Related papers: Maximally Localized States in Quantum Mechanics wi…
Small corrections to the uncertainty relations, with effects in the ultraviolet and/or infrared, have been discussed in the context of string theory and quantum gravity. Such corrections lead to small but finite minimal uncertainties in…
We analyze the emergence of a minimal length for a large class of generalized commutation relations, preserving commutation of the position operators and translation invariance as well as rotation invariance (in dimension higher than one).…
We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…
Quantum mechanical models with a minimal length are often described by modifying the commutation relation between position and momentum. Although this represents a small complication when described in momentum space, at least formally, the…
In this paper we will demonstrate that like the existence of a minimum measurable length, the existence of a maximum measurable momentum, also influence all quantum mechanical systems. Beyond the simple one dimensional case, the existence…
Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty…
We give simple representations for quantum theories in which the position commutators are non vanishing constants. A particular representation reproduces results found using the Moyal star product. The notion of exact localization being…
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…
We study the corrections to the Casimir effect in the classical geometry of two parallel metallic plates, separated by a distance $a$, due to the presence of a minimal length ($\hbar\sqrt{(\beta)}$) arising from quantum mechanical models…
Kempf et al. in Ref. [1] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length. Recently it has been revealed, in the context of doubly special relativity, that a test particles' momentum…
We address estimation of the minimum length arising from gravitational theories. In particular, we provide bounds on precision and assess the use of quantum probes to enhance the estimation performances. At first, we review the concept of…
This essay argues that when measurement processes involve energies of the order of the Planck scale, the fundamental assumption of locality may no longer be a good approximation. Idealized position measurements of two distinguishable…
We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length, $l_P$.…
The existence of a minimal length scale, a fundamental lower limit on spacetime resolution is motivated by various theories of quantum gravity as well as string theory. Classical calculations involving both quantum theory and general…
A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of…
Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines…
The narrow and subtle difference between the Hilbert spaces of operators corresponding to the purely quantum mechanical momentum and the generalized momentum that includes minimal length effects is polished. Additionally, the existence of…
The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal…
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…