Equations Of Quantum Theory Research Articles

Equations of quantum theory in the space of randomly joint quantum events

The dynamics of the system in the space of random joint events is considered. The symmetric difference of events is introduced in space based on the Kolmogorov axioms. To describe quantum effects in the dynamics of the system, an additional axiom is introduced for random joint events: “the symmetric sum of random events.” In the generated space of random joint events, an equation is constructed for the probability of a system transition between two events. It is shown that for pairwise joint events it is equivalent to the equation of quantum mechanics.

Quantum jumps, superpositions, and the continuous evolution of quantum states

The apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schrödinger's time-dependent equation also seemed to require a modification of the explanation for the origin of line spectra due to the apparent possibility of superpositions of energy eigenstates for different energy levels. Indeed, Schrödinger himself proposed a quantum beat mechanism for the generation of discrete line spectra from superpositions of eigenstates with different energies.However, these issues between old quantum theory and Schrödinger's wave mechanics were correctly resolved only after the development and full implementation of photon quantization. The second quantized scattering matrix formalism reconciles quantum jumps with continuous time evolution through the identification of quantum jumps with transitions between different sectors of Fock space. The continuous evolution of quantum states is then recognized as a sum over continually evolving jump amplitudes between different sectors in Fock space.In today's terminology, this suggests that linear combinations of scattering matrix elements are epistemic sums over ontic states. Insights from the resolution of the dichotomy between quantum jumps and continuous time evolution therefore hold important lessons for modern research both on interpretations of quantum mechanics and on the foundations of quantum computing. They demonstrate that discussions of interpretations of quantum theory necessarily need to take into account field quantization. They also demonstrate the limitations of the role of wave equations in quantum theory, and caution us that superpositions of quantum states for the formation of qubits may be more limited than usually expected.

Homogeneity of Space-time Implies the Free Schrödinger Equation

The free Schrodinger equation is shown to be a consequence of space-time homogeneity in the non-relativistic domain. First, we show that space-time translation invariance of natural laws, which is a conseqiuence of space-time homogeneity, entails that the state of a free particle with definite momentum and energy assumes the plane wave form when the time evolution of the state is linear. Next, we show that the conservation of energy and momentum, which is a consequence of space-time translation invariance, may further determine the energy-momentum relation In the non-relativistic domain. These results then lead to the free Schrodinger equation naturally. The new integrated analysis may help understand the origin of the wave equations in quantum theory.

Quantum Corrections to the Dynamics of the Expanding Universe

The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schr\"{o}dinger equation complemented by the equations of motion for the momentum operator and its time derivative in Heisenberg's form reduce to the Einstein equations with an additional source of the gravitational field of quantum nature. The spatially closed universe with cosmological constant, originally filled with a uniform scalar field and radiation, is considered as quantum cosmological system. The perfect fluid in the form of radiation defines the material reference frame. The properties of the averaged scalar field which acts like ordinary matter are investigated. After averaging over its quantum states, the free scalar field turns into the Weyssenhoff fluid characterized by the energy density, pressure, and spin of constituent particles. The cases when the contribution of the quantum effects into the gravitational interaction becomes significant on macroscopic scale are analyzed. It is demonstrated that, unless the whole, at least a part of such matter-energy constituents as dark matter and dark energy may have a quantum origin.

Теоретико-полевой подход к описанию деформирования многокомпонентных поликристаллических материалов

Most of inorganic structural materials (metallic alloys, ceramics, minerals etc.) are polycrystalline aggregates, consisted of macroscopically large quantity of single-crystal grains (crystallites). The mechanical behavior of the specimen of polycrystalline material is governed by the physical and mechanical processes in the grains and interaction of the grains. Thus the deformation of polycrystalline material is a cooperative phenomenon typical for condensed matter physics and mechanics of heterogeneous materials. The passing of these processes depends on many parameters, including stress states of individual grains and its evolution during macrodeformation. In this paper we note a mathematical analogy between the equations of the mechanics of heterogeneous polycrystalline materials and the equations of quantum theory of particles scattering. This analogy allows to apply the methods of quantum field theory to solution of the equations of solid mechanics for heterogeneous media. We consider the application of Corringa-Kohn-Rostoker method, used in quantum theory for calculating wave function of electrons in metallic alloys, to elasticity of polycrystals. This approach allows, for instance, to calculate probability distribution density function for stresses in grains under arbitrary macrodeformation of polycrystal. Application of the method to classical problem of homogenization gives new formulae for the effective moduli of disordered polycrystalline medium.

Superfluidity of classical liquid in a nanotube for even and odd numbers of neutrons in a molecule

1.1. The case of an even number of neutrons. We first note that solutions of the variational equation for the Vlasov equation do not coincide with the classical limit for the variational equations corresponding to the mean-field equations in quantum theory. We consider mean-field equations of the form ih ∂ ∂t ϕ t (x )= � − h 2 2m ∆+ Wt(x)

Do Deeper Principles Underlie Quantum Uncertainty and Nonlocality?

