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Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay for extended reservoir simulations, where relaxation maintains a bias or temperature drop across the system. Our analysis begins in the non-interacting limit, where we parameterize different discretizations to compare them on an even footing. For many-body systems, we develop a method to estimate the relaxation that best approximates the continuum by controlling virtual transitions in Kramers turnover for the current. While some discretizations are more efficient for calculating currents, there is little benefit with regard to the overall state of the system. Any gains become marginal for many-body, tensor network simulations, where the relative performance of discretizations varies when sweeping other numerical controls. These results indicate that typical reservoir discretizations have little impact on numerical costs for certain computational tools. The choice of a relaxation parameter is nonetheless crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs. [ABSTRACT FROM AUTHOR]

Open-system simulations of quantum transport provide a platform for the study of true steady states, Floquet states, and the role of temperature, time dynamics, and fluctuations, among other physical processes. They are rapidly gaining traction, especially techniques that revolve around "extended reservoirs," a collection of a finite number of degrees of freedom with relaxation that maintains a bias or temperature gradient, and have appeared under various guises (e.g., the extended or mesoscopic reservoir, auxiliary master equation, and driven Liouville–von Neumann approaches). Yet, there are still a number of open questions regarding the behavior and convergence of these techniques. Here, we derive general analytical solutions, and associated asymptotic analyses, for the steady-state current driven by finite reservoirs with proportional coupling to the system/junction. In doing so, we present a simplified and unified derivation of the non-interacting and many-body steady-state currents through arbitrary junctions, including outside of proportional coupling. We conjecture that the analytic solution for proportional coupling is the most general of its form for isomodal relaxation (i.e., relaxing proportional coupling will remove the ability to find compact, general analytical expressions for finite reservoirs). These results should be of broad utility in diagnosing the behavior and implementation of extended reservoir and related approaches, including the convergence to the Landauer limit (for non-interacting systems) and the Meir–Wingreen formula (for many-body systems). [ABSTRACT FROM AUTHOR]

The adsorption of metal atoms on nanostructures, such as graphene and nanotubes, plays an important role in catalysis, electronic doping, and tuning material properties. Quantum chemical calculations permit the investigation of this process to discover desirable interactions and obtain mechanistic insights into adsorbate behavior, of which the binding strength is a central quantity. Binding strengths, however, vary widely in the literature, even when using almost identical computational methods. To address this issue, we investigate the adsorption of a variety of metals onto graphene, carbon nanotubes, and boron nitride nanotubes. As is well-known, calculations on periodic structures require a sufficiently large system size to remove interactions between periodic images. Our results indicate that there are both direct and indirect mechanisms for this interaction, where the latter can require even larger system sizes than typically employed. The magnitude and distance of the effect depends on the electronic state of the substrate and the open- or closed-shell nature of the adsorbate. For instance, insulating substrates (e.g., boron nitride nanotubes) show essentially no dependence on system size, whereas metallic or semi-metallic systems can have a substantial effect due to the delocalized nature of the electronic states interacting with the adsorbate. We derive a scaling relation for the length dependence with a representative tight-binding model. These results demonstrate how to extrapolate the binding energies to the isolated-impurity limit. [ABSTRACT FROM AUTHOR]

We investigate protocols for optimal molecular detection with electromechanical nanoscale sensors under ambient conditions. Our models are representative of suspended graphene nanoribbons, which due to their piezoelectric and electronic properties provide responsive and versatile sensors. In particular, we analytically account for the corrections in the electronic transmission function and signal-to-noise ratio originating in environmental perturbations, such as thermal fluctuations and solvation effects. We also investigate the role of the sampling time in the current statistics. As a result, we formulate a protocol for optimal sensing based on the modulation of the Fermi level at a fixed bias and provide approximate forms for the current, linear susceptibility, and current fluctuations. We show how the algebraic tails in the thermally broadened transmission function affect the behavior of the signal-to-noise ratio and optimal sensing. These results provide further insights into the operation of graphene deflectometers and other techniques for electromechanical sensing. [ABSTRACT FROM AUTHOR]

Graphene and other 2D materials give a platform for electromechanical sensing of biomolecules in aqueous, room temperature environments. The electronic current changes in response to mechanical deflection, indicating the presence of forces due to interactions with, e.g., molecular species. We develop illustrative models of these sensors in order to give explicit, compact expressions for the current and signal-to-noise ratio. Electromechanical structures have an electron transmission function that follows a generalized Voigt profile, with thermal fluctuations giving a Gaussian smearing analogous to thermal Doppler broadening in solution/gas-phase spectroscopic applications. The Lorentzian component of the profile comes from the contact to the electrodes. After providing an accurate approximate form of this profile, we calculate the mechanical susceptibility for a representative two-level bridge and the current fluctuations for electromechanical detection. These results give the underlying mechanics of electromechanical sensing in more complex scenarios, such as graphene deflectometry. [ABSTRACT FROM AUTHOR]

