Related papers: Simulating the spectral gap with polariton graphs
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…
Exponential random graph theory is the complex network analog of the canonical ensemble theory from statistical physics. While it has been particularly successful in modeling networks with specified degree distributions, a naive model of a…
A seminal open question of Pisier and Mendel--Naor asks whether every degree-regular graph which satisfies the classical discrete Poincar\'e inequality for scalar functions, also satisfies an analogous inequality for functions taking values…
Lattice gauge theories are fundamental to our understanding of high-energy physics. Nevertheless, the search for suitable platforms for their quantum simulation has proven difficult. We show that the Abelian Higgs model in 1+1 dimensions is…
The form of the entanglement Hamiltonian varies with the parameters of the original system. Whether there is a singularity is the key problem for demonstrating/negating the universality of the relation between the entanglement spectrum and…
In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac…
We construct an isospectrum systems in terms of a real and complex potential to show that the underlying PT symmetric Hamiltonian possesses a real spectrum which is shared by its real partner.
We use a Monte Carlo simulation to calculate the spectra of mildly relativistic thermal plasmas in pair balance. We use the exact integral expression for the electron-positron thermal annihilation spectrum, and provide accurate expressions…
We study the two dimensional XY-model with high precision Monte Carlo techniques and investigate the continuum approach of the step-scaling function of its finite volume mass gap. The continuum extrapolated results are found consistent with…
We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between…
The Hofstadter model allows to describe and understand several phenomena in condensed matter such as the quantum Hall effect, Anderson localization, charge pumping, and flat-bands in quasiperiodic structures, and is a rare example of…
In a vast class of systems, which includes members as diverse as sedimenting particles and bird flocks, interactions do not stem from a potential, and are in general nonreciprocal. Thus, it is not possible to define a conventional energy…
We show that the infinite-dimensional representation of the recently introduced Logistic algebra can be interpreted as a non-trivial generalization of the Heisenberg or oscillator algebra. This allow us to construct a quantum Hamiltonian…
The density matrix, \rho, of a model polariton system is obtained numerically from a master equation which takes account of pumping and losses. In the stationary limit, the coherences between eigenstates of the Hamiltonian are three orders…
The computational cost of simulating quantum many-body systems can often be reduced by taking advantage of physical symmetries. While methods exist for specific symmetry classes, a general algorithm to find the full permutation symmetry…
Experimental evidence of strong coupling between excitons confined in a quantum well and the photonic modes of a two-dimensional dielectric lattice is reported. Both resonant scattering and photoluminescence spectra at low temperature show…
We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a…
Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems…
The Schwinger model is studied in a finite lattice by means of the P-representation. The vacuum energy, mass gap and chiral condensate are evaluated showing good agreement with the expected values in the continuum limit.
In this work we propose a new numerical approach to distinguish between regular and chaotic orbits in Hamiltonian systems, based on the simultaneous integration of both the orbit and the deviation vectors using a symplectic scheme, hereby…