arXiv subjects

Michael Zwolak

Publications and source records attributed to Michael Zwolak.

At least 19 recordsLinked to original sources

arXiv2025

Approaching the scaling limit of transport through lattices with dephasing

We examine the stationary--state equations for lattices with generalized Markovian dephasing and relaxation. When the Hamiltonian is quadratic, the single--particle correlation matrix has a closed system of equations even in the presence of these two processes. The resulting equations have a vectorized form related to, but distinct from, Lyapunov's equation. We present an efficient solution that helps to achieve the scaling limit, e.g., of the current decay with lattice length. As an example, we study the super--diffusive--to--diffusive transition in a lattice with long--range hopping and dephasing. The approach enables calculations with up to $10^4$ sites, representing an increase of $10$ to $40$ times over prior studies. This enables a more precise extraction of the diffusion exponent, enhances agreement with theoretical results, and supports the presence of a phase transition. There is a wide range of problems that have Markovian relaxation, noise, and driving. They include quantum networks for machine--learning--based classification and extended reservoir approaches (ERAs) for transport. The results here will be useful for these classes of problems.

quant-ph↗

arXiv2024

The confluence of fractured resonances at points of dynamical, many--body flare

Resonant transport occurs when there is a matching of frequencies across some spatial medium, increasing the efficiency of shuttling particles from one reservoir to another. We demonstrate that in a periodically driven, many--body titled lattice, there are sets of spatially fractured resonances. These ``emanate'' from two essential resonances due to scattering off internal surfaces created when the driving frequency and many--body interaction strength vary, a scattering reminiscent of lens flare. The confluence of these fractured resonances dramatically enhances transport. At one confluence, the interaction strength is finite and the essential resonance arises due to the interplay of interaction with the counter--rotating terms of the periodic drive. We discuss the origin and structure of the fractured resonances, as well as the scaling of the conductance with system parameters. These results furnish a new example of the richness of open, driven, many--body systems.

cond-mat.str-el↗

arXiv2023

Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit

Extended reservoirs provide a framework for capturing macroscopic, continuum environments, such as metallic electrodes driving a current through a nanoscale contact, impurity, or material. We examine the application of this approach to periodically driven systems, specifically in the context of quantum transport. As with non--equilibrium steady states in time--independent scenarios, the current displays a Kramers' turnover including the formation of a plateau region that captures the physical, continuum limit response. We demonstrate that a simple stability criteria identifies an appropriate relaxation rate to target this physical plateau. Using this approach, we study quantum transport through a periodically driven tilted lattice coupled to two metallic reservoirs held at a finite bias and temperature. We use this model to benchmark the extended reservoir approach and assess the stability criteria. The approach recovers well--understood physical behavior in the limit of weak system--reservoir coupling. Extended reservoirs enable addressing strong coupling and non--linear response as well, where we analyze how transport responds to the dynamics inside the driven lattice. These results set the foundations for the use of extended reservoir approach for periodically driven, quantum systems, such as many--body Floquet states.

cond-mat.mes-hall↗

arXiv2023

Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs

The simulation of open many-body quantum systems is challenging, requiring methods to both handle exponentially large Hilbert spaces and represent the influence of (infinite) particle and energy reservoirs. These two requirements are at odds with each other: Larger collections of modes can increase the fidelity of the reservoir representation but come at a substantial computational cost when included in numerical many-body techniques. An increasingly utilized and natural approach to control the growth of the reservoir is to cast a finite set of reservoir modes themselves as an open quantum system. There are, though, many routes to do so. Here, we introduce an accumulative reservoir construction -- an ARC -- that employs a series of partial refreshes of the extended reservoirs. Through this series, the representation accumulates the character of an infinite reservoir. This provides a unified framework for both continuous (Lindblad) relaxation and a recently introduced periodically refresh approach (i.e., discrete resets of the reservoir modes to equilibrium). In the context of quantum transport, we show that the phase space for physical behavior separates into discrete and continuous relaxation regimes with the boundary between them set by natural, physical timescales. Both of these regimes "turnover" into regions of over- and under-damped coherence in a way reminiscent of Kramers' crossover. We examine how the range of behavior impacts errors and the computational cost, including within tensor networks. These results provide the first comparison of distinct extended reservoir approaches, showing that they have different scaling of error versus cost (with a bridging ARC regime decaying fastest). Exploiting the enhanced scaling, though, will be challenging, as it comes with a substantial increase in (operator space) entanglement entropy.

