A comparison of different propagation schemes for the time dependent Schro¨dinger equation
Journal of Computational Physics
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Matrix computations (3rd ed.)
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Self-consistent-field calculations using Chebyshev-filtered subspace iteration
Journal of Computational Physics
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
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We consider dimension reduction techniques for the Liouville-von Neumann equation for the evaluation of the expectation values in a mixed quantum system. We describe several existing methods that have appeared in the literature, showing the failure of them when the system is scaled up. We introduce a new method termed direct expectation values via Chebyshev based on evaluation of a trace formula combined with a direct expansion in modified Chebyshev polynomials. This reduction is highly efficient and does not destroy any information. We demonstrate the practical application of the scheme for a nuclear spin system and compare with popular alternatives. In nuclear spin dynamics the main goal for simulations is being able to simulate a system with as many spins as possible; for this reason it is very important to have an efficient method that scales the least with respect to the number of particles. This method may be applied to autonomous quantum problems where the desired outcome of quantum simulation, rather than being a full description of the system, is only the expectation value of some observables.