Related papers: Dimensionality as a Perturbation Parameter in the …
We develop a multidimensional coupled channel method suitable for studying the interplay of bound state resonance and phonon assisted scattering of inert gas atoms from solid surfaces in one, two and three dimensions. This enables us to get…
We study the isoperimetric problem in product spaces equipped with the uniform distance. Our main result is a characterization of isoperimetric inequalities which, when satisfied on a space, are still valid for the product spaces, up a to a…
The general four parameter point interaction in one dimensional quantum mechanics is regulated. It allows the exact solution, but not the perturbative one. We conjecture that this is due to the interaction not being asymptotically free. We…
In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…
The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar…
Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the…
We show that dimensional theoretical properties of dynamical systems can considerably change because of number theoretical peculiarities of some parameter values
In this paper we study the behavior of Hamilton operators and their spectra which depend on infinitely many coupling parameters or, more generally, parameters taking values in some Banach space. One of the physical models which motivate…
We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a…
Homogenized laws for sequences of high-contrast two-phase non-symmetric conductivities perturbed by a parameter $h$ are derived in two and three dimensions. The parameter $h$ characterizes the antisymmetric part of the conductivity for an…
A very general calculational strategy is applied to the evaluation of the divergent physical amplitudes which are typical of perturbative calculations. With this approach in the final results all the intrinsic arbitrariness of the…
Building on recent work in statistical science, the paper presents a theory for modelling natural phenomena that unifies physical and statistical paradigms based on the underlying principle that a model must be nondimensionalizable. After…
The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant…
The following question was proposed by Avi Wigderson and Yuval Wigderson: Is it possible to use the method in their paper(The uncertainty principle: variations on a theme) to prove Heisenberg uncertainty principle in higher dimension R^d,…
We investigate the consequences of one extra compactified dimension for the energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to $1/|x|^2$ in non-compactified 4d space. The…
Does the Heisenberg uncertainty principle (HUP) apply along the time dimension in the same way it applies along the three space dimensions? Relativity says it should; current practice says no. With recent advances in measurement at the…
This paper presents a new systematic framework for nonlinear singularly perturbed systems in which state-dependent perturbation functions are used instead of constant perturbation coefficients. Under this framework, general results are…
In addition to the well known case of spherical coordinates the hydrogen atom separates in three further coordinate systems. Separating in a particular coordinate system defines a system of three commuting operators. We show that the joint…
The non-zero minimal length arises in various theories of gravity, leading to the so-called generalized uncertainty principle (GUP). In this short paper we analyze the GUP effects on neutron interferometry, showing that the obtained phase…