Eliade Stefanescu

We consider a quantum particle as a wave packet in the coordinate space. When the conjugate wave packet in the momentum space is considered, we find that the group velocities of these two wave packets, which describe the particle dynamics, are in agreement with the Hamilton equations only if in the time dependent phases one considers the Lagrangian instead of the Hamiltonian which leads to the conventional Schrodinger equation. We define a relativistic quantum principle asserting that a quantum particle has a finite frequency spectrum, with a cutoff propagation velocity c as a universal constant not depending on the coordinate system, and that any time dependent phase variation is the same in any system of coordinates. From the time dependent phase invariance, the relativistic kinematics is obtained. We consider two types of possible interactions: 1) An interaction with an external field, by a modification of the time dependent phase differential with the terms proportional to the differentials of the space-time coordinates multiplied with the components of this field four-potential, and 2) an interaction by a deformation of the space-time coordinates, due to a gravitational field. From the invariance of the time dependent phase with field components, we obtain a mechanical force of the form of Lorentz’s force, and three Maxwell equations: The Gauss-Maxwell equations for the electric and magnetic fluxes, and the Faraday-Maxwell equation for the electromagnetic induction. When the fourth equation, Ampere-Maxwell, is considered, the interaction field takes the form of the electromagnetic field. For a low propagation velocity of the particle waves, we get a packet of waves with the time dependent phases proportional to the relativistic Hamiltonian, as in Dirac’s famous theory of spin, and a slowly-varying amplitude with a phase proportional to the momentum and this velocity. In the framework of our theory, the spin is obtained as an all quantum effect, without any additional assumption to the quantum theory. When a space-time deformation is considered in the time dependent phase of a quantum particle, from the group velocity we get the particle dynamics according to the general theory of relativity. In this way, the relativistic dynamics, the electromagnetic field, and the spin of a quantum particle are obtained only from the invariance of the time dependent phases of the particle wave functions.

Essentially, in this paper we propose a new description of the quantum dynamics by two relativistic propagation wave packets, in the two conjugated spaces, of the coordinates and of the momentum. Compared to the Schrödinger-Dirac equation, which describes a free particle by a wave function continuously expanding in time, considered as the amplitude of a probabilistic distribution of this particle, the new equations describe a free particle as an invariant distribution of matter propagating in the two spaces, as it should be. Matter quantization arises from the equality of the integral of the matter density with the mass describing the dynamics of this density in the phases of the wave packets. In this description, the classical Lagrange and Hamilton equations are obtained as the group velocities of the two wave packets in the coordinate and momentum spaces. When to the relativistic Lagrangian we add terms with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and a scalar potential conjugated to time, we obtain the Lorentz force and the Maxwell equations as characteristics of the quantum dynamics. In this framework, the conventional Schrödinger-Dirac equations of a quantum particle in an electromagnetic field obtain additional terms explicitly depending on velocity, as is expected in the framework of relativistic theory. Such a particle wave function takes the form of a rapidly varying wave, with the frequency corresponding to the rest energy, modulated by the electric rotation with the spins ½ for Fermions, and 1 for Bosons. From the new dynamic equations, for a free particle in the coordinate and momentum spaces, we reobtain the two basic equations of the quantum field theory, but with a change of sign, and an additional term depending on momentum, to the rest mass as the eigenvalue of these equations. However, when these eigenvalues are eliminated, the wave function takes the form of a wave packet of spinors of the same form as in the conventional quantum field theory, with a normalization volume as the integral of the ratio of the energy to the rest energy, over the momentum domain which gives finite dimensions to the quantum particle, as a finite distribution of matter in the coordinate space.

Tunneling is a remarkable, essentially quantum phenomenon, standing at the basis of important applications in electronics, chemistry, biology and nuclear physics (Razavi and Pimpale, 1988). An important difficulty in the description of this phenomenon is the influence of dissipation, always present in practical cases.

ABSTRACT In a unitary approach generally used in quantum optics, we consider Lindblad's Markovian master equation and the non- Markovian master equation of Ford, Lewis and O'Connell. We show that the second-order master equation in the hierarchy obtained from a Krylov-Bogoliubov expansion corresponds to the Born approximation. By time averaging, and neglecting the rapidly varying terms, Lindblad's master equation is obtained. With these two equations, we calculate the decay spectrum. We find that for rather low dissipated energies, only the non-Markovian master equation provides correct results. Based on the independent oscillator model of the dissipative coupling, explicit expressions of the dissipative coefficients are obtained.

