arXiv subjects

Paul B. Wiegmann

Publications and source records attributed to Paul B. Wiegmann.

5 recordsLinked to original sources

arXiv2023

Anomalies in fluid dynamics: flows in a chiral background via variational principle

We study flows of barotropic perfect fluid under the simultaneous action of the electromagnetic field and the axial-vector potential, the external field conjugate to the fluid helicity. We obtain the deformation of the Euler equation by the axial-vector potential and the deformations of various currents by two external fields. We show that the divergence of the vector and axial currents are controlled by the chiral anomaly known in quantum field theories with Dirac fermions. We obtain these results by extending the variational principle for barotropic flows of a perfect fluid by coupling with the external axial-vector potential.

hep-th↗

arXiv2011

Fermi distribution of semicalssical non-eqilibrium Fermi states

When a classical device suddenly perturbs a degenerate Fermi gas a semiclassical non-equilibrium Fermi state arises. Semiclassical Fermi states are characterized by a Fermi energy or Fermi momentum that slowly depends on space or/and time. We show that the Fermi distribution of a semiclassical Fermi state has a universal nature. It is described by Airy functions regardless of the details of the perturbation. In this letter we also give a general discussion of coherent Fermi states.

cond-mat.quant-gas↗

arXiv2011

Gradient Catastrophe and Fermi Edge Resonances in Fermi Gas

A smooth spatial disturbance of the Fermi surface in a Fermi gas inevitably becomes sharp. This phenomenon, called {\it the gradient catastrophe}, causes the breakdown of a Fermi sea to disconnected parts with multiple Fermi points. We study how the gradient catastrophe effects probing the Fermi system via a Fermi edge singularity measurement. We show that the gradient catastrophe transforms the single-peaked Fermi-edge singularity of the tunneling (or absorption) spectrum to a set of multiple asymmetric singular resonances. Also we gave a mathematical formulation of FES as a matrix Riemann-Hilbert problem.

cond-mat.mes-hall↗

arXiv2005

Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model

Collective field theory for Calogero model represents particles with fractional statistics in terms of hydrodynamic modes -- density and velocity fields. We show that the quantum hydrodynamics of this model can be written as a single evolution equation on a real holomorphic Bose field -- quantum integrable Benjamin-Ono equation. It renders tools of integrable systems to studies of nonlinear dynamics of 1D quantum liquids.

cond-mat.str-el↗

arXiv2000

Integrable Structure of Interface Dynamics

We establish the equivalence of a 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation. Remarkably, the same hierarchy underlies 2D quantum gravity.

nlin.SI↗