Related papers: Quantization of the Szekeres System
We study the multichannel scattering in the classical three-body system and show that the problem can be formulated as a motion of the point mass on a curved hyper-surface of the energy of the body-system. It is proved that the local…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
We consider a one parameter family of a PT symmetric two dimensional system with quadratic non-linearities. Such systems are shown to perform periodic oscillations due to existing centers. We describe this systems by constructing a…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
We present a classical probability model appropriate to the description of quantum randomness. This tool, that we have called stochastic gauge system, constitutes a contextual scheme in which the Kolmogorov probability space depends upon…
A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…
A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…
The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Here we present a model construction procedure for the quasispherical…
The classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M.C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether point…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
We study an effective quantum description of the static gravitational potential for spherically symmetric systems up to the first post-Newtonian order. We start by obtaining a Lagrangian for the gravitational potential coupled to a static…
In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function $T$, which represents the…
Building on a model recently proposed by F. Calogero, we postulate the existence of a coherent, long--range universal tremor affecting any stable and confined classical dynamical system. Deriving the characteristic fluctuative unit of…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
It is known that solutions of Richardson equations can be represented as stationary points of the "energy" of classical free charges on the plane. We suggest to consider "probabilities" of the system of charges to occupy certain states in…
We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the…
Using the quantum effective action in the Schwinger-Keldysh formalism, we derive quantum corrections to the semiclassical Langevin dynamics of a dissipative system governed by a macroscopic degree of freedom. We discuss the connection with…
Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional…