Related papers: Dimensionless equations in non-relativistic quantu…
We describe a geometric and symmetry-based formulation of the equivalence principle in non-relativistic physics. It applies both on the classical and quantum levels and states that the Newtonian potential can be eliminated in favor of a…
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
Dimensionality is a fundamental concept in physics, which plays a hidden but crucial role in various domains, including condensed matter physics, relativity and string theory, statistical physics, etc. In quantum physics, reducing…
Entanglement is essential for quantum computation. However, disentanglement is also necessary. It can be achieved without the need of classical operations (measurements). Two examples are analyzed: the discrete Fourier transform and error…
A two-dimensional analogue of Levinson's theorem for nonrelativistic quantum mechanics is established, which relates the phase shift at threshold(zero momentum) for the $m$th partial wave to the total number of bound states with angular…
To study quantum dynamics in the non-relativistic regime, the standard practice is to use non-relativistic quantum mechanics, instead of the relativistic theory, because it is thought the approximate non-relativistic result is always close…
This short article presents a table of new equations which can be regarded as the generalized equations of the dispersionless limit of several nonlinear equations. From the definition expressed in an algebraic formula, one can get an…
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
As a phenomenon encompassing measurement incompatibility and Bell nonlocality, quantum contextuality is not only central to our understanding of quantum mechanics, but also an essential resource in many quantum information processing tasks.…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
For studying the objectivity and the quality of a given form of the Periodic system as a single whole we compare plots of functions presenting properties of elements in pairs of periods. Using mathematical statistics we introduce a…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
In this paper I shall consider various possible scalar-vector-tensor field theories which might be used to describe the Universe. After imposing numerous constraints of a physical and mathematical nature on the theories under consideration,…
An inhomogeneous Kaluza-Klein compactification to four dimensions, followed by a conformal transformation, results in a system with position dependent mass (PDM). This origin of a PDM is quite different from the condensed matter one. A…
We review the relation between scale and conformal symmetries in various models and dimensions. We present a dimensional reduction from relativistic to non-relativistic conformal dynamics.
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…
This article concludes our critical analysis on the role of non-commutativity in quantum theory. After a brief introduction of the necessary notions on point processes, we re-analyse model B proposed in "On non-commutativity in quantum…
Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum…
It is shown that the no-signaling condition is not needed in order to argue a linear quantum dynamics from standard quantum statics and the usual interpretation of quantum measurement outcomes as probabilistic mixtures.
In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.