Nonlinear Quantum Theory Research Articles

Abundant Bounded and Unbounded Solitary, Periodic, Rogue‐Type Wave Solutions and Analysis of Parametric Effect on the Solutions to Nonlinear Klein–Gordon Model

This paper exploits the modified simple equation and dynamical system schemes to integrate the Klein–Gordon (KG) model amid quadratic nonlinearity arising in nonlinear optics, quantum theories, and solid state physics. By implementing the modified simple equation (MSE) technique, we develop some disguise adaptation of analytical solutions in terms of hyperbolic, exponential, and trigonometric functions with some special parameters. We apply the dynamical system to bifurcate the model and draw distinct phase portraits on unlike parametric constraints. Following each orbit of all phase portraits, we originate bounded and unbounded solitary, periodic, and periodic rogue‐type wave solutions of the KG model. These two schemes extract widespread classes of solitary, periodic, and periodic rogue‐type wave solutions for the KG model jointly due to restrictions on parameters. We also analyze the effect of parameters on the obtained wave solutions and discuss why and when it changes its nature. We illustrate some dynamical features of the acquired solutions via the 3D, 2D, and contour graphics.

High harmonics generation in bilayer graphene at high Fermi energies induced by coherent THz-radiation

The higher-order harmonic generation process in the nonperturbative regime at the interaction of coherent electromagnetic radiation with the AB-stacked bilayer graphene at high Fermi energies is considered. The applied coherent low-frequency radiation field in the high Fermi energy zone of electrons excludes the interband transitions enhancing high harmonic rates. The developed microscopic nonlinear quantum theory for charged carriers interaction with a strong pump wave is valid near the Dirac points of the Brillouin zone. The Liouville–von Neumann equation for the density matrix in the multiphoton excitation regime is solved both analytically and numerically. Based on the numerical solutions, we examine the rates of higher-order harmonics of the pump wave of arbitrary polarization. Obtained results show that bilayer graphene serves as an effective material for the generation of higher-order harmonics from THz to the mid-IR domain of frequencies at moderate pump wave intensities.

High-harmonic generation at particle–hole multiphoton excitation in gapped bilayer graphene

A microscopic nonlinear quantum theory of the interaction of coherent electromagnetic radiation with gapped bilayer graphene is developed. The Liouville-von Neumann equation for the density matrix is solved numerically at the multiphoton excitation regime. The developed theory of interaction of charged carriers with the strong driving wave field is valid near the Dirac points of the Brillouin zone. We consider the harmonic generation process in the nonadiabatic regime of interaction when the Keldysh parameter is of the order of unity. On the basis of numerical solutions, we examine the rates of odd and even high harmonics at the particle–hole annihilation in the field of a strong pump wave of arbitrary polarization. The obtained results show that the gapped bilayer graphene can serve as an effective medium for the generation of even and odd high harmonics in the terahertz and far-infrared domains of frequencies.

Microscopic nonlinear quantum theory of absorption of coherent electromagnetic radiation in doped bilayer graphene

The microscopic quantum theory of nonlinear stimulated scattering of chiral particles in doped $AB$ stacked bilayer graphene on Coulomb field of charged impurities in the presence of strong coherent electromagnetic radiation is presented. The Liouville-von Neumann equation for the density matrix is solved analytically. Here the interaction of electrons with the scattering potential is taken into account as a perturbation. The absorption rate of nonlinear inverse-bremsstrahlung for a grand canonical ensemble of fermionic chiral particles is calculated using the obtained solution. The analysis of the obtained rate shows that in the terahertz and near-infrared range of frequencies there is significant absorption of incident radiation via multiphoton stimulated bremsstrahlung mechanism.

Third harmonic generation in gapped bilayer graphene

With the help of numerical simulations in microscopic nonlinear quantum theory of coherent electromagnetic radiation interaction with a gapped bilayer graphene, we find out the optimal values of pump wave intensity, graphene temperature, and energy gap induced by a constant electric field for practically significant third order harmonic coherent emission. The Liouville-von Neumann equation is treated numerically for the third harmonic generation in multiphoton excitation regime near the Dirac points of the Brillouin zone. We examine the rates of the third harmonic at the particle-hole annihilation in the field of a strong pump wave of linear polarization for practically real/optimal parameters of a considering system. The obtained results show that by choosing the optimal values of the main characteristic parameters, a gapped bilayer graphene can serve as an effective medium for generation of the third harmonic at room temperatures in the terahertz and far infrared domains.