quant-ph↗

arXiv2022

Amplification, inference, and the manifestation of objective classical information

Our everyday reality is characterized by objective information$\unicode{x2013}$information that is selected and amplified by the environment that interacts with quantum systems. Many observers can accurately infer that information indirectly by making measurements on fragments of the environment. The correlations between the system, $\mathcal{S}$, and a fragment, $\mathcal{F}$, of the environment, $\mathcal{E}$, is often quantified by the quantum mutual information or the Holevo quantity that bounds the classical information about $\mathcal{S}$ transmittable by a quantum channel $\mathcal{F}$. The latter is a quantum mutual information but of a classical-quantum state where measurement has selected outcomes on $\mathcal{S}$. The measurement generically reflects the influence of the remaining environment, $\mathcal{E}/\mathcal{F}$, but can also reflect hypothetical questions to deduce the structure of $\mathcal{S}\mathcal{F}$ correlations. Recently, Touil et al. examined a different Holevo quantity, one from a quantum-classical state (a quantum $\mathcal{S}$ to a measured $\mathcal{F}$). As shown here, this quantity upper bounds any accessible classical information about $\mathcal{S}$ in $\mathcal{F}$ and can yield a tighter bound than the typical Holevo quantity. When good decoherence is present$\unicode{x2013}$when the remaining environment, $\mathcal{E}/\mathcal{F}$, has effectively measured the pointer states of $\mathcal{S}$$\unicode{x2013}$this accessibility bound is the accessible information. For the specific model of Touil et al., the accessible information is related to the error probability for optimal detection and, thus, has the same behavior as the quantum Chernoff bound. The latter reflects amplification and provides a universal approach, as well as a single-shot framework, to quantify records of the missing, classical information about $\mathcal{S}$.

quant-ph↗

arXiv2021

Dual current anomalies and quantum transport within extended reservoir simulations

Quantum transport simulations are rapidly evolving and now encompass well-controlled tensor network techniques for many-body limits. One powerful approach combines matrix product states with extended reservoirs. In this method, continuous reservoirs are represented by explicit, discretized counterparts and a chemical potential or temperature drop is maintained by external relaxation. Currents are strongly influenced by relaxation when it is very weak or strong, resulting in a simulation analog of Kramers' turnover for solution-phase chemical reactions. At intermediate relaxation, the intrinsic conductance, that given by the Landauer or Meir-Wingreen expressions, moderates the current. We demonstrate that strong impurity scattering (i.e., a small steady-state current) reveals anomalous transport regimes within this methodology at weak-to-moderate and moderate-to-strong relaxation. The former is due to virtual transitions and the latter to unphysical broadening of the populated density of states. Thus, the turnover analog has $five$ standard transport regimes, further constraining the parameters that lead to recovery of the intrinsic conductance. In the worst case, the common strategy of choosing a relaxation strength proportional to the reservoir level spacing can prevent convergence to the continuum limit. This advocates a simulation strategy where one utilizes the current versus relaxation turnover profiles to identify simulation parameters that most efficiently reproduce the intrinsic physical behavior.

cond-mat.mes-hall↗

arXiv2021

Performance of Reservoir Discretizations in Quantum Transport Simulations

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 a given reservoir discretization may have little impact on numerical efficiency for certain computational tools. The choice of a relaxation parameter, however, is crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs.

cond-mat.mes-hall↗

arXiv2021

Comment on "Quantum transport with electronic relaxation in electrodes: Landauer-type formulas derived from the driven Liouville-von Neumann approach" [The Journal of Chemical Physics 153, 044103 (2020)]

