Custodial Chiral Symmetry in a Su-Schrieffer-Heeger Electrical Circuit with Memory.

Custodial symmetries are common in the standard model of particle physics. They arise when quantum corrections to a parameter are proportional to the parameter itself. Here, we show that a custodial symmetry of the chiral type is also present in a classical Su-Schrieffer-Heeger (SSH) electrical circuit with memory. In the absence of memory, the SSH circuit supports a symmetry-protected topological edge state. Memory induces nonlinearities that break chiral symmetry explicitly and spread the state across the circuit. However, the resulting state is still protected against perturbations by the ensuing custodial chiral symmetry. These predictions can be verified experimentally and demonstrate the interplay between symmetry and memory.

Thousand-fold Increase in Plasmonic Light Emission via Combined Electronic and Optical Excitations.

Surface plasmon enhanced processes and hot-carrier dynamics in plasmonic nanostructures are of great fundamental interest to reveal light-matter interactions at the nanoscale. Using plasmonic tunnel junctions as a platform supporting both electrically and optically excited localized surface plasmons, we report a much greater (over 1000× ) plasmonic light emission at upconverted photon energies under combined electro-optical excitation, compared with electrical or optical excitation separately. Two mechanisms compatible with the form of the observed spectra are interactions of plasmon-induced hot carriers and electronic anti-Stokes Raman scattering. Our measurement results are in excellent agreement with a theoretical model combining electro-optical generation of hot carriers through nonradiative plasmon excitation and hot-carrier relaxation. We also discuss the challenge of distinguishing relative contributions of hot carrier emission and the anti-Stokes electronic Raman process. This observed increase in above-threshold emission in plasmonic systems may open avenues in on-chip nanophotonic switching and hot-carrier photocatalysis.

Directed percolation and numerical stability of simulations of digital memcomputing machines.

Digital memcomputing machines (DMMs) are a novel, non-Turing class of machines designed to solve combinatorial optimization problems. They can be physically realized with continuous-time, non-quantum dynamical systems with memory (time non-locality), whose ordinary differential equations (ODEs) can be numerically integrated on modern computers. Solutions of many hard problems have been reported by numerically integrating the ODEs of DMMs, showing substantial advantages over state-of-the-art solvers. To investigate the reasons behind the robustness and effectiveness of this method, we employ three explicit integration schemes (forward Euler, trapezoid, and Runge-Kutta fourth order) with a constant time step to solve 3-SAT instances with planted solutions. We show that (i) even if most of the trajectories in the phase space are destroyed by numerical noise, the solution can still be achieved; (ii) the forward Euler method, although having the largest numerical error, solves the instances in the least amount of function evaluations; and (iii) when increasing the integration time step, the system undergoes a "solvable-unsolvable transition" at a critical threshold, which needs to decay at most as a power law with the problem size, to control the numerical errors. To explain these results, we model the dynamical behavior of DMMs as directed percolation of the state trajectory in the phase space in the presence of noise. This viewpoint clarifies the reasons behind their numerical robustness and provides an analytical understanding of the solvable-unsolvable transition. These results land further support to the usefulness of DMMs in the solution of hard combinatorial optimization problems.

Application of Floquet theory to dynamical systems with memory.

We extend the recently developed generalized Floquet theory [Phys. Rev. Lett. 110, 170602 (2013)] to systems with infinite memory, i.e., a dependence on the whole previous history. In particular, we show that a lower asymptotic bound exists for the Floquet exponents associated to such cases. As examples, we analyze the cases of an ideal 1D system, a Brownian particle, and a circuit resonator with an ideal transmission line. All these examples show the usefulness of this new approach to the study of dynamical systems with memory, which are ubiquitous in science and technology.

An energy-resolved atomic scanning probe.

We propose a method to probe the local density of states (LDOS) of atomic systems that provides both spatial and energy resolution. The method combines atomic and tunneling techniques to supply a simple, yet quantitative and operational, definition of the LDOS for both interacting and non-interacting systems: It is the rate at which particles can be siphoned from the system of interest by a narrow energy band of non-interacting states contacted locally to the many-body system of interest. Ultracold atoms in optical lattices are a natural platform for implementing this broad concept to visualize the energy and spatial dependence of the atom density in interacting, inhomogeneous lattices. This includes models of strongly correlated condensed matter systems, as well as ones with non-trivial topologies.