Microscopic nonlinear quantum theory of absorption of strong electromagnetic radiation in doped graphene

Microscopic nonlinear quantum theory of absorption of strong electromagnetic radiation in doped graphene

Microscopic nonlinear relativistic quantum theory of absorption of powerful x-ray radiation in plasma

The microscopic quantum theory of plasma nonlinear interaction with the coherent shortwave electromagnetic radiation of arbitrary intensity is developed. The Liouville-von Neumann equation for the density matrix is solved analytically considering a wave field exactly and a scattering potential of plasma ions as a perturbation. With the help of this solution we calculate the nonlinear inverse-bremsstrahlung absorption rate for a grand canonical ensemble of electrons. The latter is studied in Maxwellian, as well as in degenerate quantum plasma for x-ray lasers at superhigh intensities and it is shown that one can achieve the efficient absorption coefficient in these cases.

Nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in a dielectric medium

A nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in an isotropic dielectric medium is presented. A quantum model based on the Klein-Gordon equation is used. The growth rates of beam instabilities caused by the effect of stimulated Cherenkov radiation have been determined in the linear approximation. Mechanisms of the nonlinear saturation of relativistic quantum Cherenkov beam instabilities have been analyzed and the corresponding analytical solutions have been obtained.

Nonlinear relativistic quantum theory of Cherenkov emission of longitudinal Langmuir waves in a plasma

A nonlinear relativistic quantum theory of stimulated Cherenkov emission of longitudinal waves by a relativistic monoenergetic electron beam in a cold isotropic plasma is presented. The theory makes use of a quantum model based on the Klein-Gordon equation. The instability growth rates are obtained in the linear approximation and are shown to go over to the familiar growth rates in the classical limit. The mechanisms for the nonlinear saturation of relativistic Cherenkov beam instabilities are described with allowance for quantum effects, and the corresponding analytic solutions are derived.

Vacuum Cherenkov effect in logarithmic nonlinear quantum theory

We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics – cone angle, flash duration, radiation yield and spectral distribution – are computed. It turns out that the radiation yield is proportional to the square of the proper energy scale of the vacuum which serves also as the vacuum instability threshold and the natural ultraviolet cutoff. While the analysis is mainly based on the theory engaging the logarithmic nonlinear quantum wave equation, some of the obtained results must be valid for any Lorentz-invariance violating theory describing the vacuum by (effectively) continuous medium in the long-wavelength approximation.

Nonlinear quantum mechanics, the superposition principle, and the quantum measurement problem

There are four reasons why our present knowledge and understanding of quantum mechanics can be regarded as incomplete. (1) The principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. (2) There is no universally agreed upon explanation for the process of quantum measurement. (3) There is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. (4) Most importantly, the concept of time is classical and hence external to quantum mechanics: there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the aforesaid problems. We use a physically motivated model for a nonlinear Schrodinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects (lifetime is too small). It also suggests that ongoing laboratory experiments may be able to detect the finite superposition lifetime for mesoscopic objects in the near future.

Classical and quantum description of electron trapping during the Cherenkov beam instability in plasma

A nonlinear quantum theory of the Cherenkov instability of a nonrelativistic monoenergetic electron beam in a cold plasma is constructed. It is shown that the instability of a low-density beam is almost purely quantum in nature and results from the emission of one quantum of a plasma wave—a plasmon—by the beam electrons. The number of emitted (and absorbed) plasmons increases with beam density, so, in the limit of high-density beams, the instability becomes a classical Cherenkov beam instability in plasma. Some analytic solutions and estimates are found, detailed numerical results are obtained, and the evolution of the quantum distribution function of the beam electrons in different regimes of the beam instability is investigated.

Uncertainty features of microscopic particles described by nonlinear Schrüdinger equation

Abstract The uncertainty relationship between position and momentum of the microscopic particles is calculated by nonlinear quantum theory in which the states of the particles are described by a nonlinear Schrudinger equation. The results show that the uncertainty relation differs from that in the quantum mechanics and has a minimum value in this case. This means that the position and momentum of the particles could be determined simultaneously to a certain degree, which could be caused by the wave–corpuscle duality of the microscopic particles described by the nonlinear Schrudinger equation.