In a recent article, Chiang and Hsu [The Journal of Chemical Physics 153, 044103 (2020)] examine one and two site electronic junctions identically connected to finite reservoirs. For these two examples, they derive analytical solutions, as well as provide asymptotic analyses, for the steady-state current from the driven Liouville-von Neumann (DLvN) equation - an open system approach to transport in non-interacting systems where relaxation maintains a bias. The two site junction they examine has destructive interference, which they show leads to slow convergence of the DLvN to the Landauer limit with respect to reservoir size and relaxation. We previously derived the general solution for the steady-state current in both the DLvN and its many-body analog [Gruss et al., Scientific Reports 6, 24514 (2016)]. The many-body analog is a Lindblad master equation, which, when restricted to non-interacting systems, is exactly the DLvN. Here, we demonstrate that applying the more general expression to identical left and right reservoirs (i.e., finite reservoirs with the same density of states and coupling to the system) and Markovian relaxation provides a simple analytic form that applies to arbitrary, but identically connected, junctions. Moreover, we briefly discuss the convergence of the current to the Landauer and Meir-Wingreen result for non-interacting and interacting systems, respectively. Convergence occurs as the reservoirs' lesser Green's functions begin conforming to the fluctuation-dissipation theorem. Our approach sheds light on the behavior Chiang and Hsu observe for destructive interference. Finally, we show that the analytical results yield the asymptotic formulas derived in Gruss et al.

quant-ph↗

arXiv2021

Analytic expressions for the steady-state current with finite extended reservoirs

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 maintain 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).

quant-ph↗

arXiv2020

Diffusion Limitations and Translocation Barriers in Atomically Thin Biomimetic Pores

Ionic transport in nano- to sub-nano-scale pores is highly dependent on translocation barriers and potential wells. These features in the free-energy landscape are primarily the result of ion dehydration and electrostatic interactions. For pores in atomically thin membranes, such as graphene, other factors come into play. Ion dynamics both inside and outside the geometric volume of the pore can be critical in determining the transport properties of the channel due to several commensurate length scales, such as the effective membrane thickness, radii of the first and the second hydration layers, pore radius, and Debye length. In particular, for biomimetic pores, such as the graphene crown ether we examine here, there are regimes where transport is highly sensitive to the pore size due to the interplay of dehydration and interaction with pore charge. Picometer changes in the size, e.g., due to a minute strain, can lead to a large change in conductance. Outside of these regimes, the small pore size itself gives a large resistance, even when electrostatic factors and dehydration compensate each other to give a relatively flat -- e.g., near barrierless -- free energy landscape. The permeability, though, can still be large and ions will translocate rapidly after they arrive within the capture radius of the pore. This, in turn, leads to diffusion and drift effects dominating the conductance. The current thus plateaus and becomes effectively independent of pore-free energy characteristics. Measurement of this effect will give an estimate of the magnitude of kinetically limiting features, and experimentally constrain the local electromechanical conditions.

cond-mat.mes-hall↗

arXiv2020

Open System Tensor Networks and Kramers' Crossover for Quantum Transport

Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes - such as quantum transport or quenches - where entanglement growth is linear in time. Matrix-product-state decompositions of the resulting out-of-equilibrium states require a bond dimension that grows exponentially, imposing a hard limit on simulation timescales. However, in the case of transport, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be made logarithmic. Here, we apply this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access steady states, time dynamics and noise, and periodic driving (e.g., Floquet states). We demonstrate the approach by calculating the transport characteristics of an open, interacting system. These results open a path to scalable and numerically systematic many-body transport calculations with tensor networks.

cond-mat.str-el↗

arXiv2020

Breaking the entanglement barrier: Tensor network simulation of quantum transport

The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global dynamics elevates many particles into excited states, and can lead to macroscopic entanglement and the failure of tensor networks. Here, we show that for quantum transport -- one of the most important cases of this failure -- the fundamental issue is the canonical basis in which the scenario is cast: When particles flow through an interface, they scatter, generating a "bit" of entanglement between spatial regions with each event. The frequency basis naturally captures that -- in the long-time limit and in the absence of inelastic scattering -- particles tend to flow from a state with one frequency to a state of identical frequency. Recognizing this natural structure yields a striking -- potentially exponential in some cases -- increase in simulation efficiency, greatly extending the attainable spatial- and time-scales, and broadening the scope of tensor network simulation to hitherto inaccessible classes of non-equilibrium many-body problems.

cond-mat.str-el↗

arXiv2020

Metal adsorbate interactions and the convergence of density functional calculations

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. However, binding strengths 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 depend 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.

cond-mat.mes-hall↗

arXiv2020

Optimal in situ electromechanical sensing of molecular species

We investigate protocols for optimal molecular detection with electromechanical nanoscale sensors in 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 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.

