Related papers: The Laughlin liquid in an external potential
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
By definition, the exterior asymptotic energy of a solution to a wave equation on $\mathbb{R}^{1+N}$ is the sum of the limits as $t\to \pm\infty$ of the energy in the the exterior $\{|x|>|t|\}$ of the wave cone. In our previous work (JEMS…
We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the…
There exists a simple relationship between a quantum-mechanical bound-state wave function and that of nearby scattering states, when the scattering energy is extrapolated to that of the bound state. This relationship is demonstrated…
We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any…
We study the trapping of Abelian anyons (quasiholes and quasiparticles) by a local potential (e.g., induced by an AFM tip) in a microscopic model of fractional quantum Hall liquids with long-range Coulomb interaction and edge confining…
We introduce an effective thermodynamics for multipartite entangled pure states and derive an upper bound on extractable energy with feedback control from a subsystem under a local Hamiltonian. The inequality that gives the upper bound…
We compare the exact diagonalization ground wave function (calculated wothout any restriction) of a two dimensional droplet submitted to a perpendicular magnetic field with the Laughlin ansatz as the number of electrons increases. The fully…
We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external…
The free energy of quenched disordered systems is bounded above by the free energy of the corresponding annealed system. This bound may be improved by applying the annealing procedure, which is just Jensen inequality, after having modified…
In order to investigate specific aspects of bound state calculations in a non-relativistic framework, we consider the energy-levels of a massive scalar particle, which moves in an external field and interacts in addition with a massless…
It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…
When a Bose-Einstein condensate rotates in a purely harmonic potential with an angular frequency which is close to the trap frequency, its many-body state becomes highly correlated, with the most well-known being the bosonic Laughlin state.…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
We analyze the proposal of achieving a Mott state of Laughlin wave functions in an optical lattice [M. Popp {\it et al.}, Phys. Rev. A 70, 053612 (2004)] and study the consequences of considering the anharmonic corrections to each single…
A simple one-dimensional model is proposed, in which N spinless repulsively interacting fermions occupy M>N degenerate states. It is argued that the energy spectrum and the wavefunctions of this system strongly resemble the spectrum and…
Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed.
We have used different methods to obtain the bound states of a Hamiltonian of a relativistic two scalar particle system in a local potential. The potentials we are interested in are binding and confining potentials, that are associated with…
We numerically explore the behavior of repelling and aligning self-propelled polar particles (boids) in 2D enclosed by a damped flexible and elastic loop-shaped boundary. We observe disordered, polar ordered (or jammed) and circulating…
In classical mechanics, a particle cannot escape from an unbounded potential well. Naively, one would expect a similar result to hold in wave mechanics, since high barriers make tunneling difficult. However, this is not always the case and…