# General solutions for quantum dynamical systems driven by time-varying Hamiltonians: applications to NMR

@article{Giscard2019GeneralSF, title={General solutions for quantum dynamical systems driven by time-varying Hamiltonians: applications to NMR}, author={Pierre-Louis Giscard and Christian Bonhomme}, journal={arXiv: Quantum Physics}, year={2019} }

Comprehending the dynamical behaviour of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood. Since the inception of Magnus’ expansion in 1954, no fundamentally novel mathematical method for solving the quantum equations of motion with a time-varying Hamiltonian has been devised. We report here of an entirely different non-perturbative approach, termed path-sum, which is always guaranteed to…

## 7 Citations

### Analog of Hamilton-Jacobi theory for the time-evolution operator

- MathematicsPhysical Review A
- 2019

In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the…

### Lanczos-like method for the time-ordered exponential

- Computer Science, MathematicsArXiv
- 2019

A Lanczos-like algorithm capable of evaluating the time-ordered exponential function by producing a tridiagonalization of the original differential system is presented in a theoretical setting.

### Representations of two-qubit and ququart states via discrete Wigner functions

- Mathematics
- 2019

By means of a well-grounded mapping scheme linking Schwinger unitary operators and generators of the special unitary group $\mathrm{SU(N)}$, it is possible to establish a self-consistent theoretical…

### On the tridiagonalization of systems of coupled linear differential equations

- Computer Science, Mathematics
- 2020

If all the non-constant coefficients are smooth functions then tridiagonalisation is always possible using only piecewise smooth functions and isolated Dirac delta distributions, which formally establishes the convergence and good behavior of the recently published Lanczos-like algorithm.

### Tridiagonalization of systems of coupled linear differential equations with variable coefficients by a Lanczos-like method

- Mathematics, Computer Science
- 2020

### Exponential Perturbative Expansions and Coordinate Transformations

- PhysicsMathematical and Computational Applications
- 2020

We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet–Magnus…

## References

SHOWING 1-10 OF 69 REFERENCES

### Two-level quantum dynamics, integrability, and unitary NOT gates (4 pages)

- Physics
- 2005

We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical…

### Analytically solvable driven time-dependent two-level quantum systems.

- PhysicsPhysical review letters
- 2012

A simple algorithm is presented that generates an unlimited number of exact analytical solutions to the time-dependent Schrödinger equation and is particularly relevant to qubit control in quantum computing applications.

### Exact solution for quantum dynamics of a periodically driven two-level system

- Physics
- 2010

We present a family of exact analytic solutions for nonlinear quantum dynamics of a two-level system (TLS) subject to a periodic-in-time external field. In constructing the exactly solvable models,…

### Operator-based triple-mode Floquet theory in solid-state NMR.

- PhysicsThe Journal of chemical physics
- 2007

This work describes an extension of the analytical operator-based Floquet description of NMR experiments to situations with three incommensurate frequencies and treats the application of two continuous-wave (cw) radio-frequency fields under magic-angle spinning.

### Flow Equation Approach to Periodically Driven Quantum Systems

- PhysicsPhysical Review X
- 2019

We present a theoretical method to generate a highly accurate {\em time-independent} Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal…

### Quantum mechanical simulation of solid effect dynamic nuclear polarisation using Krylov-Bogolyubov time averaging and a restricted state-space.

- PhysicsPhysical chemistry chemical physics : PCCP
- 2012

A strategy is described for simulations of solid effect dynamic nuclear polarisation that reduces substantially the dimension of the quantum mechanical problem and accelerates individual spin calculations by orders of magnitude, thus making it possible to simulate the polarisation dynamics of systems with up to 25 nuclear spins.

### Nonequilibrium dynamical mean-field theory and its applications

- Physics
- 2014

The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new…

### Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator

- Physics
- 2005

Recent experiments on quantum behavior in microfabricated solid-state systems suggest tantalizing connections to quantum optics. Several of these experiments address the prototypical problem of…

### Theoretical Perspectives of Spin Dynamics in Solid-State Nuclear Magnetic Resonance and Physics

- Physics
- 2018

Since the first demonstrations of nuclear magnetic resonance (NMR) in condensed matter in 1946, the field of NMR has yielded a continuous flow of conceptual advances and methodological innovations…