We consider wave packets of free particles with a general energymomentum dispersion relation E(p). The spreading of the wave packet is determined by the velocity v = ∂pE. The position-velocity uncertainty relation ∆x∆v ≥ 1 2 |〈∂2 pE〉| is saturated by minimal uncertainty wave packets Φ(p) = A exp(−αE(p) + βp). In addition to the standard minimal Gaussian wave packets corresponding to the non-rel...

We use the results of ultraprecise cold-atom-recoil experiments to constrain the form of the energy-momentum dispersion relation, a structure that is expected to be modified in several quantum-gravity approaches. Our strategy of analysis applies to the nonrelativistic (small speeds) limit of the dispersion relation, and is therefore complementary to an analogous ongoing effort of investigation ...

We give a pedagogical discussion of the physics underlying dispersion relation-derived parameterizations of form factors describing B → πlν̄ and B → Dlν̄. Moments of the dispersion relations are shown to provide substantially tighter constraints on the f+(t) form factor describing B̄ → πlν than the unweighted dispersion relation alone. Heavy quark spin symmetry relations between the B → πlν̄ and B ...

In solenoidal beam transport systems, motions in the x and y directions are coupled by the vXB force. A two-dimensional coupled mode description of the beam breakup (BBU) instability is presented; its dispersion relation is derived and compared with the one-dimensional BBU dispersion relation. In the two-dimensional description, instability growth is doubled and two additional wave modes are fo...

Measurements of the dispersion relation for shear Alfvén waves as a function of the perpendicular wave number are reported for the regime in which V(A) approximately V(Te). By measuring the parallel phase velocity of the waves, the measurements can be compared directly to theoretical predictions of the dispersion relation for a parameter regime in which particle kinetic effects become important...