No matter how you look at the equations of quantum theory, they allow a tiny object to behave in ways that defy intuition. Scientists are hoping to someday get beyond the discomfort that led Einstein to declare that [God] does not play dice.

Beam Optics and Signal Analysis in a Quantumlike Approach

The application of the tomographic map introduced recently in quantum mechanics is discussed in connection with classical problems that are described by equations formally coinciding with the equations of quantum theory. Examples of the classical problems such as charged‐particle‐beam transport and analytic‐signal analysis are reviewed. Some aspects of possible applications in quantum computing and quantum communication are discussed.

QUANTUM CHRONOTOPOLOGY AND TIME ASYMMETRY IN FIELD THEORY

A new, physical definition of the time elements is mathematically given. Their union constitutes a disconnected time topological space, [Formula: see text]. Based on the properties of this time–space and using the theory of random quantum fields previously developed, a nonunitary evolution operator, [Formula: see text], is derived. [Formula: see text] breaks down into two disjunct, spontaneously renormalized evolution operators by quantizing the random field action integral: one operator is unitary, [Formula: see text], and the other non-measure-preserving, [Formula: see text]. [Formula: see text] coincides, apart from the renormalization, with the evolution operator of the standard QFT. U ump (τ) breaks time symmetry in QFT. It reconciles the time reversal invariance of the basic equations of quantum theory with the irreversibility of the macroscopic, and some microscopic, phenomena. It provides a basis for the CP violation in the neutral K0 meson decay. Functional integrals arising in the theory have in the limit countably additive measures.

Non-negativity condition for cellular automata and other massively parallel computer algorithms

The importance of satisfying the non-negativity condition given in the original paper (1993 J. Phys. A: Math. Gen. 26 L209) in derivations and computer algorithms is noted. When the non-negativity condition is ignored, as was done by G?mez-Vilar and Sol?, non-physical results may be obtained. In contrast, when the step sizes go to zero in a manner consistent with the non-negativity condition, it can be shown that the difference equations are pointwise consistent with the continuum equations of quantum theory.

An alternative approach to quantum phenomena

This paper outlines the qualitative foundations of a “quasiclassical” theory in which particles are pictured as spatially extended periodic excitations of a universal background field, interacting with each other via nonlinearity in the equations of motion for that field, and undergoing collapse to a much smaller volume if and when they are detected. The theory is based as far as possible directly on experiment, rather than on the existing quantum mechanical formalism, and it offers simple physical interpretations of such concepts as mass, 4-momentum, interaction, potentials, and quantization; it may lead directly to the standard equations of quantum theory, such as the multiparticle Schrodinger equation, without going through the conventional process of “quantizing” a classical theory. The theory also provides an alternative framework in which to discuss wave-particle duality and the quantum “measurement problem”; in particular, it is suggested that the unpredictability of quantum phenomena may arise from “deterministic chaos” in the behavior of the background field.

The Aharonov-Bohm effect and the visuality in quantum mechanics

An attempt is made to examine the physical nature of the Aharonov-Bohm effect. A model is proposed which may be used to obtain the basic equation of quantum theory and to visualize particle interference.

Dynamical algebra of invariants of integra-differential equations of quantum theory

The Heisenberg-Weyl dynamical algebra of invariants for the special type of integro-difierential equations of quantum theory is developed.

Symmetry Conditions on Nonlinear Spinor Field Functionals/The symmetry conditions of nonlinear spinor theory of elementary particles, i.e. the definitions of quantum numbers, are given for the nonlinear spinor field functionals.

The operator equations of quantum theory can be replaced formally by functional equations of corresponding Schwinger functionals 1-3. To give this formalism a physical and mathematical meaning one has to develop a complete functional quantum theory as has been proposed in a preceding paper4. Then the complete physical information has to be given by functional operations only. Especially the quantum numbers of ordinary quantum theory have to be reproduced functionally. As the quantum numbers are defined by the eigenvalues of the generators of the corresponding invariance groups, one has to investigate these quantities in functional space. This is done in this paper. To have a definite model we consider the nonlinear spinor field with noncanonical relativistic Heisenberg quantization 5 the form invariance group of which is the Poincare group. Although this model has still other symmetry properties we restrict ourselves to the discussion of the quantum number conditions resulting from this group, as the considerations for other groups and models are quite analogous.

A Classical Theory of Electromagnetism and Gravitation

ATTEMPTS to obtain a unified theory of gravitational and electromagnetic phenomena1 have assumed the form of generalizing the equations of general relativity theory, so that they incorporate terms which may be identified with electromagnetic potentials and charge and current distributions. At the moment it seems that these attempts will not lead to an explanation of such quantum theoretical results as the indeterminacy principle, and their very complexity makes it difficult to see how they will yield a hint as to necessary modifications of the equations of quantum theory required to overcome the difficulties inherent in its present form. In any event, such a synthesis of gravitational and electromagnetic phenomena in quantum theory is generally regarded as secondary in importance, since gravitational forces on elementary particles are extremely small.