For a tunneling system we consider the coupling to the dissipative environment of the coordinate q, the momentum p and the potential function U(q). In the frame of the quantum theory of open systems we derive a quantum master equation, fundamental constraints and uncertainty relations. We obtain an analytical expression of the tunneling spectrum and show that at thermal equilibrium

ABSTRACT We derive a quantum master equation for a system of femions coupled to the blackbody radiation field and to many other excitations of the surrounding particles. In comparison with other master equations for many-level systems, the new master equation depends on microscopic coefficients (as functions of physical constants, matrix elements, densitie of the environment states, and occupation probabilities of these states), and includes two additional terms: (1) a term depending on the selfconsistent field of the collective motion of the system or of other surrounding particles, and (2) a non-Markovian term.

An essential problem of the quantum information systems is the controllability and observability of the quantum states, generally described by Lindblad's master equation with phenomenological coefficients. However, in its general form, this equation describes a decay of the mean-values, but not necessarily the expected decaying transitions. We propose a quantum master equation with microscopic coefficients where these transitions are correctly

We established a master equation for a system of fermions coupled by electric dipol interaction with the free electromagnetic field. This equation has a Lindblad equation form, with a hamiltonian part corresponding to the shell model and a dissipative part with microscopic coefficients depending on physical constants, matrix elements, and temperature. The dependence on the transition energy of the dissipative coefficients satisfies asymptothycal conditions for the energy transfer in full agreement with the principle of the detailed balance.

The Maxwell-Bloch equations for the steady state, with boundary conditions for a Fabry-Perot cavity, are integrated. In the mean-field approximation, the transmittivity characteristic, obtained for the general case of absorptive-dispersive optical bistability, leads to the Agrawall-Carmichael characteristic for a small atomic detuning and to the McCall characteristic for pure-dispersive optical bistability. The applicability of this theory in the dominant-dispersive case is discussed.

We derive a quantum master equation for a system of fermions coupled to the blackbody radiation field through the electric-dipole interaction. This equation is of Lindblad's form, with a hamiltonian part of the shell-model, and a dissipative art with microscopic coefficients, depending on physical constants, matrix elements, and parametrically only on temperature.

In a previous paper, we derived a master equation for fermions, of Lindblad's form, with coefficients depending on microscopic quantities. In this paper, we study the properties of the dissipative coefficients taking into account the explicit expressions of: (a) the matrix elements of the dissipative potential, evaluated from the condition that, essentially, this potential induces transitions among the system eigenstates without significantly modifying these states, (b) the densities of the environment states according to the Thomas–Fermi model, and (c) the occupation probabilities of these states taken as a Fermi–Dirac distribution. The matrix of these coefficients correctly describes the system dynamics: (a) for a normal, Fermi–Dirac distribution of the environment population, the decays dominate the excitation processes; (b) for an inverted (exotic) distribution of this population, specific to a clustering state, the excitation processes are dominant.

Tunneling is essentially a quantum process standing at the basis of important applications in electronics, chemistry, biology and nuclear physics. In principle, we can conceive it as a transition from a “localized” state Ψo of the compound nucleus to a state Ψ i of the reaction channel. If the physical system is closed, the energy is conserved within the limits of Heisenberg’s uncertainty principle. However, in nuclear physics, the experimental spectra of some fission modes with cold fragments, display important line shifts and broadenings1. This means that the proper fragmentation process is assisted by dissipative processes, leading to energy loss and diffusion. Consequently, an open physical system must be considered.

In this paper, we formulate a physical principle, and propose a semiconductor device producing coherent electromagnetic energy by heat absorption from the environment. This device is a superradiant semiconductor chip, included in a Fabry-Perot cavity, and in intimate contact with a huge radiator. This radiator is designed for a very efficient heat transfer from the environment to the semiconductor structure, which by operation becomes colder than the environment. This structure is composed of a packet of n-i-p-n semiconductor elements that we call superradiant transistors, operating by current injection. On the basis of a physical model of the dissipative superradiant dynamics, we recently elaborated in the framework of the quantum theory of open systems, we show that the energy of the electromagnetic field radiated by quantum transitions in the emitter-base junctions is much larger than the energy electrically dissipated by injection of electrons, the energy difference being obtain...