Simulations are increasingly employing explicit reservoirs—internal, finite regions—to drive electronic or particle transport. This naturally occurs in simulations of transport via ultracold atomic gases. Whether the simulation is numerical or physical, these approaches rely on the rapid development of the steady state. We demonstrate that steady state formation is a manifestation of the Gibbs phenomenon well-known in signal processing and in truncated discrete Fourier expansions. Each particle separately develops into an individual steady state due to the spreading of its wave packet in energy. The rise to the steady state for an individual particle depends on the particle energy—and thus can be slow—and ringing oscillations appear due to filtering of the response through the electronic bandwidth. However, the rise to the total steady state—the one from all particles—is rapid, with time scale π/W, where W is the bandwidth. Ringing oscillations are now also filtered through the bias window, and they decay with a higher power. The Gibbs constant—the overshoot of the first ring—can appear in the simulation error. These results shed light on the formation of the steady state and support the practical use of explicit reservoirs to simulate transport at the nanoscale or using ultracold atomic lattices. [ABSTRACT FROM AUTHOR]

The interconversion between the left- and right-handed helical folds of a polypeptide defines a dual-funneled free energy landscape. In this context, the funnel minima are connected through a continuum of unfolded conformations, evocative of the classical helix-coil transition. Physical intuition and recent conjectures suggest that this landscape can be mapped by assigning a left- or right-handed helical state to each residue. We explore this possibility using all-atom replica exchange molecular dynamics and an Ising-like model, demonstrating that the energy landscape architecture is at odds with a two-state picture. A three-state model—left, right, and unstructured—can account for most key intermediates during chiral interconversion. Competing folds and excited conformational states still impose limitations on the scope of this approach. However, the improvement is stark: Moving from a two-state to a three-state model decreases the fit error from 1.6 kBT to 0.3 kBT along the left-to-right interconversion pathway. [ABSTRACT FROM AUTHOR]

Open-system approaches are gaining traction in the simulation of charge transport in nanoscale and molecular electronic devices. In particular, "extended reservoir" simulations, where explicit reservoir degrees of freedom are present, allowfor the computation of both real-time and steady-state properties but require relaxation of the extended reservoirs. The strength of this relaxation, influences the conductance, giving rise to a "turnover" behavior analogous to Kramers turnover in chemical reaction rates. We derive explicit, general expressions for the weak and strong relaxation limits. For weak relaxation, the conductance increases linearly with γ and every electronic state of the total explicit system contributes to the electronic current according to its "reduced" weight in the two extended reservoir regions. Essentially, this represents two conductors in series--one at each interface with the implicit reservoirs that provide the relaxation. For strong relaxation, a "dual" expression-one with the same functional form-results, except nowproportional to 1/γ and dependent on the system of interest's electronic states, reflecting that the strong relaxation is localizing electrons in the extended reservoirs. Higher order behavior (e.g., γ2 or 1/γ2) can occur when there is a gap in the frequency spectrum. Moreover, inhomogeneity in the frequency spacing can give rise to a pseudo-plateau regime. These findings yield a physically motivated approach to diagnosing numerical simulations and understanding the influence of relaxation, and we examine their occurrence in both simple models and a realistic, fluctuating graphene nanoribbon. [ABSTRACT FROM AUTHOR]

Understanding dissipative and decohering processes is fundamental to the study of quantum systems. An accurate and generic method for investigating these processes is to simulate both the system and environment, which, however, is computationally very demanding. We develop a novel approach to constructing finite representations of the environment based on the influence of different frequency scales on the system’s dynamics. As an illustration, we analyze a solvable model of an optical mode decaying into a reservoir. The influence of the environment modes is constant for small frequencies, but drops off rapidly for large frequencies, allowing for a very sparse representation at high frequencies that gives a significant computational speedup in simulating the environment. This approach provides a general framework for simulating open quantum systems. [ABSTRACT FROM AUTHOR]

Master equations are increasingly popular for the simulation of time-dependent electronic transport in nanoscale devices. Several recent Markovian approaches use "extended reservoirs"-explicit degrees of freedom associated with the electrodes-distinguishing them from many previous classes of master equations. Starting from a Lindblad equation, we develop a common foundation for these approaches. Due to the incorporation of explicit electrode states, these methods do not require a large bias or even "true Markovianity" of the reservoirs. Nonetheless, their predictions are only physically relevant when the Markovian relaxation is weaker than the thermal broadening and when the extended reservoirs are "sufficiently large," in a sense that we quantify. These considerations hold despite complete positivity and respect for Pauli exclusion at any relaxation strength.