Relativity of representations in quantum mechanics

Only the position representation is used in introductory quantum mechanics and the momentum representation is not usually presented until advanced undergraduate courses. To emphasize the relativity of the representations of the abstract formulation of quantum mechanics, two examples of representations related to the operators aX+(1-a)P and (XP+PX)/2 are presented.Comment: 10 pages, no figures, accepted in Am.J.Phy

THz Dynamics of Nanoconfined Water by Ultrafast Optical Spectroscopy

We investigated the vibrational dynamics and the structural relaxation of water nanoconfined in porous silica samples with pore size of 4 nm at different levels of hydration and temperature. We used as spectroscopic technique the time-resolved optical Kerr effect, which enables to investigate the ultrafast water dynamics in a wide time (0.1-10 picosecond) or frequency (10-0.1 THz) window. At low levels of hydration, corresponding to two complete superficial water layers, no freezing occurs and the water remains mobile at all the investigated temperatures, while at the fully hydration we witness to a partial ice formation at about 248 K that coexists with the part of surface water remaining in the supercooled state. At low hydration, both structural and vibrational dynamics show significant modifications compared to the bulk liquid water due to the strong interaction of the water molecules with silica surfaces. Inner water, instead, reveals relaxation dynamics very similar to the bulk one.Comment: 10 pages 9 figure

Transverse-momentum resummation for heavy-quark hadroproduction

We consider the production of a pair of heavy quarks ($Q{\bar Q}$) in hadronic collisions. When the transverse momentum $q_T$ of the heavy-quark pair is much smaller than its invariant mass, the QCD perturbative expansion is affected by large logarithmic terms that must be resummed to all-orders. This behavior is well known from the simpler case of hadroproduction of colourless high-mass systems, such as vector or Higgs boson(s). In the case of $Q{\bar Q}$ production, the final-state heavy quarks carry colour charge and are responsible for additional soft radiation (through direct emission and interferences with initial-state radiation) that complicates the evaluation of the logarithmically-enhanced terms in the small-$q_T$ region. We present the all-order resummation structure of the logarithmic contributions, which includes colour flow evolution factors due to soft wide-angle radiation. Resummation is performed at the completely differential level with respect to the kinematical variables of the produced heavy quarks. Soft-parton radiation produces azimuthal correlations that are fully taken into account by the resummation formalism. These azimuthal correlations are entangled with those that are produced by initial-state collinear radiation. We present explicit analytical results up to next-to-leading order and next-to-next-to-leading logarithmic accuracy.Comment: Some comments expanded and references added. Version published on NP