mentioned algebras commute with the operator of the Dirac equation in the external Coulomb field, and, therefore, determine the algebras of invariance of such Dirac equation. Hence, the spin s=(1,0) Bose symmetry of the Dirac equation for the free spinor field, proved recently in our papers, is extended here for the Dirac equation interacting with external Coulomb field. Relativistic hydrogen atom is modeling here by such Dirac equation. We are able to prove for the relativistic hydrogen atom both the fermionic and bosonic symmetries known from our papers about the case of non-interacting spinor field. New symmetry operators were found on the basis of new gamma matrix representations of the Clifford and SO(8) algebras, which were found recently in our papers. Hidden symmetries were found both in the canonical Foldy--Wouthuysen and in the covariant Dirac representations. The symmetry operators, which are simple and graceful in the Foldy--Wouthuysen representation, become non-local in the Dirac model., Comment: 11 pages

Certain duality of relative entropy can fail for chiral conformal net with nontrivial representations. In this paper we quantify such statement by defining a quantity which measures the failure of such duality, and identify this quantity with relative entropy and global index associated with multi-interval subfactors for a large class of conformal nets. In particular we show that the duality holds for a large class of conformal nets if and only if they are holomorphic. The same argument also applies to CFT in two dimensions. In particular we show that the duality holds for a large class of CFT in two dimensions if and only if they are modular invariant. We also obtain various limiting properties of relative entropies which naturally follow from our formula., Comment: corrections about nets associated with lattices, Cor. 2.16 added

Virtual particles expected to occur in microscopic processes as they are introduced, for instance by Feynman in the Quantum Electro Dynamics, as photons performing in an anonymous way in the interaction between two electrons. This note describes macroscopic virtual particles as they appear in classical evanescent modes and in quantum mechanical tunneling particles. Remarkably, these large virtual particles are present in wave mechanics of elastic, electromagnetic, and Schr\"odinger fields., Comment: 17 pages, 5 figures

In this paper, we proposed an experimental implementation of quantum random number generator(QRNG) with inherent randomness of quantum tunneling effect of electrons. We exploited InGaAs/InP diodes, whose valance band and conduction band shared a quasi-constant energy barrier. We applied a bias voltage on the InGaAs/InP avalanche diode, which made the diode works under Geiger mode, and triggered the tunneling events with a periodic pulse. Finally, after data collection and post-processing, our quantum random number generation rate reached 8Mb/s, and final data was verified by NIST test and Diehard test. Our experiment is characterized as an innovative low-cost, photonic source free, integratable or even chip-achievable method in quantum random number generation., Comment: 6 pages, 10 figures

The electronic transport properties of a point-contact system formed by a single Co atom adsorbed on Cu (100) and contacted by a copper tip is evaluated in the presence of intra-atomic Coulomb interactions and spin-orbit coupling. The calculations are performed using equilibrium Green's functions evaluated within density functional theory completed with a Hubbard $U$ term and spin-orbit interaction, as implemented in the Gollum package. We show that the contribution to the transmission between electrodes of spin-flip components is negative and scaling as $\lambda^2/\Gamma^2$ where $\lambda$ is the SOC and $\Gamma$ the Co atom-electrode coupling. Hence, due to this unfavorable ratio, SOC effects in transport in this system are small. However, we show that the spin-flip transmission component can increase by two orders of magnitude depending on the value of the Hubbard $U$ term. These effects are particularly important in the contact regime because of the prevalence of $d$-electron transport, while in the tunneling regime, transport is controlled by the $sp$-electron transmission and results are less dependent on the values of $U$ and SOC. Using our electronic structure and the elastic transmission calculations, we discuss the effect of $U$ and SOC on the well-known Kondo effect of this system., Comment: 6 figures

The non-selective and selective measurements of a self-adjoint observable $A$ in quantum mechanics are interpreted as `jumps' of the state of the measured system into a decohered or pure state, respectively, characterized by the spectral projections of $A$. However, one may try to describe the measurement results as asymptotic states of a dynamical process, where the non-unitarity of time evolution arises as an effective description of the interaction of the measured system with the measuring device. The dynamics we present is a two-step dynamics: the first step is the non-selective measurement or decoherence, which is known to be described by the linear, deterministic Lindblad equation. The second step is a process from the resulted decohered state to a pure state, which is described by an effective non-linear `randomly chosen' toy model dynamics: the pure states arise as asymptotic fixed points, and their emergent probabilities are the relative volumes of their attractor regions., Comment: 13 pages, 2 figures

Next investigations in our program of transition from the He atom to the complex atoms description have been presented. The method of interacting configurations in the complex number representation is under consideration. The spectroscopic characteristics of the Mg and Ca atoms in the problem of the electron-impact ionization of these atoms are investigated. The energies and the widths of the lowest autoionizing states of Mg and Ca atoms are calculated. Few results in the photoionization problem on the autoionizing states above the n=2 threshold of helium-like Be ion are presented., Comment: 6 pages, 4 tables. arXiv admin note: text overlap with arXiv:1608.04078

Performing perfect/conclusive quantum state exclusion means to be able to discard with certainty at least one out of n possible quantum state preparations by performing a measurement of the resulting state. This task of state exclusion has recently been studied at length in arXiv:1306.4683v3, and it is at the heart of the celebrated PBR thought experiment (arXiv:1111.3328v3). When all the preparations correspond to pure states and there are no more of them than their common dimension, it is an open problem whether POVMs give any additional power for this task with respect to projective measurements. This is the case even for the simple case of three states in three dimensions, which is mentioned in arXiv:quant-ph/0206110 as unsuccessfully tackled. In this paper, we give an analytical proof that in this case considering POVMs does indeed not give any additional power with respect to projective measurements. To do so, we first make without loss of generality some assumptions about the structure of an optimal POVM. The justification of these assumptions involves arguments based on convexity, rank and symmetry properties. We show then that any pure states perfectly excluded by such a POVM meet the conditions identified in arXiv:quant-ph/0206110 for perfect exclusion by a projective measurement of three pure states in three dimensions. We also discuss possible generalizations of our work, including an application of Quadratically Constrained Quadratic Programming that might be of special interest., Comment: v4: Added discussion on using Quadratically Constrained Quadratic Programming to obtain potential generalizations. Using the Quantum journal template

