Related papers: Quasihole wavefunctions for the Calogero model
Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As…
It is known that non-commutative fluids used to model the Fractional Quantum Hall effect give Calogero--Moser systems. The group-theoretic description of these as reductions of free motion on type A Lie algebras leads directly to Laughlin…
Existing techniques for synthesizing gauge fields are able to bring a two-dimensional cloud of harmonically trapped bosonic atoms into a regime where the occupied single-particle states are restricted to the lowest Landau level (LLL).…
General Relativity predicts the existence of quadratic quasi-normal modes at second order in perturbation theory. Building on our recent work, we compute the amplitudes and polarizations of these modes for non-rotating black holes, showing…
We show that the quasiparticle kinetic theory for quantum and classical Calogero models reduces to the free-streaming Boltzmann equation. We reconcile this simple emergent behaviour with the strongly interacting character of the model by…
An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in…
It is well known that the quasinormal modes (or resonant states) of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the…
Recent results are surveyed regarding the spectrum and eigenfunctions of the inverse square Calogero model with harmonic confinement and its relativistic analogue.
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics…
Features of biphoton polarization-frequency ququarts are considered. Their wave functions are defined as functions of both polarization and frequency variables of photons with the symmetry obligatory for two-boson states taken into account.…
We find self-adjoint extensions of the rational Calogero model in presence of the harmonic interaction. The corresponding eigenfunctions may describe the near-horizon quantum states of certain types of black holes.
The Dunkl Laplacian is used to define the Hamiltonian of a modified quantum harmonic oscillator, associated with any finite reflection group. The potential is a sum of the inverse squares of the linear functions whose zero sets are the…
A system of active colloidal particles driven by harmonic potentials to oscillate about the vertices of a regular polygon, with hydrodynamic coupling between all particles, is described by a piece-wise linear model which exhibits various…
We derive many-body single- and multi-reference wave functions for quantum Monte Carlo of periodic systems with an anti-symmetric portion that explicitly integrates over the Brillouin zone of one-particle Bloch states. The wave functions…
Linear perturbations of spherically symmetric spacetimes in general relativity are described by radial wave equations, with potentials that depend on the spin of the perturbing field. In previous work we studied the quasinormal mode…
The scattering of an electromagnetic plane wave from Young pinholes upon a quasi-homogeneous (QH) anisotropic medium is studied within the accuracy of the first-order Born approximation. By assuming that the diffractive wave from pinholes…
The spectrum of an exactly solvable non-relativistic system of a charged particle interacting with a quantized electromagnetic mode is studied with various polarizations. Quasiparticle dispersion relations can be derived from the…
Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor $\nu =1/m$, on Riemann sufaces with Poincare metric. The same is done for…
We propose an ansatz for the wave function of a non-interacting quantum particle in a deterministic quasicrystalline potential. It is applicable to both continuous and discrete models and includes Sutherland's hierarchical wave function as…