Dehydration as a Universal Mechanism for Ion Selectivity in Graphene and Other Atomically Thin Pores.

Ion channels play a key role in regulating cell behavior and in electrical signaling. In these settings, polar and charged functional groups, as well as protein response, compensate for dehydration in an ion-dependent way, giving rise to the ion selective transport critical to the operation of cells. Dehydration, though, yields ion-dependent free-energy barriers and thus is predicted to give rise to selectivity by itself. However, these barriers are typically so large that they will suppress the ion currents to undetectable levels. Here, we establish that graphene displays a measurable dehydration-only mechanism for selectivity of K+ over Cl-. This fundamental mechanism, one that depends only on the geometry and hydration, is the starting point for selectivity for all channels and pores. Moreover, while we study selectivity of K+ over Cl- we find that dehydration-based selectivity functions for all ions, that is, cation over cation selectivity (e.g., K+ over Na+). Its likely detection in graphene pores resolves conflicting experimental results, as well as presents a new paradigm for characterizing the operation of ion channels and engineering molecular/ionic selectivity in filtration and other applications.

Observation of ionic Coulomb blockade in nanopores.

Emergent behaviour from electron-transport properties is routinely observed in systems with dimensions approaching the nanoscale. However, analogous mesoscopic behaviour resulting from ionic transport has so far not been observed, most probably because of bottlenecks in the controlled fabrication of subnanometre nanopores for use in nanofluidics. Here, we report measurements of ionic transport through a single subnanometre pore junction, and the observation of ionic Coulomb blockade: the ionic counterpart of the electronic Coulomb blockade observed for quantum dots. Our findings demonstrate that nanoscopic, atomically thin pores allow for the exploration of phenomena in ionic transport, and suggest that nanopores may also further our understanding of transport through biological ion channels.

Polynomial-time solution of prime factorization and NP-complete problems with digital memcomputing machines.

We introduce a class of digital machines, we name Digital Memcomputing Machines, (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space, and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We prove this by making a connection with the dynamical systems theory. This leads us to a set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept of self-organizing logic gates and circuits (SOLCs). These are logic gates and circuits able to accept input signals from any terminal, without distinction between conventional input and output terminals. They can solve boolean problems by self-organizing into their solution. They can be fabricated either with circuit elements with memory (such as memristors) and/or standard MOS technology. Using tools of functional analysis, we prove mathematically the following constraints for the poly-resource resolvability: (i) SOLCs possess a global attractor; (ii) their only equilibrium points are the solutions of the problems to solve; (iii) the system converges exponentially fast to the solutions; (iv) the equilibrium convergence rate scales at most polynomially with input size. We finally provide arguments that periodic orbits and strange attractors cannot coexist with equilibria. As examples, we show how to solve the prime factorization and the search version of the NP-complete subset-sum problem. Since DMMs map integers into integers, they are robust against noise and hence scalable. We finally discuss the implications of the DMM realization through SOLCs to the NP = P question related to constraints of poly-resources resolvability.

Absence of periodic orbits in digital memcomputing machines with solutions.

In Traversa and Di Ventra [Chaos 27, 023107 (2017)] we argued, without proof, that if the non-linear dynamical systems with memory describing the class of digital memcomputing machines (DMMs) have equilibrium points, then no periodic orbits can emerge. In fact, the proof of such a statement is a simple corollary of a theorem already demonstrated in Traversa and Di Ventra [Chaos 27, 023107 (2017)]. Here, we point out how to derive such a conclusion. Incidentally, the same demonstration implies absence of chaos, a result we have already demonstrated in Di Ventra and Traversa [Phys. Lett. A 381, 3255 (2017)] using topology. These results, together with those in Traversa and Di Ventra [Chaos 27, 023107 (2017)], guarantee that if the Boolean problem the DMMs are designed to solve has a solution, the system will always find it, irrespective of the initial conditions.

Programmable redox state of the nickel ion chain in DNA.

