Related papers: Simulating the spectral gap with polariton graphs
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…
The gas of interacting excitons in quantum wells is studied. We obtain the Hamiltonian of this gas by the projection of the electron-hole plasma Hamiltonian to exciton states and an expansion in a small density. Matrix elements of the…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
The scattering and bound states of the many-body systems, related to the short-range Dyson model, are studied. First, we show that the scattering states can be realized as coherent states and the scattering Hamiltonian can be connected to a…
We report observation of coherent oscillations in the relaxation dynamics of an exciton-polariton condensate driven by parametric scattering processes. As a result of the interbranch scattering scheme and the nonlinear polariton-polariton…
A class of variational schemes for the hydrodynamic-electrodynamic model of lossless free-electron gas in a quasineutral background is developed for high-quality simulations of surface plasmon polaritons. The Lagrangian density of lossless…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
We consider discrete one dimensional nonlinear equations and present the procedure of lifting them to Z-graded graphs. We identify conditions which allow one to lift one dimensional solutions to solutions on graphs. In particular, we prove…
Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between…
We study the spectral gap of frustrated spin (qubit) Hamiltonians constructed from quantum subsystem (gauge) codes. Such a Hamiltonian can be block diagonalized, with blocks labelled by eigenvalues of extensively many integrals of motion…
We consider a Hamiltonian with cutoffs describing the weak decay of spin one massive bosons into the full family of leptons. The Hamiltonian is a self-adjoint operator in an appropriate Fock space with a unique ground state. We prove a…
We present an approximate analytic expression for the photoluminescence spectral function of a model polariton system, which describes a quantum dot, with a finite number of fermionic levels, strongly interacting with the lowest photon mode…
Polarization is a powerful diagnostic tool to constrain the site of the high-energy pulsed emission and particle acceleration in gamma-ray pulsars. Recent particle-in-cell simulations of pulsar magnetosphere suggest that high-energy…
Cavity-polaritons in semiconductor microstructures have emerged as a promising system for exploring nonequilibrium dynamics of many-body systems. Key advances in this field, including the observation of polariton condensation,…
In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…
The growing interest in exciton-polaritons has driven the need to manipulate their motion and engineer their band structures to the forefront of contemporary research. This study explores the band structures that emerge from a spatially…
We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…
We present a new algorithm to analytically continue the self-energy of quantum many-body systems from Matsubara frequencies to the real axis. The method allows straightforward, unambiguous computation of electronic spectra for lattice…
We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable…
In this paper we study spectral properties of graphs which are constructed from two given invertible graphs by bridging them over a bipartite graph. We analyze the so-called HOMO-LUMO spectral gap which is the difference between the…