Related papers: Dimensionless equations in non-relativistic quantu…
The quantum-classical isomorphism for self-consistent field theory, which allows quantum particles in space-time to be represented as classical one-dimensional threads embedded in a five dimensional thermal-space-time, is summarized and…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and…
Recently it has been shown that the spinnless one particle quantum mechanics can be obtained in the framework of entirely classical subquantum kinetics. In the present paper we argue that, within the same scheme and without any extra…
When model predictions inform downstream decision making, a natural question is under what conditions can the decision-makers simply respond to the predictions as if they were the true outcomes. Calibration suffices to guarantee that simple…
Meshless methods are a promising candidate to reliably simulate materials undergoing large deformations. Unlike mesh based methods like the FEM, meshless methods are not limited in the amount of deformation they can reproduce since there…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.
A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there…
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process…
Despite the conceptual importance of contextuality in quantum mechanics, there is a hitherto limited number of applications requiring contextuality but not entanglement. Here, we show that for any quantum state and observables of…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
Non-linear nature of Einstein equation introduces genuine relativistic higher order corrections to the usual Newtonian fluid equations describing the evolution of cosmological perturbations. We study the effect of such novel non-linearities…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of…
Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…
Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…