DNA is a nanowire in nature which chelates Ni ions and forms a conducting chain in its base-pairs (Ni-DNA). Each Ni ion in Ni-DNA exhibits low (Ni(2+)) or high (Ni(3+)) oxidation state and can be switched sequentially by applying bias voltage with different polarities and writing times. The ratio of low and high oxidation states of Ni ions in Ni-DNA represents a programmable multistate memory system with an added capacitive component, in which multistate information can be written, read, and erased. This study also indicates that the biomolecule-based self-organized nanostructure can be used as a template for nanodevice fabrication.

Driving knots on DNA with AC/DC electric fields: topological friction and memory effects.

The dynamical properties of entangled polyelectrolytes are investigated theoretically and computationally for a proposed novel micromanipulation setup. Specifically, we investigate the effects of DC and AC electric fields acting longitudinally on knotted DNA chains, modelled as semiflexible chains of charged beads, under mechanical tension. We consider various experimentally accessible values of the field amplitude and frequency as well as several of the simplest knot types. In particular, we consider both torus and twist knots because they are respectively known to be able or unable to slide along macroscopic threads and ropes. Strikingly, this qualitative distinction disappears in this microscopic context because all the considered knot types acquire a systematic drift in the direction of the electric force. Notably, the knot drift velocity and diffusion coefficient in zero field (both measurable also experimentally) can be used to define a characteristic "frictional" lengthscale for the various knot types. This previously unexplored length provides valuable information on the extent of self-interactions in the nominal knotted region. It is finally observed that the motion of a knot can effectively follow the AC field only if the driving period is larger than the knot relaxation time (for which the self-diffusion time provides an upper bound). These results suggest that salient aspects of the intrinsic dynamics of knots in DNA chains could be probed experimentally by means of external, time-dependent electric fields.

Correlation dynamics and enhanced signals for the identification of serial biomolecules and DNA bases.

Nanopore-based sequencing has demonstrated a significant potential for the development of fast, accurate, and cost-efficient fingerprinting techniques for next generation molecular detection and sequencing. We propose a specific multilayered graphene-based nanopore device architecture for the recognition of single biomolecules. Molecular detection and analysis can be accomplished through the detection of transverse currents as the molecule or DNA base translocates through the nanopore. To increase the overall signal-to-noise ratio and the accuracy, we implement a new 'multi-point cross-correlation' technique for identification of DNA bases or other molecules on the single molecular level. We demonstrate that the cross-correlations between each nanopore will greatly enhance the transverse current signal for each molecule. We implement first-principles transport calculations for DNA bases surveyed across a multilayered graphene nanopore system to illustrate the advantages of the proposed geometry. A time-series analysis of the cross-correlation functions illustrates the potential of this method for enhancing the signal-to-noise ratio. This work constitutes a significant step forward in facilitating fingerprinting of single biomolecules using solid state technology.

Collective dynamics and long-range order in thermal neuristor networks.

In the pursuit of scalable and energy-efficient neuromorphic devices, recent research has unveiled a novel category of spiking oscillators, termed "thermal neuristors." These devices function via thermal interactions among neighboring vanadium dioxide resistive memories, emulating biological neuronal behavior. Here, we show that the collective dynamical behavior of networks of these neurons showcases a rich phase structure, tunable by adjusting the thermal coupling and input voltage. Notably, we identify phases exhibiting long-range order that, however, does not arise from criticality, but rather from the time non-local response of the system. In addition, we show that these thermal neuristor arrays achieve high accuracy in image recognition and time series prediction through reservoir computing, without leveraging long-range order. Our findings highlight a crucial aspect of neuromorphic computing with possible implications on the functioning of the brain: criticality may not be necessary for the efficient performance of neuromorphic systems in certain computational tasks.

Nanofluidic logic with mechano-ionic memristive switches.

Neuromorphic systems are typically based on nanoscale electronic devices, but nature relies on ions for energy-efficient information processing. Nanofluidic memristive devices could thus potentially be used to construct electrolytic computers that mimic the brain down to its basic principles of operation. Here we report a nanofluidic device that is designed for circuit-scale in-memory processing. The device, which is fabricated using a scalable process, combines single-digit nanometric confinement and large entrance asymmetry and operates on the second timescale with a conductance ratio in the range of 9 to 60. In operando optical microscopy shows that the memory capabilities are due to the reversible formation of liquid blisters that modulate the conductance of the device. We use these mechano-ionic memristive switches to assemble logic circuits composed of two interactive devices and an ohmic resistor.

