Related papers: Structure Calculations Without Effective Interacti…
In this paper we propose and analyze an algorithm for identifying spectral gaps of a real symmetric matrix $A$ by simultaneously approximating the traces of spectral projectors associated with multiple different spectral slices. Our method…
We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one…
We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions $\mathcal G_3$. In this description, both the quantum states and Hermitian operators are written as elements of $\mathcal G_3$. By writing…
The Lanczos algorithm, introduced by Cornelius Lanczos, has been known for a long time and is widely used in computational physics. While often employed to approximate extreme eigenvalues and eigenvectores of an operator, recently interest…
The Lanczos method is one of the most powerful and fundamental techniques for solving an extremal symmetric eigenvalue problem. Convergence-based error estimates depend heavily on the eigenvalue gap. In practice, this gap is often…
We present a new approach to compute low lying eigenvalues and corresponding eigenvectors for strongly correlated many-body systems. The method was inspired by the so-called Automated Multilevel Sub-structuring Method (AMLS). Originally, it…
A practical computation method to find the eigenvalues and eigenspinors of quantum mechanical Hamiltonian is presented. The method is based on reduction of the eigenvalue equation to well known geometric algebra rotor equation and,…
We propose a new concept of a relatively inexact stochastic subgradient and present novel first-order methods that can use such objects to approximately solve convex optimization problems in relative scale. An important example where…
Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though…
In modeling quantum systems or wave phenomena, one is often interested in identifying eigenstates that approximately carry a specified property; scattering states approximately align with incoming and outgoing traveling waves, for instance,…
We present an efficient method to solve the impurity Hamiltonians involved in Dynamical Mean-Field Theory at low but finite temperature, based on the extension of the Lanczos algorithm from ground state properties alone to excited states.…
The graph Laplacian, a typical representation of a network, is an important matrix that can tell us much about the network structure. In particular its eigenpairs (eigenvalues and eigenvectors) incubate precious topological information…
The classical formalism of the Moment Problem has been combined with a cumulant approach and applied to the extensive many-body problem. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the…
We present a new method for computing the lowest few eigenvalues and the corresponding eigenvectors of a nuclear many-body Hamiltonian represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). The…
We propose a two-sided Lanczos method for the nonlinear eigenvalue problem (NEP). This two-sided approach provides approximations to both the right and left eigenvectors of the eigenvalues of interest. The method implicitly works with…
Hamiltonian operators are used in the theory of integrable partial differential equations to prove the existence of infinite sequences of commuting symmetries or integrals. In this paper it is illustrated the new Reduce package \cde for…
We study the algebraic structure of the eigenvalues of a Hamiltonian that corresponds to a many-body fermionic system. As the Hamiltonian is quadratic in fermion creation and/or annihilation operators, the system is exactly integrable and…
We establish uniqueness and radial symmetry of ground states for higher-order nonlinear Schr\"odinger and Hartree equations whose higher-order differentials have small coefficients. As an application, we obtain error estimates for…
Calculating the observables of a Hamiltonian requires taking matrix elements of operators in the eigenstate basis. Since eigenstates are only defined up to arbitrary phases that depend on Hamiltonian parameters, analytical expressions for…
We apply the algebraic method to the Bateman Hamiltonian and obtain its natural frequencies and ladder operators from the adjoint or regular matrix representation of that operator. Present analysis shows that the eigenfunctions compatible…