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We derive a non-Markovian master equation for the long-time dynamics of a system of Fermions interacting with a coherent electromagnetic field, in an environment of other Fermions, Bosons, and free electromagnetic field. This equation is applied to a superradiant p-in semiconductor heterostructure with quantum dots in a Fabry-Perot cavity, we recently proposed for converting environmental heat into coherent electromagnetic energy. While a current is injected in the device, a superradiant field is generated by quantum transitions in quantum dots, through the very thin i-layers. Dissipation is described by correlated transitions of the system and environment particles, transitions of the system particles induced by the thermal fluctuations of the self-consistent field of the environment particles, and non-local in time effects of these fluctuations. We show that, for a finite spectrum of states and a sufficiently weak dissipative coupling, this equation preserves the positivity of the density matrix during the whole evolution of the system. The preservation of the positivity is also guaranteed in the rotating-wave approximation. For a rather short fluctuation time on the scale of the system dynamics, these fluctuations tend to wash out the non-Markovian integral in a long-time evolution, this integral remaining significant only during a rather short memory time. We derive explicit expressions of the superradiant power for two possible configurations of the superradiant device: (1) a longitudinal device, with the superradiant mode propagating in the direction of the injected current, i.e. perpendicularly to the semiconductor structure, and (2) a transversal device, with the superradiant mode propagating perpendicularly to the injected current, i.e. in the plane of the semiconductor structure. The active electrons, tunneling through the i-zone between the two quantum dot arrays, are coupled to a coherent superradiant mode, and to a dissipative environment including four components, namely: (1) the quasi-free electrons of the conduction n-region, (2) the quasi-free holes of the conduction p-region, (3) the vibrations of the crystal lattice, and (4) the free electromagnetic field. To diminish the coupling of the active electrons to the quasi-free conduction electrons and holes, the quantum dot arrays are separated from the two

We consider a quantum particle as a wave packet in the coordinate space. When the conjugate wave packet in the momentum space is considered, we find that the group velocities of these two wave packets, which describe the particle dynamics, are in agreement with the Hamilton equations only if in the time dependent phases one considers the Lagrangian instead of the Hamiltonian which leads to the conventional Schrodinger equation. We define a relativistic quantum principle asserting that a quantum particle has a finite frequency spectrum, with a cutoff propagation velocity c as a universal constant not depending on the coordinate system, and that any time dependent phase variation is the same in any system of coordinates. From the time dependent phase invariance, the relativistic kinematics is obtained. We consider two types of possible interactions: 1) An interaction with an external field, by a modification of the time dependent phase differential with the terms proportional to the d...

Essentially, in this paper we propose a new description of the quantum dynamics by two relativistic propagation wave packets, in the two conjugated spaces, of the coordinates and of the momentum. Compared to the Schrödinger-Dirac equation, which describes a free particle by a wave function continuously expanding in time, considered as the amplitude of a probabilistic distribution of this particle, the new equations describe a free particle as an invariant distribution of matter propagating in the two spaces, as it should be. Matter quantization arises from the equality of the integral of the matter density with the mass describing the dynamics of this density in the phases of the wave packets. In this description, the classical Lagrange and Hamilton equations are obtained as the group velocities of the two wave packets in the coordinate and momentum spaces. When to the relativistic Lagrangian we add terms with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and a scalar potential conjugated to time, we obtain the Lorentz force and the Maxwell equations as characteristics of the quantum dynamics. In this framework, the conventional Schrödinger-Dirac equations of a quantum particle in an electromagnetic field obtain additional terms explicitly depending on velocity, as is expected in the framework of relativistic theory. Such a particle wave function takes the form of a rapidly varying wave, with the frequency corresponding to the rest energy, modulated by the electric rotation with the spins ½ for Fermions, and 1 for Bosons. From the new dynamic equations, for a free particle in the coordinate and momentum spaces, we reobtain the two basic equations of the quantum field theory, but with a change of sign, and an additional term depending on momentum, to the rest mass as the eigenvalue of these equations. However, when these eigenvalues are eliminated, the wave function takes the form of a wave packet of spinors of the same form as in the conventional quantum field theory, with a normalization volume as the integral of the ratio of the energy to the rest energy, over the momentum domain which gives finite dimensions to the quantum particle, as a finite distribution of matter in the coordinate space.

A semiconductor device for the environment heat conversion in coherent electromagnetic energy by a super radiant quantum decay and a thermal excitation of a system of electrons in a super lattice of n-i-p-n transistors with quantum dots on the two sides of the i-layer, and potential barriers for separating the quantum transition n-i-p regions from the adjacent conduction n and p regions. When an electron current is injected in a perpendicular direction on the transistor arrays, a super radiant field is generated in the plane of these arrays, with a power mainly obtained by a heat absorption that is much larger than the absorbed electric power. The device also includes an input heat absorber, and an output Fabry-Perot resonator with total transmission for the electromagnetic energy extraction from the device active region.