Kondo memory in driven strongly correlated quantum dots.

We investigate the real-time current response of strongly correlated quantum dot systems under sinusoidal driving voltages. By means of an accurate hierarchical equations of motion approach, we demonstrate the presence of prominent memory effects induced by the Kondo resonance on the real-time current response. These memory effects appear as distinctive hysteresis line shapes and self-crossing features in the dynamic current-voltage characteristics, with concomitant excitation of odd-number overtones. They emerge as a cooperative effect of quantum coherence-due to inductive behavior-and electron correlations-due to the Kondo resonance. We also show the suppression of memory effects and the transition to classical behavior as a function of temperature. All these phenomena can be observed in experiments and may lead to novel quantum memory applications.

Generalized Floquet theory: application to dynamical systems with memory and Bloch's theorem for nonlocal potentials.

Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic coefficients. Here, we extend the theory by proving a theorem for the general class of systems including linear operators commuting with the period-shift operator. The present theorem greatly expands the range of applicability of Floquet theory to a multitude of phenomena that were previously inaccessible with this type of analysis, such as dynamical systems with memory. As an important extension, we also prove Bloch's theorem for nonlocal potentials.

Fast DNA sequencing by electrical means inches closer.

The sequencing of the human genome offered a glimpse of future medical practices, where information retrieved from the genome could be harnessed to inform treatment decisions. However, making DNA sequencing accessible enough for widespread use poses a number of challenges. This perspective article traces the progress made in the field so far and looks at how close we may be already to real-life applications.

On the physical properties of memristive, memcapacitive and meminductive systems.

We discuss the physical properties of realistic memristive, memcapacitive and meminductive systems. In particular, by employing the well-known theory of response functions and microscopic derivations, we show that resistors, capacitors and inductors with memory emerge naturally in the response of systems-especially those of nanoscale dimensions-subjected to external perturbations. As a consequence, since memristances, memcapacitances and meminductances are simply response functions, they are not necessarily finite. This means that, unlike what has always been argued in some literature, diverging and non-crossing input-output curves of all these memory elements are physically possible in both quantum and classical regimes. For similar reasons, it is not surprising to find memcapacitances and meminductances that acquire negative values at certain times during dynamics, while the passivity criterion of memristive systems imposes always a non-negative value on the resistance at any given time. We finally show that ideal memristors, namely those whose state depends only on the charge that flows through them (or on the history of the voltage), are subject to very strict physical conditions and are unable to protect their memory state against the unavoidable fluctuations, and therefore are susceptible to a stochastic catastrophe. Similar considerations apply to ideal memcapacitors and meminductors.

Self-averaging of digital memcomputing machines.

Digital memcomputing machines (DMMs) are a new class of computing machines that employ nonquantum dynamical systems with memory to solve combinatorial optimization problems. Here, we show that the time to solution (TTS) of DMMs follows an inverse Gaussian distribution, with the TTS self-averaging with increasing problem size, irrespective of the problem they solve. We provide both an analytical understanding of this phenomenon and numerical evidence by solving instances of the 3-SAT (satisfiability) problem. The self-averaging property of DMMs with problem size implies that they are increasingly insensitive to the detailed features of the instances they solve. This is in sharp contrast to traditional algorithms applied to the same problems, illustrating another advantage of this physics-based approach to computation.

Ionic memcapacitive effects in nanopores.

Using molecular dynamics simulations, we show that, when subject to a periodic external electric field, a nanopore in ionic solution acts as a capacitor with memory (memcapacitor) at various frequencies and strengths of the electric field. Most importantly, the hysteresis loop of this memcapacitor shows both negative and diverging capacitance as a function of the voltage. The origin of this effect stems from the slow polarizability of the ionic solution due to the finite mobility of ions in water. We develop a microscopic quantitative model which captures the main features we observe in the simulations and suggest experimental tests of our predictions. We also suggest a possible memory mechanism due to the transport of ions through the nanopore itself, which may be observed at small frequencies. These effects may be important both in DNA sequencing proposals using nanopores and possibly in the dynamics of action potentials in neurons.