Spontaneous emission of a two--level atom in free space is modified by other atoms in its vicinity leading to super- and sub-radiance. In particular, for atomic distances closer than the transition wavelength the maximally entangled antisymmetric superposition state of two individually excited atomic dipole moments possesses no total dipole moment and will not decay spontaneously at all. Such a two-atom dark state does not exist, if the atoms possess alternative decay channels towards other atomic lower energy states. However, we show here that for any atomic state with $N-1$ independent spontaneous decay channels one can always find a $N$-particle highly entangled state, which completely decouples from the free radiation field and does not decay. Moreover, we show that this state is the unique state orthogonal to the subspace spanned by the lower energy states with this property. Its sub-radiant property largely survives at finite atomic distances., Comment: 6 pages 5 figures

A numerical algorithm that computes the decomposition of any finite-dimen\-sio\-nal unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight on the group structure, is inspired by quantum mechanical notions. After generating two adapted states (these objects will be conveniently defined in {\bf Def.\,II.1}) and after appropriate algebraic manipulations, the algorithm returns the block matrix structure of the representation in terms of its irreducible components. It also provides an adapted orthonormal basis. The algorithm can be used to compute the Clebsch--Gordan coefficients of the tensor product of irreducible representations of a given compact Lie group. The performance of the algorithm is tested on various examples: the decomposition of the regular representation of two finite groups and the computation of Clebsch--Gordan coefficients of two examples of tensor products of representations of $SU(2)$., Comment: Updated paper. arXiv admin note: text overlap with arXiv:1512.08248

In this paper relativistic-invariant phenomenological Lagrangians of interaction between spin-1 particles and electromagnetic field were obtained in the Duffin-Kemmer-Petiau formalism on the basis of the covariant model that takes into account both spin polarizabilities and gyrations of the above-mentioned particles. It was shown that in the suggested covariant model with regard to the crossing symmetry, spatial parity and gauge invariance conservation laws, definite spin polarizabilities and gyrations of spin-1 particles contribute to the expansion of Compton scattering amplitude, starting from the corresponding orders on energy of pfotons that is in the agreement with low-energy theorems for that process., Comment: 14 pages

The beginning of the application of the method of interacting configurations in the complex number representation to the compound atomic systems has been presented. The spectroscopic characteristics of the Be atom in the problem of the electron-impact ionization of this atom are investigated. The energies and the widths of the lowest autoionizing states of Be atom are calculated., Comment: 5 pages

Long-baseline interferometry (LBI) is used to reconstruct the image of faint thermal objects. The image quality, for a given exposure time, is in general limited by a low signal-to-noise ratio (SNR). We show theoretically that a significant increase of the SNR, in a LBI, is possible by adding or subtracting photons to the thermal beam. At low photon counts, photon addition-subtraction technology strongly enhances the image quality. We have experimentally realized a nondeterministic physical protocol for photon subtraction. Our theoretical predictions are supported by experimental results., Comment: 4 pages, 5 figures

Theoretical comment for the registration of longitudinal electric waves in interacting laser beams is given. Recent information on longitudinal electric and scalar waves in plasma, plasmons, waveguides, antennas and nano-structures is considered. The link between the longitudinal electromagnetic waves and the system of Maxwell equations is demonstrated. The longitudinal wave component of the electric field strength vector is found as the exact solution of the standard Maxwell equations with specific gradient-type case of electric current and charge densities. The corresponded scalar wave is found as well. The necessary comment on the paper of K.J. van Vlaenderen and A. Waser is given. The possible experimental situation is discussed briefly. Following the Bialynicki-Birula's proposition to give the name for the well known complex 3-vector of electromagnetic field strengths, the suggestion to call the much more interesting 4-vector of this kind as Riemann--Silberstein--Darwin vector is given., Comment: 23 pages

The investigation of arXiv 1409.2766v2 [quant-ph] has been continued by the general form of the numerous equations with partial values of arbitrary spin, which were considered in above mentioned preprint. The general forms of quantum-mechanical and covariant equations for arbitrary spin together with the general description of the arbitrary spin field formalism are presented. The corresponding relativistic quantum mechanics of arbitrary spin is given as the system of axioms. Previously ignored partial example of the spin s=(0,0) particle-antiparticle doublet is considered. The partial example of spin s=(3/2,3/2) particle-antiparticle doublet is highlighted. The new 64 dimensional Clifford--Dirac algebra over the field of real numbers is suggested. The general operator, which transformed the relativistic canonical quantum mechanics of arbitrary spin into the locally covariant field theory, has been introduced. Moreover, the study of the place of the results given in arXiv 1409.2766v2 [quant-ph] among the results of other authors is started. The review of the different investigations in the area of relativistic canonical quantum mechanics is given and the brief analysis of the existing approaches to the covariant field theory of arbitrary spin is initiated. The consideration of some important details of arXiv 1409.2766v2 [quant-ph] is improved., Comment: 42 p. arXiv admin note: text overlap with arXiv:1409.2766

We argue that not all the theoretical content of the Bohr model has been captured by the definitive quantum formalism currently in use. In particular, the notion of quantum leap seems to refer to non-dynamic features, closely related to non-locality, which have not yet been formalized in a satisfactory way., Comment: 6 pages, 32 references