Lindblad equation and its semiclassical limit of the Anderson-Holstein model

Cao, Yu; Lu, Jianfeng

doi:10.1063/1.4993431

Cited by 9 publications

(11 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) as a succinct GQME. Our model error of O λ 3 improves the model error O λ 3 /α 3 of the Lindblad equation with α ≪ 1 representing the time scale separation between the system and the bath, which (surprisingly) had not been precisely characterized until recently [CL17a]. A specific example of the GQME (Eq.…”

Section: Resultsmentioning

confidence: 66%

“…A notable example is the dynamics of qubits coupled to a boson bath [WC13]. There are also many other important examples, e.g., the Anderson-Holstein model [CL17a] where H S also includes the kinetic and potential energy terms. In electronic transport problems, the Hamiltonian is often expressed in terms of molecular or atomic orbitals [GN05].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems

Li¹,

Wang²

2021

Preprint

View full text Add to dashboard Cite

Non-Markovian open quantum systems are the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important applications are non-Markovian. Although for special cases such as Hamiltonian evolution and Lindblad evolution, quantum simulation algorithms have been extensively studied, efficient quantum simulations of the dynamics of non-Markovian open quantum systems remain underexplored. The most immediate obstacle for studying such systems is the lack of a universal succinct description of their dynamics. In this work, we fulfill the gap of studying such dynamics by 1) providing a succinct representation of the dynamics of non-Markovian open quantum systems with quantifiable error, and 2) developing an efficient quantum algorithm for simulating such dynamics with cost O(t polylog(t/ǫ)) for evolution time t and precision ǫ. Our derivation of the succinct representation is based on stochastic Schrödinger equations, which could lead to new alternatives to deal with other types of open quantum systems.

show abstract

Section: Resultsmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems

Li¹,

Wang²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Let E V be the characteristic scale of molecule-metal coupling energy, we are ready to perform the following rescaling (similar as in [36]):…”

Section: Quantum Dynamics Of Nuclei At Metal Surfacesmentioning

confidence: 99%

“…Let us first consider the following example where U 0 and U 1 are harmonic potentials. This is the scenario that are widely used in the modeling of nonadiabatc dynamics at metal surfaces [36,20,16]. Example 1 (harmonic oscillators).…”

Section: Accuracy and Convergence Testmentioning

confidence: 99%

Efficient Frozen Gaussian Sampling Algorithms for Nonadiabatic Quantum Dynamics at Metal Surfaces

Huang¹,

Xu²,

Zhou³

2022

Preprint

View full text Add to dashboard Cite

In this article, we propose a Frozen Gaussian Sampling (FGS) algorithm for simulating nonadiabatic quantum dynamics at metal surfaces with a continuous spectrum. This method consists of a Monte-Carlo algorithm for sampling the initial wave packets on the phase space and a surface-hopping type stochastic time propagation scheme for the wave packets. We prove that to reach a certain accuracy threshold, the sample size required is independent of both the semiclassical parameter ε and the number of metal orbitals N , which makes it one of the most promising methods to study the nonadiabatic dynamics. The algorithm and its convergence properties are also validated numerically. Furthermore, we carry out numerical experiments including exploring the nuclei dynamics, electron transfer and finite-temperature effects, and demonstrate that our method captures the physics which can not be captured by classical surface hopping trajectories.

show abstract

“…At the same time, other formalisms that describe hopping-based transport, such as the rate equation and quantum master equation approaches, − are restricted to the regime in which the coupling of the molecule with the electrodes is weak, which makes them inadequate to describe the processes of coherent tunneling or ballistic transport. Hence, novel models could adequately describe processes in which ballistic and hopping-type mechanisms simultaneously contribute to the overall charge transport.…”

Section: Introductionmentioning

confidence: 99%

Charge Transport in Conjugated and Saturated Hydrocarbons: Comparing Ballistic and Cotunneling Contributions

Cabrera-Tinoco,

Moreira,

Borja-Castro

et al. 2023

J. Phys. Chem. A

View full text Add to dashboard Cite

The comparison between electrical transport in C n H 2 n +2 S 2 alkane and C n H n +2 S 2 alkene ( n = 4, 6, 8, 10) is studied by using a generalized Breit-Wigner approach and considering coherent transport mechanisms and eventual changes in the state of charge (i.e., cotunneling processes) for both molecules. In general, the conductance of alkanes tends to be smaller than that of similar-sized alkenes. However, cotunneling processes have an important participation in the overall transport in the case of alkanes but not for the alkene family. The progressive changes in both the eigenenergies of the relevant frontier molecular orbitals of the charged species and their spatial localization play decisive roles in the observed differences. While the molecular orbitals of the charged species of the conjugated molecules are hardly affected by the applied voltage, their saturated counterparts are quite sensitive to the external field. With this, successive avoided-crossing events between the molecular orbitals of the single-charged alkane molecules can lead to the appearance of nonballistic conduction channels that make no negligible contributions to the molecular transport.

show abstract

Lindblad equation and its semiclassical limit of the Anderson-Holstein model

Cited by 9 publications

References 36 publications

Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems

Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems

Efficient Frozen Gaussian Sampling Algorithms for Nonadiabatic Quantum Dynamics at Metal Surfaces

Charge Transport in Conjugated and Saturated Hydrocarbons: Comparing Ballistic and Cotunneling Contributions

Contact Info

Product

Resources

About