Related papers: Hole probability for noninteracting fermions in a …
The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over the interval $(0,s)$ by working on the…
Within the newly formulated composite fermion hierarchy the filling fraction of a spherical quantum Hall system is obtained when it can be expressed as an odd or even denominator fraction. A plot of $\nu\frac{2S}{N-1}$ as a function of $2S$…
We treat the trapped two-component Fermi system, in which unlike fermions interact through a two-body short-range potential having no bound state but an infinite scattering length. By accurately solving the Schroedinger equation for up to…
Composite fermions (CFs) of the fractional quantum Hall effect are described as spherical products of electron and vortex spinors, built from underlying L=1/2 ladder operators aligned so that the spinor angular momenta Le and Lv are…
The problem of a nonrelativistic particle with an internal color degree of freedom, with and without spin, moving in a free random gauge background is discussed. Freeness is a concept developed recently in the mathematical literature…
We consider the $1d$ one-component plasma (OCP) in thermal equilibrium, consisting of $N$ equally charged particles on a line, with pairwise Coulomb repulsion and confined by an external harmonic potential. We study two observables: (i) the…
The evaluation of the absorption coefficients are important for particle emission caused by Hawking radiation. In the case of cosmological particle emission from the event horizon in De Sitter space, it is known that the scalar wave…
The fractional quantum Hall states are non-Fermi liquids of electrons, in that their ground states and low energy excitations are described not in terms of electrons but in terms of composite fermions which are bound states of electrons and…
Cold-atom experiments which measure Fermi-gas properties near unitarity confine fermionic atoms to a region of space using trapping potentials of various shapes. The presence of a trapping potential introduces a new characteristic physical…
We analyze pairing of fermions in two dimensions for fully-gapped cases with broken parity (P) and time-reversal (T), especially cases in which the gap function is an orbital angular momentum ($l$) eigenstate, in particular $l=-1$ (p-wave,…
Consider the random graph $G({\mathcal P}_{n},r)$ whose vertex set ${\mathcal P}_{n}$ is a Poisson point process of intensity $n$ on $(- \frac{1}{2}, \frac{1}{2}]^d$, $d \geq 2$. Any two vertices $X_i,X_j \in {\mathcal P}_{n}$ are connected…
Many-particle systems pose commonly known computational challenges in quantum theory. The obstacles arise from the difficulty in finding sets of eigenvalues and eigenvectors of the underlying Hamiltonian while enforcing fermion or boson…
Suppose that a $d$-dimensional domain is filled with a gas of (in general, interacting) diffusive particles with density $n_0$. A particle is absorbed whenever it reaches the domain boundary. Employing macroscopic fluctuation theory, we…
This paper studies false vacuum lumps surrounded by the true vacuum in a real scalar field potential in flat spacetime. Fermions reside in the core of the lump, which are coupled with the scalar field via Yukawa interaction. Such lumps are…
A fluctuating-valence impurity in a metal is quantum-critical unlike a Kondo impurity which has the properties of a local Fermi-liquid. A systematic theory for the fluctuating-valence lattice is constructed, based on the hybridization and…
We present a density-functional theory for the one dimensional harmonically trapped Bose-Fermi mixture with repulsive contact interactions. The ground state density distribution of each component is obtained by solving the Kohn-Sham…
We present an analytic theory unraveling the microscopic mechanism of instabilities within interacting $D$-dimensional Fermi liquid. Our model consists of a $D$-dimensional electron gas subject to an instantaneous electron-electron…
Let f:=(f^1,\...,f^n) be a sparse random polynomial system. This means that each f^i has fixed support (list of possibly non-zero coefficients) and each coefficient has a Gaussian probability distribution of arbitrary variance. We express…
Consider an isotropic spherical Gaussian random field T with values in R^{d}. We investigate two problems: (i) When is the level set T^{-1}(t) nonempty with positive probability for any t\in R^{d} ? (ii) If the level set is nonempty, what…
We define the three-body scattering hypervolume $D_F$ for identical spin-polarized fermions in two dimensions, by considering the wave function of three such fermions colliding at zero energy and zero orbital angular momentum. We derive the…