Chirality detected in Hartley’s electronic oscillator

Chirality is an elusive asymmetry important in science and technology and confined mainly to the quantum realm. This paper reports the observation of chirality in a classical (that is, not quantum) scenario, namely in stability diagrams of an autonomous electronic oscillator with a junction-gate field-effect transistor (JFET) and a tapped coil. As the number of spikes (local maxima) of stable oscillations changes along closed parameter paths, they generate two types of intricate structures. Surprisingly, such pair of structures are artful images of each other when reflected on a mirror. They are dual chiral pairs interconnecting families of stable oscillations in closed loops. Chiral pairs should not be difficult to detect experimentally. This chirality is conjectured to be a generic property of nonlinear oscillators governed by classical (that is, not quantum) equations.

Ulam stability for nonautonomous quantum equations

We establish the Ulam stability of a first-order linear nonautonomous quantum equation with Cayley parameter in terms of the behavior of the nonautonomous coefficient function. We also provide details for some cases of Ulam instability.

Quantum Theory of Massless Particles in Stationary Axially Symmetric Spacetimes

Quantum equations for massless particles of any spin are considered in stationary uncharged axially symmetric spacetimes. It is demonstrated that up to a normalization function, the angular wave function does not depend on the metric and practically is the same as in the Minkowskian case. The radial wave functions satisfy second order nonhomogeneous differential equations with three nonhomogeneous terms, which depend in a unique way on time and space curvatures. In agreement with the principle of equivalence, these terms vanish locally, and the radial equations reduce to the same homogeneous equations as in Minkowski spacetime.

Hyers–Ulam Stability for Cayley Quantum Equations and Its Application to h-Difference Equations

The main purpose of this study is to clarify the Hyers–Ulam stability (HUS) for the Cayley quantum equation. In addition, the result obtained for all parameters is applied to HUS of h-difference equations with a specific variable coefficient using a new transformation.

Experiment Regarding Magnetic Fields with Gravity

We observed the Earth's gravity to produce electricity in the magnetic sea. The gravity generator (GG) generated currents and voltages on the mesoscopic scale when we connected it in the vacuum. Gravity interacts to generate electricity in the Earth’s direction or the opposite direction by the repulsive magnetic force. The ground-based device simulates the potential energy (voltages) between gravity and magnetic seas. The GG increased simulations of gravity quantum effects using different physical set-ups. A trapped gravity was set to behave as free relativistic quantum particles or fluids, which made it possible to measure the particle position as a function of time and study the magnetic sea for different initial superpositions of positive- negative-gravity spinor state. It might explain the relativistic quantum equations, antigravity, and the heating mechanism of the Sun.

Space-Time in Quantum Theory

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of light c not being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constant h requires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced by an infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics: To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values of h, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action.

Experiment Regarding Magnetic Fields with Gravity

We observed the Earth's gravity to produce electricity in the magnetic sea. The gravity generator (GG) generated currents and voltages on the mesoscopic scale when we connected it in the vacuum. Gravity interacts to generate electricity in the Earth’s direction or the opposite direction by the repulsive magnetic force. The ground-based device simulates the potential energy (voltages) between gravity and magnetic seas. The GG increased simulations of gravity quantum effects using different physical set-ups. A trapped gravity was set to behave as free relativistic quantum particles or fluids, which made it possible to measure the particle position as a function of time and study the magnetic sea for different initial superpositions of positive- negative-gravity spinor state. It might explain the relativistic quantum equations, antigravity, and the heating mechanism of the Sun.

A new insight to the scaling-law fluid associated with the Mandelbrot scaling law

This paper addresses a non-traditional approach for the scaling-law fluid-flows described by fractal scaling-law vector calculus associated with the Mandelbrot scaling law. Their quantum equations were proposed to control the fluid-flows associated with the Mandelbrot scaling law. This gives a new insight into the descriptions for the scaling-law behaviors of the fluid-flows in the Mandelbrot scaling-law phenomena.

Solving Quantum Equations with Gauge Fields: How Explicit Integrators Based on a Bipartite Lattice and Affine Transformations Can Help

We proposed an explicit numerical integrator consisting of affine transformation pairs resulting from the checkerboard lattice for spatial discretization. It can efficiently solve time evolution equations that describe dynamical quantum phenomena under gauge fields, e.g., generation, motion, interaction of quantum vortices in superconductors or superfluids.

Effective theories as truncated trans-series and scale separated compactifications

We study the possibility of realizing scale-separated type IIB Anti-de Sitter and de Sitter compactifications within a controlled effective field theory regime defined by low-energy and large (but scale-separated) compactification volume. The approach we use views effective theories as truncations of the full quantum equations of motion expanded in a trans-series around this asymptotic regime. By studying the scalings of all possible perturbative and non-perturbative corrections we identify the effects that have the right scaling to allow for the desired solutions. In the case of Anti-de Sitter, we find agreement with KKLT-type scenarios, and argue that non-perturbative brane-instantons wrapping four-cycles (or similarly scaling effects) are essentially the only ingredient that allows for scale separated solutions. We also comment on the relation of these results to the AdS swampland conjectures. For the de Sitter case we find that we are forced to introduce an infinite number of relatively unsuppressed corrections to the equations of motion, leading to a breakdown of effective theory. This suggests that if de Sitter vacua exist in the string landscape, they should not be thought of as residing within the same effective theory as the AdS or Minkowski compactifications, but rather as defining a separate asymptotic regime, presumably related to the others by a duality transformation.