Related papers: Precise Wigner-Weyl calculus for the honeycomb lat…
Electrons in artificial lattices enable explorations of the impact of repulsive Coulomb interactions in a tunable system. We have trapped two-dimensional electrons belonging to a gallium arsenide quantum well in a nanofabricated lattice…
Asymptotically, we analytically derive the form of eigenvectors for two Fisher-Hartwig symbols besides those which were previously investigated in a $2016$ work due to Movassagh and Kadanoff, in which the authors characterized the…
The trace of an arbitrary product of quantum operators with the density operator is rendered as a multiple phase space integral of the product of their Weyl symbols with the Wigner function. Interspersing the factors with various evolution…
The single harmonic oscillator and double-well potentials are important systems in quantum mechanics. The single harmonic oscillator is {\it the} paradigm in physics, and is taught in nearly all beginner undergraduate classes, while the…
We study Hecke operators on vector-valued modular forms for the Weil representation $\rho_L$ of a lattice $L$. We first construct Hecke operators $\mathcal{T}_r$ that map vector-valued modular forms of type $\rho_L$ into vector-valued…
We study a system of electrons on a one-dimensional lattice, interacting through the long range Coulomb forces, by means of a variational technique which is the strong coupling analog of the Gutzwiller approach. The problem is thus the…
The Wigner function of a finite-dimensional system can be constructed via dual pairing of a density matrix with the Stratonovich-Weyl kernel. Following Kenfack and $\dot{\text{Z}}$yczkowski, we consider the indicator of nonclassicality of a…
The experimental verification of chiral anomaly in Weyl semimetals is an active area of investigation in modern condensed matter physics, which typically relies on the combined signatures of longitudinal magnetoconductance (LMC) along with…
A microscopic theory of electronic spectrum and superconductivity within the $t$-$J$ model on the honeycomb lattice is formulated. The Dyson equation for the normal and anomalous Green functions for the two-band model in terms of the…
Classical pseudo-differential calculus on $\mathbb{R}^{d}$ can be viewed as a (non-commutative) functional calculus for the standard position and momentum operators $(Q_{1}, \dots , Q_{d})$ and $(P_{1}, \dots , P_{d})$. We generalise this…
Recent advances in the Langlands program shed light on a vast area of modern mathematics from an unconventional viewpoint, including number theory, gauge theory, representation, knot theory and etc. By applying to physics, these novel…
Hamiltonians whose symbols are not simply real valued, but matrix or, more generally, endomorphism valued functions appear in many places in physics, examples being the Dirac equation, multicomponent wave equations like electrodynamics in…
In this paper, given a module $W$ for a vertex operator algebra $V$ and a nonzero complex number $z$ we construct a canonical (weak) $V\otimes V$-module ${\cal{D}}_{P(z)}(W)$ (a subspace of $W^{*}$ depending on $z$). We prove that for…
A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…
In this study, we compare the Wigner function $W$, its modulus, and the Husimi distribution $H$ in a one-dimensional quantum system exhibiting a transition from a single-well to a double-well configuration, using the quasi-exactly solvable…
Eugene Wigner predicted long ago that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice. A variety of two-dimensional systems have shown…
A microscopic theory of the electronic spectrum and of superconductivity within the t-J model on the honeycomb lattice is developed. We derive the equations for the normal and anomalous Green functions in terms of the Hubbard operators by…
In this work, we study the topological properties and magnon Hall effect of a three-dimensional ferromagnet in the ABC stacking honeycomb lattice, motivated by the recent inelastic neutron scattering study of CrI$_3$. We show that the…
The interplay between topology and electronic correlation effects offers a rich avenue for discovering emergent quantum phenomena in condensed matter systems. In this work, starting from the Weyl-Hubbard model, we investigate the quantum…
The chiral Luttinger liquid model for the edge dynamics of a two-dimensional electron gas in a strong magnetic field is derived from coarse-graining and a lowest Landau level projection procedure at arbitrary filling factors $\nu<1$ --…