Fundamental subjects of quantum mechanics and general relativity are presented in a unitary framework. Based on the fundamental quantum laws of Planck-Einstein and De Broglie, a quantum particle is described by wave packets in the conjugate spaces of the coordinates and momentum. With the time dependent phases proportional to the Lagrangian, the group velocities of these wave packets are in agreement with the fundamental Hamilton equations.  When the relativistic Lagrangian, as a function of the metric tensor and the matter velocity field, is considered, the wave velocities are equal to the wavefunction coordinate velocity, which means that these waves describe the matter propagation. The equality of the integrals of the matter densities over the coordinate and momentum spaces, with the mass in the Lagrangian of the time dependent phases, which describes the particle dynamics, represents the mass quantization rule. Describing the interaction of a quantum particle with the electromagnetic field by a modification of the particle dynamics determined by additional terms in the time dependent phases, with an electric potential conjugated to time, and a vector potential conjugated to the coordinates, Lorentz’s force and Maxwell’s equations are obtained. With Dirac’s Hamiltonian, and operators satisfying the Clifford algebra, dynamic equations similar to those used in the quantum field theory are obtained, but with an additional relativistic function, depending on the velocity, and the matter-field momentum. We obtain particle and antiparticle wavefunctions describing matter and anti-mater distributions. Unlike the conventional Fermi’s golden rule, in the new theory the particle transitions are described by the Lagrangian matrix elements over the Lagrangian eigenstates and the densities of these states. Transition rates are obtained for the two possible processes, with the spin conservation, or with the spin inversion. In this framework, we consider Dirac’s formalism of the general relativity, with the basic concepts of the Christoffel symbols, covariant derivative, scalar density and the matter conservation, the geodesic dynamics, curvature tensor, Bianci equations, Ricci tensor, Einstein’s gravitation law, and the Schwarzschild metric tensor. From the action integrals for the gravitational field, matter, electromagnetic field, and electric charge, we obtain the generalized Lorentz force and Maxwell equations for general relativity. It is shown that the gravitation equation is not modified by the electromagnetic field. For a black hole, the velocity and the acceleration of a particle are obtained. At the formation of a black hole, as a perfectly spherical object of matter gravitationally concentrated inside the Schwarzschild boundary, the central matter explodes, the inside matter being carried out towards this boundary, but reaching there only in an infinite time. Based on this model, we conceive our universe as a huge black hole, with its essential properties, as Big Bang, Inflation, the low large-scale density, the redshift, the quasi-inertial behavior of the distant bodies, the dark matter and the dark energy, entirely explained by the general relativity. For a quantum particle in a gravitational wave, we obtained a rotation of the metric tensor perpendicular to the propagation direction of this wave, with the angular momentum 2, that we call the graviton spin, and a rotation of the particle matter, with a half-integer spin for Fermions, and an integer spin for Bosons. We apply this theory to a two-particle and a particle-antiparticle collision, and a two-body decay of a quantum particle. In this framework, we also obtain a unitary description of the four forces acting in nature. A system of equations for the quark coordinates in a proton, is obtained.
Keywords: wave packet, group velocity, Schrödinger picture, Heisenberg picture, scalar potential, vector potential, Lorentz force, Maxwell equations, geodesic equation, Dirac Hamiltonian, spin, spinor, two-body collision, Hamiltonian, covariant derivative, Schwarzschild metric tensor, Clifford algebra, vertex, two-body decay, Inflation, redshift, vacuum impedance, contravariant coordinate, antiparticle, Fermi's golden rule, Pauli spin operators, Lagrange equations, Lagrangian, Christoffel symbol, metric tensor, Feynman diagram, black hole, four-vector, covariant coordinate, time-space interval, density of states, Dirac spin operators, wave velocity, the least action, curvature, Schwarzschild singularities, Big Bang, Schwarzschild boundary, virtual photon, Bianci equations, Ricci tensor, graviton spin, Einstein’s equation of gravitation, weak interaction, strong interaction, flavour space, colour space, up quark, down quark, red quark, green quark, blue quark, quantum electrodynamics, quantum flavour-dynamics, quantum chromodynamics, red gluon, green gluon, blue gluon, nucleon, Gell-Mann operators, grand unified theory

