Related papers: Hidden scale in quantum mechanics
The properties of quantum mechanics with a discrete phase space are studied. The minimum uncertainty states are found, and these states become the Gaussian wave packets in the continuum limit. With a suitably chosen Hamiltonian that gives…
Localized quantum wave packets can be produced in a variety of physical systems and are the subject of much current research in atomic, molecular, chemical, and condensed-matter physics. They are particularly well suited for studying the…
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent…
The study addresses the quantum spreading of a localized stationary flow of high energy particles. Results demonstrate that as particle energy increases, the spreading speed of the particle wave packet diminishes rapidly. Concurrently,…
We study the dynamics of a particle in continuous time and space, the displacement of which is governed by an internal degree of freedom (spin). In one definite limit, the so-called quantum random walk is recovered but, although quite…
It is demonstrated that in contrast to the well-known case with a quantum particle moving freely in a real line, the wave packets corresponding to the coherent states for a free quantum particle on a circle do not spread but develop…
We introduce power-law tail quantum wave packets. We show that they can be seen as eigenfunctions of a Hamiltonian with a physical potential. We prove that the free evolution of these packets presents an asymptotic decay of the maximum of…
We develop a quantum landscape approach to characterize the long-time behavior of wave packet spreading in linear open quantum systems. Instead of treating diffusion, localization, and collapse of the wave packet as separate dynamical…
We investigate theoretically a dilute stream of free quantum particles passing through a macroscopic circular aperture of matter-waves and then moving in a space at a finite temperature, taking into account the dissipative coupling with the…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
Quantum transport in a lattice is distinct from its counterpart in continuum media. Even a free wave packet travels differently in a lattice than in the continuum. We describe quantum scattering in a one dimensional lattice using three…
The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially…
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with…
Wave localization is a fundamental phenomenon that appears universally in both natural materials and artificial structures and plays a crucial role in understanding the various physical properties of a system. Usually, a localized state has…
The properties of the s-wave for a quasi-free particle with position-dependent mass(PDM) have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the free quantum particle…
Can the interplay between quantum mechanics and classical optics offer new perspectives on wavepacket dynamics? Building on this connection, we show that local momenta with both super-oscillatory and suboscillatory characteristics can arise…
Electronic properties of quantum materials solids are often well understood via the low energy dispersion of Bloch bands, motivating single band approximations in many metals and semiconductors. However, a closer look reveals length and…
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…
Coherence lengths of one particle states described by quantum wave functions are studied. We show that one particle states in various situations are not described by simple plane waves but are described by wave packets that are…
The broadening of one-dimensional Gaussian wave packets is presented in all textbooks on quantum mechanics. It is used to elucidate Heisenberg's uncertainty relation. The behaviour on a lattice is drastically different if the amplitude…