cond-mat.mes-hall↗

arXiv2019

Topology, Landscapes, and Biomolecular Energy Transport

While ubiquitous, energy redistribution remains a poorly understood facet of the nonequilibrium thermodynamics of biomolecules. At the molecular level, finite-size effects, pronounced nonlinearities, and ballistic processes produce behavior that diverges from the macroscale. Here, we show that transient thermal transport reflects macromolecular energy landscape architecture through the topological characteristics of molecular contacts and the nonlinear processes that mediate dynamics. While the former determines transport pathways via pairwise interactions, the latter reflects frustration within the landscape for local conformational rearrangements. Unlike transport through small-molecule systems, such as alkanes, nonlinearity dominates over coherent processes at even quite short time- and length-scales. Our exhaustive all-atom simulations and novel local-in-time and space analysis, applicable to both theory and experiment, permit dissection of energy migration in biomolecules. The approach demonstrates that vibrational energy transport can probe otherwise inaccessible aspects of macromolecular dynamics and interactions that underly biological function.

physics.bio-ph↗

arXiv2019

Revealing the emergence of classicality in nitrogen-vacancy centers

The origin of classical reality in our quantum world is a long-standing mystery. Here, we examine a nitrogen vacancy center evolving naturally in the presence of its environment to study quantum Darwinism - the proliferation of information about preferred quantum states throughout the world via the environment. This redundantly imprinted information accounts for the perception of objective reality, as it is independently accessible by many without perturbing the system of interest. To observe the emergence of redundant information, we implement a novel dynamical decoupling scheme that enables the measurement/control of several nuclear spins (the environment E) interacting with a nitrogen vacancy (the system S). In addition to showing how to create entangled SE states relevant to quantum metrology, we demonstrate that under the decoherence of S, redundant information is imprinted onto E, giving rise to classical objectivity - a consensus of the nuclear spins about the state of S. This provides the first laboratory verification of the objective classical world emerging from the underlying quantum substrate.

quant-ph↗

arXiv2019

Colloquium: Ionic phenomena in nanoscale pores through 2D materials

Ion transport through nanopores permeates through many areas of science and technology, from cell behavior to sensing and separation to catalysis and batteries. Two-dimensional materials, such as graphene, molybdenum disulfide (MoS$_2$), and hexagonal boron nitride (hBN), are recent additions to these fields. Low-dimensional materials present new opportunities to develop filtration, sensing, and power technologies, encompassing ion exclusion membranes, DNA sequencing, single molecule detection, osmotic power generation, and beyond. Moreover, the physics of ionic transport through pores and constrictions within these materials is a distinct realm of competing many-particle interactions (e.g., solvation/dehydration, electrostatic blockade, hydrogen bond dynamics) and confinement. This opens up alternative routes to creating biomimetic pores and may even give analogues of quantum phenomena, such as quantized conductance, in the classical domain. These prospects make membranes of 2D materials -- i.e., 2D membranes -- fascinating. We will discuss the physics and applications of ionic transport through nanopores in 2D membranes.opores in 2D membranes.

cond-mat.mes-hall↗

arXiv2019

Optimal transport and colossal ionic mechano-conductance in graphene crown ethers

Biological ion channels balance electrostatic and dehydration effects to yield large ion selectivities alongside high transport rates. These macromolecular systems are often interrogated through point mutations of their pore domain, limiting the scope of mechanistic studies. In contrast, we demonstrate that graphene crown ether pores afford a simple platform to directly investigate optimal ion transport conditions, i.e., maximum current densities and selectivity. Crown ethers are known for selective ion adsorption. When embedded in graphene, however, transport rates lie below the drift-diffusion limit. We show that small pore strains -- 1 % -- give rise to a colossal -- 100 % -- change in conductance. This process is electromechanically tunable, with optimal transport in a primarily diffusive regime, tending toward barrierless transport, as opposed to a knock-on mechanism. Measurements of mechanical current modulation will yield direct information on the local electrostatic conditions of the pore. These observations suggest a novel setup for nanofluidic devices while giving insight into the physical foundation of evolutionarily--optimized ion transport in biological pores.

cond-mat.mes-hall↗