Quantum dynamics simulation with approximate eigenstates

1995 ◽  
Vol 103 (15) ◽  
pp. 6665-6676 ◽  
Author(s):  
Tim H. Murphrey ◽  
Peter J. Rossky
Keyword(s):  
Quantum Dynamics ◽  
Dynamics Simulation

scholarly journals Open Quantum Dynamics Theory on the Basis of Periodical System-Bath Model for Discrete Wigner Function

2021 ◽  
Author(s):  
Yuki Iwamoto ◽  
Yoshitaka Tanimura
Keyword(s):  
Distribution Function ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Wigner Distribution ◽  
Equations Of Motion ◽  
Heat Bath ◽  
Planck Equation ◽  
Mesh Size ◽  
Dynamics Simulation ◽  
Open Quantum

Abstract Discretizing distribution function in a phase space for an efficient quantum dynamics simulation is non-trivial challenge, in particular for a case that a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM) most notably by a quantum Fokker-Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we find that a two-dimensional (2D) periodically invariant system-bath (PISB) model with two heat baths is an ideal platform not only for a periodical system but also for a system confined by a potential. We then derive the numerically ''exact'' hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. The stability of the present scheme is demonstrated in a high-temperature Markovian case by numerically integrating the discrete QFPE with by a coarse mesh for a 2D free rotor and harmonic potential systems for an initial condition that involves singularity.

Quantum dynamics simulation of the ultrafast photoionization of Li2

2001 ◽  
Vol 114 (3) ◽  
pp. 1259-1271 ◽  
Author(s):  
Lorenzo Pesce ◽  
Zohar Amitay ◽  
Radoslaw Uberna ◽  
Stephen R. Leone ◽  
Mark Ratner ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Dynamics Simulation

scholarly journals Quantum dynamics simulation of intramolecular singlet fission in covalently linked tetracene dimer

2021 ◽  
Vol 155 (19) ◽  
pp. 194101
Author(s):  
Sam Mardazad ◽  
Yihe Xu ◽  
Xuexiao Yang ◽  
Martin Grundner ◽  
Ulrich Schollwöck ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Dynamics Simulation ◽  
Singlet Fission ◽  
Covalently Linked

scholarly journals Time-dependent unbounded Hamiltonian simulation with vector norm scaling

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 459
Author(s):  
Dong An ◽  
Di Fang ◽  
Lin Lin
Keyword(s):  
Quantum Dynamics ◽  
Computational Cost ◽  
Quantum Simulation ◽  
Operator Norm ◽  
Time Dependent ◽  
Dynamics Simulation ◽  
Initial Vector ◽  
Worst Case ◽  
Unitary Evolution ◽  
Vector Norm

The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable discretization, the norm of the Hamiltonian can be very large, which significantly increases the simulation cost. However, the operator norm measures the worst-case error of the quantum simulation, while practical simulation concerns the error with respect to a given initial vector at hand. We demonstrate that under suitable assumptions of the Hamiltonian and the initial vector, if the error is measured in terms of the vector norm, the computational cost may not increase at all as the norm of the Hamiltonian increases using Trotter type methods. In this sense, our result outperforms all previous error bounds in the quantum simulation literature. Our result extends that of [Jahnke, Lubich, BIT Numer. Math. 2000] to the time-dependent setting. We also clarify the existence and the importance of commutator scalings of Trotter and generalized Trotter methods for time-dependent Hamiltonian simulations.

scholarly journals Strong Influence of Decoherence Corrections and Momentum Rescaling in Surface Hopping Dynamics of Transition Metal Complexes

2019 ◽  
Author(s):  
Felix Plasser ◽  
Sebastian Mai ◽  
Maria Fumanal ◽  
Etienne Gindensperger ◽  
Chantal Daniel ◽  
...  
Keyword(s):  
Transition Metal ◽  
Transition Metal Complexes ◽  
Quantum Dynamics ◽  
Transition Metal Complex ◽  
Coupling Model ◽  
Dynamics Simulation ◽  
Small Energy ◽  
Nonadiabatic Coupling ◽  
Surface Hopping ◽  
Better Than

The reliability of different parameters in the surface hopping method is assessed for a vibronic coupling model of a challenging transition metal complex, where a large number of electronic states of different multiplicities are met within a small energy range. In particular, the effect of two decoherence correction schemes and of various strategies for momentum rescaling and treating frustrating hops during the dynamics is investigated and compared against an accurate quantum dynamics simulation. The results show that small differences in the surface hopping protocol can strongly affect the results. We find a clear preference for momentum rescaling along the nonadiabatic coupling vector and trace this effect back to an enhanced number of frustrated hops. Furthermore, reflection of the momentum after frustrated hops is shown to work better than to ignore the process completely. The study also highlights the importance of the decoherence correction but neither of the two methods employed, energy based decoherence and augmented fewest switches surface hopping, performs completely satisfactory. More generally, the study emphasises the importance of the often neglected parameters in surface hopping and shows that there is still need for simple, robust, and generally applicable correction schemes.

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