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It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show…
An exactly solvable strongly correlated electron model with two independent parameters is constructed in the frame of the quantum inverse scattering method, which can be seen as a generalization of the Bariev model. Through the Bethe ansatz…
In signal analysis, among the effort of seeking for efficient representations of a signal into the basic ones of meaningful frequencies, to extract principal frequency components, consecutively one after another or $n$ at one time, is a…
Radical revision on the conventional spacetime picture, illusion or emergent phenomenon, has been the focus of the speculations on the unified frameworks for fundamental interactions in nature. Compared to strong experimental credence to…
The belief propagation algorithm has been recognized in the information theory community as a soft-decision iterative decoding algorithm. It is the most powerful algorithm found so far for attacking hard optimization problems in channel…
The wave-structure of moving electrons is analyzed on a fundamental level by employing a modified de Broglie relation. Formalizing the wave-function $\psi$ in real notation yields internal energy components due to mass oscillations. The…
We present exact solutions of the Schr\"odinger equation for a quantum system with complex mass subjected to a complex Morse potential in the extended complex phase space. The normalized eigenfunctions and corresponding eigenspectra are…
A universal energy eigenvalue equation is proposed in this paper. It is proven that the unique set of eigenfunctions or preferred basis exists for any non-isolated sub-system. Applying the new eigenvalue equation to the relative motion of a…
The Billera-Holmes-Vogtmann (BHV) space of weighted trees can be embedded in Euclidean space, but the extrinsic Euclidean mean often lies outside of treespace. Sturm showed that the intrinsic Frechet mean exists and is unique in treespace.…
The theoretical foundations of quantum mechanics and de Broglie--Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal…
I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then…
Spectral analysis is performed on the Born equation, a strongly singular integral equation modeling the interactions between electromagnetic waves and arbitrarily shaped dielectric scatterers. Compact and Hilbert--Schmidt operator…
Using weak wave turbulence theory analysis, we distinguish three main regimes for 2D stratified fluids in the dimensionless parameter space defined by the Froude number and the Reynolds number: discrete wave turbulence, weak wave…
Nowhere dense classes of graphs are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness,…
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…
We study in this work an integral formulation for the radiative transfer equation (RTE) in anisotropic media with truncated approximation to the scattering phase function. The integral formulation consists of a coupled system of integral…
By analysing probabilistic foundations of quantum theory we understood that the so called quantum calculus of probabilities (including Born's rule) is not the main distinguishing feature of "quantum". This calculus is just a special variant…
Thermoelectric transport coefficients are determined for semiconductor quantum wires with weak thickness fluctuations. Such systems exhibit anomalies in conductance near 1/4 and 3/4 of 2e^2/h on the rising edge to the first conductance…
The "main road" open by de Broglie's and Schroedinger's discovery of matter waves and of their eigen-functions branched off, as is well known, into different "sub-routes". The most widely accepted one is Standard Quantum Mechanics (SQM),…
We show that the operational quantum formalism -- the Born rule, L\"uders state updating, quantum interference, non-Markovian effective dynamics, and Bell inequality violation at the Tsirelson bound $2\sqrt{2}$ -- arises within…