Related papers: Quantum Uncertainty as an Intrinsic Clock
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…
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We…
The semiclassical gravity describes gravitational back-reactions of the classical spacetime interacting with quantum matter fields but the quantum effects on the background is formally defined as higher derivative curvatures. These induce…
Unbound wave packets propagating to macroscopic space and time coordinates become proportional to their (Fourier transform) momentum distribution at earlier times whereby the asymptotic coordinates and the initial momenta are connected…
Unimodular gravity is based on a modification of the usual Einstein-Hilbert action that allows one to recover general relativity with a dynamical cosmological constant. It also has the interesting property of providing, as the momentum…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations…
An exact invariant operator of time-dependent coupled oscillators is derived using the Liouville-von Neumann equation. The unitary relation between this invariant and the invariant of two uncoupled simple harmonic oscillators is…
The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…
Wavefunction collapse is usually seen as a discontinuous violation of the unitary evolution of a quantum system, caused by the observation. Moreover, the collapse appears to be nonlocal in a sense which seems at odds with General…
Indistinguishability of particles is normally considered to be an inherently quantum property which cannot be possessed by a classical theory. However, Saunders has argued that this is incorrect, and that classically indistinguishable…
Discrepancies and accords between quantum (QM) and classical mechanics (CM) related to expectation values and periods are found for both the simple harmonic oscillator (SHO) and a free particle in a box (FPB), which may apply generally.…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
We consider the quantum mechanical behavior of a driven particle in an infinite 1D potential well. We show that the time dependent perturbation series is induced by the delicate non-trivial properties of the momentum operator in this case,…
Dynamics of a particle is formulated from classical principles that are amended by the uncertainty principle. Two best known quantum effects: interference and tunneling are discussed from these principles. It is shown that identical to…
The problem of time evolution in quantum cosmology is studied in the context of a dust-filled, spatially flat Friedmann-Robertson-Walker universe. In this model, two versions of the commonly-adopted notion of internal time can be…
We study the classical and quantum mechanics of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. The quasi-energy spectral properties of the model are obtained from…
Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet (UV) modifications of quantum theory due to gravity, this work shows that generic infrared (IR)…