Related papers: Emergence of $\pi$ from Equatorial Quantum Localiz…
We consider the semiclassical quantization condition for the energy of an electron in a magnetic field in the case when the electron orbit lies on a Fermi-surface pocket surrounding the Weyl point of a topological semimetal and analyze the…
We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and…
The trace formula for the density of single-particle levels in the two-dimensional radial power-law potentials, which nicely approximate the radial dependence of the Woods-Saxon potential and quantum spectra in a bound region, was derived…
Structure of eigenstates in a periodic quasi-1D waveguide with a rough surface is studied both analytically and numerically. We have found a large number of "regular" eigenstates for any high energy. They result in a very slow convergence…
We generalize the derivation of the Wallis formula for $\pi$ from a variational computation of the spectrum of the Hydrogen atom. We obtain infinite product formulas for certain combinations of gamma functions, which include irrational…
We introduce a new methodology to characterize properties of quantum spacetime in a strongly quantum-fluctuating regime, using tools from topological data analysis. Starting from a microscopic quantum geometry, generated nonperturbatively…
It is argued that the classical local inertial frame used to define rotational states of quantum systems is only approximate, and that geometry itself must also be rotationally quantized at the Planck scale. A Lorentz invariant statistical…
We reexamine the model of relativistic particle with higher-derivative term linear on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here.…
We show how to obtain all covariant field equations for massless particles of arbitrary integer, or half-integer, helicity in four dimensions from the quantization of the rigid particle, whose action is given by the integrated extrinsic…
In non-Hermitian quasicrystals, mobility edges (ME) separating localized and extended states in complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. Such ME are of topological nature, i.e. the energies of…
We derive an exact, continuous-variable path integral (PI) representation of the canonical partition function for electronically nonadiabatic systems. Utilizing the Stock-Thoss (ST) mapping for an N-level system, matrix elements of the…
Quantum-mechanical observables for spatial and spacetime localization are considered from a lattice-theoretic perspective. It is shown that when replacing the lattice of all complex orthogonal projections underlying the Born rule by the…
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough…
We study quantum mechanically the self-similar black hole formation by collapsing scalar field and find the wave functions that give the correct semiclassical limit. In contrast to classical theory, the wave functions for the black hole…
The present contribution is based on the assumption that the probabilistic character of quantum mechanics does not originate from uncertainties caused by the process of measurement or observation, but rather reflects the presence of…
An one-parameter regularization freedom of the Hamiltonian constraint for loop quantum gravity is analyzed. The corresponding spatially flat, homogenous and isotropic model includes the two well-known models of loop quantum cosmology as…
We propose a novel phenomenological model of quantum gravitational collapse inspired by loop quantum gravity that ensures a completely regular spacetime evolution. By incorporating quantum gravitational modifications based on local rather…
We show that the Wald Noether charge entropy is canonically conjugate to the opening angle at the horizon. Using this canonical relation we extend the Wheeler-DeWitt equation to a Schroedinger equation in the opening angle, following Carlip…
It is shown in this paper that minisuperspace quantization of homogeneous and isotropic geometries with phantom scalar fields, when examined in the light of the Bohm-de Broglie interpretation of quantum mechanics, does not eliminate, in…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…