Driven Liouville von Neumann Equation in Lindblad Form

Hod, Oded; Rodríguez-Rosario, César A.; Zelovich, Tamar; Frauenheim, Thomas

doi:10.1021/acs.jpca.5b12212

Cited by 37 publications

(53 citation statements)

References 98 publications

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“…20 Expression (5) has been further derived from the time-dependent non-equilibrium Green's function formalism 24 and shown to be equivalent to Lindblad dynamics in the limit of infinite leads. 25 …”

Section: Driven Liouville-von Neumann Approachmentioning

confidence: 99%

“…Previous applications of Equation (5) have included an "extended molecule" region. 20,25 In the presence of this extended region, much larger than the molecule itself, the latter is physically separated from the leads and the overlap elements coupling the electrode and the molecule sites become negligible, so that what effectively remains in the off-diagonal blocks are the mixed elements between the leads and neighboring sections of the extended molecule. This circumstance, added to the use of sufficiently large electrodes that can easily compensate for the charge drained through the off-diagonal blocks, minimizes the relative weight of the coherences in the dynamics, which in EOM (5) are damped to zero by absorbing-only contributions.…”

Section: First-principles Formulationmentioning

confidence: 99%

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Electron transport in real time from first-principles

Morzan

Ramirez

Lebrero

et al. 2017

The Journal of Chemical Physics

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While the vast majority of calculations reported on molecular conductance have been based on the static non-equilibrium Green's function formalism combined with density functional theory (DFT), in recent years a few time-dependent approaches to transport have started to emerge. Among these, the driven Liouville-von Neumann equation [C. G. Sánchez et al., J. Chem. Phys. 124, 214708 (2006)] is a simple and appealing route relying on a tunable rate parameter, which has been explored in the context of semi-empirical methods. In the present study, we adapt this formulation to a density functional theory framework and analyze its performance. In particular, it is implemented in an efficient allelectron DFT code with Gaussian basis functions, suitable for quantum-dynamics simulations of large molecular systems. At variance with the case of the tight-binding calculations reported in the literature, we find that now the initial perturbation to drive the system out of equilibrium plays a fundamental role in the stability of the electron dynamics. The equation of motion used in previous tight-binding implementations with massive electrodes has to be modified to produce a stable and unidirectional current during time propagation in time-dependent DFT simulations using much smaller leads. Moreover, we propose a procedure to get rid of the dependence of the current-voltage curves on the rate parameter. This method is employed to obtain the current-voltage characteristic of saturated and unsaturated hydrocarbons of different lengths, with very promising prospects. Published by AIP Publishing. [http://dx

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Section: Driven Liouville-von Neumann Approachmentioning

confidence: 99%

Section: First-principles Formulationmentioning

confidence: 99%

Electron transport in real time from first-principles

Morzan

Ramirez

Lebrero

et al. 2017

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…This is relevant for, e.g., exciton kinetics [27], resonant tunneling in heterostructures [28,29], and carrier capture [30]. Thus, establishing a Lindblad master equation, where coherences are fully taken into account beyond the secular approximation, is a matter of high interest and several proposals have been made recently [16,27,31,32].…”

Section: Introductionmentioning

confidence: 99%

Phenomenological position and energy resolving Lindblad approach to quantum kinetics

2018

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A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which goes beyond the common secular approximation. This allows for the treatment of systems, where coherences are generated by the bath couplings while avoiding the negative occupations occurring in the Bloch-Wangsness-Redfield kinetic equations. The versatility and accuracy of the approach is verified by its application to three entirely different physical systems: (i) electric transport through a double-dot system coupled to electronic reservoirs, (ii) exciton kinetics in coupled chromophores in the presence of a heat bath, and (iii) the simulation of quantum cascade lasers, where the coherent electron transport is established by scattering with phonons and impurities.

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“…From quantum cavities [1][2][3] and superconducting qubits [4][5][6][7][8][9] , through quantum dots [10][11][12][13][14][15], molecular junctions [16][17][18][19][20][21][22][23][24][25][26][27] and cold atoms [28][29][30][31] , to excitons traveling in photosynthetic complexes [32][33][34][35], open quantum systems show dynamics which can be far richer and more surprising than their coherent (environment-free) counterparts.…”

Section: A Introductionmentioning

confidence: 99%

Quantum transport under ac drive from the leads: A Redfield quantum master equation approach

Purkayastha

2017

Phys. Rev. B

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Evaluating the time-dependent dynamics of driven open quantum systems is relevant for a theoretical description of many systems, including molecular junctions, quantum dots, cavity-QED experiments, cold atoms experiments and more. Here, we formulate a rigorous microscopic theory of an out-of-equilibrium open quantum system of non-interacting particles on a lattice weakly coupled bilinearly to multiple baths and driven by periodically varying thermodynamic parameters like temperature and chemical potential of the bath. The particles can be either bosonic or fermionic and the lattice can be of any dimension and geometry. Based on Redfield quantum master equation under Born-Markov approximation, we derive a linear differential equation for equal time two-point correlation matrix, sometimes also called single-particle density matrix, from which various physical observables, for example, current, can be calculated. Various interesting physical effects, such as resonance, can be directly read-off from the equations. Thus, our theory is quite general gives quite transparent and easy-to-calculate results. We validate our theory by comparing with exact numerical simulations. We apply our method to a generic open quantum system, namely a double-quantum dot coupled to leads with modulating chemical potentials. Two most important experimentally relevant insights from this are : (i) time-dependent measurements of current for symmetric oscillating voltages (with zero instantaneous voltage bias) can point to the degree of asymmetry in the system-bath coupling, and (ii) under certain conditions, time-dependent currents can exceed time-averaged currents by several orders of magnitude, and can therefore be detected even when the average current is below the measurement threshold. A. IntroductionThe dynamics of a quantum system coupled to an external environment (so-called "open" quantum system) are a result of the intricate interplay between the coherent evolution of the quantum degrees of freedom, the structure of the environment and the form and strength of the system-environment coupling. From quantum cavities [1-3] and superconducting qubits [4][5][6][7][8][9] , through quantum dots [10][11][12][13][14][15], molecular junctions [16][17][18][19][20][21][22][23][24][25][26][27] and cold atoms [28][29][30][31] , to excitons traveling in photosynthetic complexes [32][33][34][35], open quantum systems show dynamics which can be far richer and more surprising than their coherent (environment-free) counterparts.Recent ideas of designing a quantum state by engineering a specific environment [36][37][38][39][40][41][42] or by a periodic modulation of the open system's Hamiltonian [16,43,44] open a path to new forms of control over quantum systems. Combining these two concepts of time-periodic modulations and environment (bath) engineering, here we study the dynamics of open quantum systems where the environment thermodynamic parameters are periodically modulated. Even though there exists formally exact methods of treating such set-ups...

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Driven Liouville von Neumann Equation in Lindblad Form

Cited by 37 publications

References 98 publications

Electron transport in real time from first-principles

Electron transport in real time from first-principles

Phenomenological position and energy resolving Lindblad approach to quantum kinetics

Quantum transport under ac drive from the leads: A Redfield quantum master equation approach

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