Wave-kinetic approach to the Schrödinger–Newton equation

Abstract

We discuss the Schrödinger-Newton (SN) equation in the context of cold atom physics. For that purpose, we establish the wave-kinetic equation equivalent to the SN equation, which stays valid in different physical scenarios relevant to cold atoms. They include: (1) the usual scenario of matter confined in a self-gravitating field, (2) atomic molasses, confined and cooled by laser beams in a magneto-optical trap (MOT), (3) Bose-Einstein condensates, with or without long range dipolar interactions, and (4) electron states in a quantum plasma. We show that these different systems can be described by a formally identical equation, and they also manifest similar elementary excitations. The wave-kinetic equation is obtained by following the well-known Wigner-Moyal procedure, allowing the representation of quantum states in a classical phase-space. It is particularly well suited to discuss kinetic properties associated with Landau damping, as shown. We also consider generalisation of the SN equation onto the relativistic domain, and its impact on the proposed wave-kinetic description.

Fingerprints of nonequilibrium stationary distributions in dispersion relations

“…Such a formal analogy between plasmas and self-gravitataing systems is well-known and, indeed, is also manifest in the classical regime, i.e., in the Vlasov–Poisson kinetic approach. However, as recently observed by Mendonça 39 , this analogy goes even further and applies to other physical problems as well. This can be made more transparent by rewriting the SP model in the form of an integro-differential equation as where is an arbitrary external potential.…”

“…Typical systems obeying the SP model are quantum plasmas 34 , 35 and self-gravitating systems 36 – 38 . However, as pointed out recently 39 , the applicability of the SP model goes well beyond the usual scenario of plasmas and self-gravitating systems and covers a large spectrum of systems, manifesting similar elementary excitations, such as Bose-Einstein condensates (BECs) and optical molasses.…”

Schrödinger–Newton Model with a Background

“…The same equation also applies to a variety of different systems, such as atomic gases in interaction with laser beams [10][11][12] and quantum plasmas [13][14][15]. A bridge with Bose-Einstein condensates can also be established [16,17]. These similarities open the way for studies of laboratory analogues of gravity [18][19][20].…”

“…This form of the SN equation is interesting because it stays valid for a number of other physical systems, which helps in the discussion of possible laboratory simulations of gravitational processes, as shown in [17]. Our formulation is valid for a flat space-time described by the Minkowski metric tensor η αβ = diag.…”

“…This procedure was introduced to transform the Schrödinger equation into a Liouville-type equation and is able to describe the quantum state of a system in classical phase-space. We recently showed that this approach can be used to bridge many different physical phenomena, including laser-cooled atoms, Bose-Einstein condensates, turbulent quasi-particles, and quantum plasmas [17]. It is also well adapted to bridge classical, relativistic, and quantum physics.…”