Related papers: New Classical Limits of Quantum Theories
At large quantum numbers, the probability densities for particle-in-a-box or simple harmonic oscillator converge to the classical result upon coarse-graining the quantum mechanical probability densities by introducing a finite resolution in…
Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the…
All quantum field theories that describe interacting bosonic elementary particles, share the feature that the zeroth order perturbation expansion describes non-interacting harmonic oscillators. This is explained in the paper. We then…
Two novel and direct quantum mechanical representations of the Black-Scholes model are constructed based on the (Wick-rotated) quantization of two specific mechanical systems. The quantum setup is achieved by means of the associated…
The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the ``failure" of the Ehrenfest theorem is clarified in terms of the already defined notion of…
This paper establishes an aspect of Bohr's correspondence principle, i.e. that quantum mechanics converges in the high frequency limit to classical mechanics, for commuting semiclassical unitary operators. We prove, under minimal…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
This paper is devoted to the study of the classical limit of quantum mechanics. In more detail we will elaborate on a method introduced by Hepp in 1974 for studying the asymptotic behavior of quantum expectations in the limit as Plank's…
In quantum systems with large $n$ (radial quantum number) or large angular momentum the semiclassical (WKB) approximation is valid. A physical content of the semiclassical approximation is that the quantum fluctuations effects are…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
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…
We reason in support of the universality of quantum spectral fluctuations in chaotic systems, starting from the pioneering work of Sieber and Richter who expressed the spectral form factor in terms of pairs of periodic orbits with…
Old and new puzzles of cosmology are reexamined from the point of view of quantum theory of the universe developed here. It is shown that in proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the…
In general quantum systems there are two kinds of spacetime modes, those that fluctuate and those that do not. Fluctuating modes have normalizable wavefunctions. In the context of 2D gravity and ``non-critical'' string theory these are…
According to Dirac, fundamental laws of Classical Mechanics should be recovered by means of an "appropriate limit" of Quantum Mechanics. In the same spirit it is reasonable to enquire about the fundamental geometric structures of Classical…
A modular quantum architecture is given for the space-time, particles, and fields of the Standard Model and General Relativity. It assumes a right-handed neutrino, so that based on their multiplet structure all fundamental fermions have…
While in first and second quantization the fundamental operators are respectively coordinates and fields (functions), an extension of quantum field theory can be achieved if the usual pair of conjugate momenta is represented by functionals.…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
We study the classical and quantum rotation numbers of the free rotation of asymmetric top molecules. We show numerically that the quantum rotation number converges to its classical analog in the semi-classical limit. Different asymmetric…
Topologically ordered quantum liquids are highly sought-after quantum phases of matter, and recently, fractional Chern insulators (FCIs) joined the few experimental realizations of such phases. Here, we ask whether a gapped classical,…