Fundamental subjects of quantum mechanics and general relativity are presented in a unitary framework. A quantum particle is described by wave packets in the two conjugate spaces of the coordinates and momentum. With the time dependent phases proportional to the Lagrangian, the group velocities of these wave packets are in agreement with the fundamental Hamilton equations.  When the relativistic Lagrangian, as a function of the metric tensor and the matter velocity field, is considered, the wave velocities are equal to the matter velocity. This means that these waves describe the matter propagation, and that the equality of the integrals of the matter densities over the spatial and the momentum spaces, with the mass in the Lagrangian of the time dependent phases, which describes the particle dynamics, represent a mass quantization rule.
Describing the interaction of a quantum particle with the electromagnetic field by a modification of the particle dynamics, induced by additional terms in the time dependent phases, with an electric potential conjugated to time, and a vector potential conjugated to the coordinates, Lorentz’s force and Maxwell’s equations are obtained. With Dirac’s Hamiltonian, and operators satisfying the Clifford algebra, dynamic equations similar to those used in the quantum field theory and particle physics are obtained, but with an additional relativistic function, depending on the velocity, and the matter-field momentum. For particles and antiparticles, wavefunctions for finite matter distributions are obtained.
The particle transitions, and Fermi’s golden rule, are described by the Lagrangian matrix elements over the Lagrangian eigenstates and densities of these states. Transition rates are obtained for the two possible processes, with the spin conservation or with the spin inversion.
Dirac’s formalism of general relativity, with basic concepts of Christoffel symbols, covariant derivative, scalar density and matter conservation, the geodesic dynamics, curvature tensor, Bianci equations, Ricci tensor, Einstein’s gravitation law and the Schwarzschild matric elements, are presented in detail.
From the action integrals for the gravitational field, matter, electromagnetic field, and electric charge, Lorentz’s force and Maxwell’s equations in the general relativity are obtained. It is also shown that the gravitational field is not modified by the electromagnetic field.
For a black hole, the velocity and the acceleration of a particle are obtained. It is shown that, in the perfect spherical symmetry hypothesis, an outside particle is attracted only up to three times the Schwarzschild radius, between this distance and the Schwarzschild radius the particle being repelled, so that it reaches this boundary only in an infinite time, with null velocity and null acceleration. At the formation of a black hole, as a perfectly spherical object of matter gravitationally concentrated inside the Schwarzschild boundary, the central matter explodes, the inside matter being carried out towards this boundary, but reaching there only in an infinite time, with null velocity and null acceleration. In this way, our universe is conceived as a huge black hole. Based on this model, the essential properties, as big bang, inflation, the low large-scale density, the quasi-inertial behavior of the distant bodies, redshift, the dark matter and the dark energy, are unitarily explained.
From the description of a gravitational wave by harmonically oscillating coordinates, the wave equation for the metric tensor is obtained, the propagation direction of such a wave being taken for reference. For a quantum particle as a distribution of matter interacting with a gravitational field, according to the proposed model, it is obtained that this field rotates with the angular momentum 2, called the graviton spin, as a rotation of the metric tensor which is correlated to the matter velocity, as the particle matter rotates with a half-integer spin for Fermions, and an integer spin for Bosons.

Essentially, in this paper we propose a new description of the quantum dynamics by two relativistic propagation wave packets, in the two conjugated spaces, of the coordinates and of the momentum. Compared to the Schrödinger-Dirac equation, which describes a free particle by a wave function continuously expanding in time, considered as the amplitude of a probabilistic distribution of this particle, the new equations describe a free particle as an invariant distribution of matter propagating in the two spaces, as it should be. Matter quantization arises from the equality of the integral of the matter density with the mass describing the dynamics of this density in the phases of the wave packets. In this description, the classical Lagrange and Hamilton equations are obtained as the group velocities of the two wave packets in the coordinate and momentum spaces. When to the relativistic Lagrangian we add terms with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and a scalar potential conjugated to time, we obtain the Lorentz force and the Maxwell equations as characteristics of the quantum dynamics. In this framework, the conventional Schrödinger-Dirac equations of a quantum particle in an electromagnetic field obtain additional terms explicitly depending on velocity, as is expected in the framework of relativistic theory. Such a particle wave function takes the form of a rapidly varying wave, with the frequency corresponding to the rest energy, modulated by the electric rotation with the spins ½ for Fermions, and 1 for Bosons. From the new dynamic equations, for a free particle in the coordinate and momentum spaces, we reobtain the two basic equations of the quantum field theory, but with a change of sign, and an additional term depending on momentum, to the rest mass as the eigenvalue of these equations. However, when these eigenvalues are eliminated, the wave function takes the form of a wave packet of spinors of the same form as in the conventional quantum field theory, with a normalization volume as the integral of the ratio of the energy to the rest energy, over the momentum domain which gives finite dimensions to the quantum particle, as a finite distribution of matter in the coordinate space.