ct 2 00 5 Localization in space for free particle in ultrametric quantum mechanics
نویسندگان
چکیده
Free evolution for quantum particle in general ultrametric space is considered. We find that if mean zero wave packet is localized in some ball in the ultrametric space then its evolution remains localized in the same ball.
منابع مشابه
ua nt - p h / 05 08 21 3 v 1 2 9 A ug 2 00 5 Localization for free ultrametric quantum particle
Free evolution for quantum particle in generic ultrametric space is considered. We prove that if mean zero wave packet is localized in some space domain then its evolution remains localized in the same domain. In the present note we consider ultrametric quantum mechanics with real time and ultrametric space. Quantum mechanics with ultrametric (p–adic and adelic) space was considered in many wor...
متن کاملar X iv : g r - qc / 0 61 01 42 v 1 2 7 O ct 2 00 6 Is quantum mechanics based on an invariance principle ?
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through the requirement of an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations acting on the position and momentum uncertainties are induced by isotropic space dilatations. This invariance imposes a change in the laws of cl...
متن کاملContinuous-time quantum walks on ultrametric spaces
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric space for the walk. This result presents a striking contrast to the classical random walk case. Moreover we clarify a difference between the ultrametric spa...
متن کاملar X iv : 0 80 3 . 12 93 v 2 [ he p - th ] 1 5 M ar 2 00 8 Lobachevsky geometry of ( super ) conformal mechanics
We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system. Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane) fI CP 1 . We also extend this picture to the N = 2k superconformal mechanics described in terms of Lobache...
متن کاملua nt - p h / 01 11 06 0 v 1 9 N ov 2 00 1 Localization and causality for a free particle
Theorems (most notably by Hegerfeldt) prove that an initially localized particle whose time evolution is determined by a positive Hamiltonian will violate causality. We argue that this apparent paradox is resolved for a free particle described by either the Dirac equation or the Klein-Gordon equation because such a particle cannot be localized in the sense required by the theorems.
متن کامل