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Facultad de Ingeniería, Universidad de Buenos Aires, Avenida Paseo Colón 850, C1063ACL Buenos Aires, Argentina

and

Laboratorio Tandar, GIyA, Departamento de Física Teórica, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, C1429BNP Buenos Aires, Argentina

Facultad de Ingeniería y Ciencias Agrarias, Pontificia Universidad Católica Argentina, Avenida Alicia Moreau de Justo 1500, C1107AAZ Buenos Aires, Argentina

Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, Argentina

E-mail Address: grzemba@gmail.com

Corresponding author.

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https://doi.org/10.1142/S0217751X24501562Cited by:0 (Source: Crossref)

Abstract

The effective field theory of the Calogero–Sutherland model represents a universality class of quantum hydrodynamic fluids in one spatial dimension. It describes quantum compressible fluids involving both chiralities in which the chiral density field obeys the quantum Benjamin–Ono equation. An extension of this theory to describe a laminar flow of the Calogero–Sutherland fluids in a rectangular geometry with small transverse width and the topology of a ribbon, is considered here. The physical picture is based on the edge states in the hierarchical quantum Hall effect, which may be seen as a collection of parallel one-dimensional quantum incompressible fluids moving along but confined within the transverse microscopic width of the edge of the sample. The effective theory is thus defined as the direct product of two one-dimensional theories of the Calogero–Sutherland class so that one involves motion while the other is confining. Charge transport may be induced by coupling the system to an external electromagnetic field that yields a global translation of the ground state. The effective theory describes quantum solitonic excitations along the direction of the flow and possesses a two-dimensional electric current density which shows a Wigner semicircle law profile in the transverse direction, suggesting a Poiseuille-like behavior but without dissipative viscous effects since the velocity of the fluid is not a well-defined quantum field. This simple physical picture predicts interesting phenomena with distinctive signatures that may be tested in real samples.

Keywords:

PACS: 11.25.Hf, 11.40.Ex, 03.70.+k, 03.75.Kk, 05.60.Gg, 11.10.Kk, 67.40.Hf

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