Related papers: Emergence of $\pi$ from Equatorial Quantum Localiz…
We consider classical models of the kicked rotor type, with piecewise linear kicking potentials designed so that momentum changes only by multiples of a given constant. Their dynamics display quasi-localization of momentum, or quadratic…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
A curve attaining the Hasse-Weil bound is called a maximal curve. Usually classical error-correcting codes obtained from a maximal curve have good parameters. However, the quantum stabilizer codes obtained from such classical…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
The behaviour of a quantum rod, pivoted at its lower end on an impenetrable floor and restricted to moving in the vertical plane under the gravitational potential is studied analytically under the approximation that the rod is initially…
We study the time-of-arrival problem for relativistic particles constrained to move on a ring, formulating the problem entirely within Quantum Field Theory (QFT). In contrast to its counterpart for motion in a line, the circle topology…
We derive the Schr\"odinger equation for a particle confined to the surface of a normal and a binormal helical nanoribbon, obtain the quantum potentials induced by their respective curved surface geometries, and study the localized states…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
We provide an introduction to deformation quantisation and discuss the application of the formalism in solving the evolution problem for many-body systems in terms of semiclassical expansion. In any fixed order of expansion over the…
We investigate the particle and kinetic-energy densities for a system of $N$ fermions bound in a local (mean-field) potential $V(\bfr)$. We generalize a recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev.\ Lett. {\bf…
General nonequilibrium quantum transport equations are derived for a coupled system of charge carriers, Dirac spin, isospin (or valley spin), and pseudospin, such as either one of the band, layer, impurity, and boundary pseudospins.…
The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism…
Quantum integrable systems and their classical counterparts are considered. We show that the symplectic structure and invariant tori of the classical system can be deformed by a quantization parameter $\hbar$ to produce a new (classical)…
Partial transport barriers in the chaotic sea of Hamiltonian systems influence classical transport, as they allow for a small flux between chaotic phase-space regions only. We establish for higher-dimensional systems that quantum transport…
Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…