p -wave contacts of quantum gases in quasi-one-dimensional and quasi-two-dimensional traps

The length scale separation in dilute quantum gases quasi-one-dimensional or quasi-two-dimensional traps has spatially divided the system into two distinct regimes. Whereas universal relations defined strict one dimensions apply a that is much larger than characteristic of transverse confinements, physical observables short distances are inevitably governed by three-dimensional contacts. Here, we show $p$-wave contacts different scales intrinsically connected relation, which depends on simple geometric factor confinements. While this relation derived for contacts, it establishes concrete example how dimensional crossover interplays with and arbitrary partial wave scatterings.