THE INEVITABLE NONLINEARITY OF QUANTUM GRAVITY FALSIFIES THE MANY-WORLDS INTERPRETATION OF QUANTUM MECHANICS

There are fundamental reasons why there should exist a reformulation of quantum mechanics which does not refer to a classical space–time manifold. It follows that quantum mechanics as we know it is a limiting case of a more general nonlinear quantum theory, with the nonlinearity becoming significant at the Planck mass/energy scale. This nonlinearity is responsible for a dynamically induced collapse of the wave function, during a quantum measurement, and it hence falsifies the many-worlds interpretation of quantum mechanics. We illustrate this conclusion using a mathematical model based on a generalized Doebner–Goldin equation. The non-Hermitian part of the Hamiltonian in this norm-preserving, nonlinear, Schrödinger equation dominates during a quantum measurement, and leads to a breakdown of linear superposition.

Square-integrable solutions to a family of nonlinear schrödinger equations from nonlinear quantum theory

We consider nonlinear Schrodinger equations which have been proposed as fundamental equations of nonlinear quantum theories. The equations are singular in that the wave function ψ appears in the denominator of rational expressions. To avoid the problem of zeros of ψ it is natural to make the ansatz ψ = e ν . This ansatz, however, conflicts with the—physically motivated—requirement that the solutions ψ be square integrable. We show that this conflict can be resolved by considering an unusual function space whose definition involves the derivative ∇ ν of ν . This function space turns out to be dense subset of L 2 and the equations can be solved in the L 2 -sense (as desired) by first solving an evolutionary system for ∇ ν and then transforming back to ψ.

Patient-practitioner-remedy (PPR) entanglement. Part 6. Miasms revisited: non-linear quantum theory as a model for the homeopathic process

The possibility that non-linear quantum theory could be used to model PPR entanglement is discussed in relation to the treatment of miasms. In this model, miasms are imagined as disease entities behaving like solitary waves, or ‘solitons’ which, when trapped in a therapeutic state space, requiring equally soliton-like (miasmatic or high potency) remedies to effectively ‘annihilate’ them.

Thermally Biological Effects and Its Medical Functions of the Infrared Rays Absorbed by Living Systems

thermally biological effects of infrared lights absorbed have been studied by nonlinear quantum theory and molecular biological theory on the basis of structures of cell and water molecules. There is a large number of water in the living systems, it play an important role in living activity, and has a lot of biological functions. There would be no life without water. We can confirm that the thermally biological effect is a result produced by disorder motions of bio-water-molecules according to the essence of heat, feature of molecular structure of water, theory of molecular physics, principle of resonante absorption and experimental fact that infrared light can heat liquid water. Therefore, mechanism of this effect is that the infrared light absorbed results in the quantum vibrations of water molecules with hydrogen bonds, the vibrational energy again transformes as thermal energy of disorder motions of a great number of water molecules in the living systems. The heating waters can cause a lot of biological effects and phenomena to occur in the living systems. Therefore, the infrared lights absorbed by the living systems have some medical functions.

Covariant Regularization of Nonlinear Spinorfield Quantum Theories and Probability Interpretation

Abstract By a decomposition theorem a higher order nonlinear spinorfield equation can be transformed into a set of first order nonlinear spinorfield equations, i. e. into an auxiliary field formulation which allows canonical quantization. The quantum dynamics of the auxiliary fields is expressed in algebraic Schrödinger representation and admits only unphysical state spaces with indefinite metric. Regularization of the classical theory is transferred into quantum field theory by a noninvertible map from the corresponding auxiliary field state space into an associated physical state space, the metric of which is positive definite. For the effective dynamics in the physical state space probability current conservation is proved, and for physical states which describe composite particle configurations the existence of the state space is demonstrated

Comment on “Consistency, amplitudes, and probabilities in quantum theory”

In a recent article [Phys. Rev. A 57, 1572 (1998)] Caticha has concluded that ``nonlinear variants of quantum mechanics are inconsistent.'' In this note we identify what it is that nonlinear quantum theories have been shown to be inconsistent with.

Calculation of highly excited vibrational energy levels of CH 3 CN molecule by non-linear quantum theory

A three-parameter nonlinear dynamical model, i.e., the quantized discrete self-trapping equation, was used to calculate the highly excited CH stretching vibrational energy levels of liquid phase CH3CN molecule in the electronic ground state up to n=7. The calculated results show that the experimental energy levels can be well described by the model.