arXiv subjects

M. A. Novotny

Publications and source records attributed to M. A. Novotny.

At least 19 recordsLinked to original sources

arXiv2025

Universal Scaling of Electron Transmission for Nearly Ballistic and Quantum Dragon Nanodevices

We predict two different universal scaling regimes for the quantum transmission of metallic nanodevices following the addition of a small amount of uncorrelated disorder. A nanodevice is connected to two thin semi-infinite uniform leads, and the Non-Equilibrium Green's Function (NEGF) methodology yields the electron transmission ${\cal T}(E)$ as a function of the injected electron energy $E$. Ballistic nanodevices have no disorder and have ${\cal T}(E)=1$ for all $E$ that allow electron propagation in the leads. Quantum dragon nanodevices can have extremely strong properly correlated disorder, and still have ${\cal T}(E)=1$ for all $E$. Additional uncorrelated site disorder leads to Fano resonances in ${\cal T}(E)$. Averaging over the uncorrelated disorder we predict using perturbation theory two universal scaling regimes for ${\cal T}_{\rm ave}(E)$. The functional form of both universal scaling regimes depend on the device length and width, energy, and variance of the uncorrelated disorder. The second scaling regime, valid for small but somewhat larger uncorrelated disorder than the first scaling regime, also has the form dependent on the density of states of the system. These two scaling regimes are demonstrated to be valid via large scale computer calculations.

cond-mat.mes-hall↗

arXiv2022

Benchmarking quantum annealers using symmetries in embedded subgraphs

We investigate an efficient, generic method for evaluating the performance of quantum annealing devices that does not require the prior knowledge of the true ground state of the benchmark problem. This approach exploits symmetry properties inherent to the ground states of a composite Hamiltonian comprising the benchmark problem Hamiltonian and its symmetric counterpart. Using this method, we compare the performance of two generations of D-Wave machines. Although we do not observe a noticeable difference in the probability of finding solutions with the required symmetry, our results suggest that the current generation of D-Wave machines notably outperforms its predecessor in finding states closer to those with the required symmetry.

quant-ph↗

arXiv2021

Example Exact Solutions of the Time-independent Gross-Pitaevskii and Schrödinger Equations

A prescription is given to obtain some exact results for certain external potentials $V\left({\vec r}\right)$ of the time-independent Gross-Pitaevskii and Schrödinger equations. The study motivation is the ability to program $V\left({\vec r}\right)$ experimentally in Bose-Einstein condensates. Rather than derive wavefunctions that are solutions for a given $V\left({\vec r}\right)$, we ask which $V\left({\vec r}\right)$ will have a given pdf (probability density function) $P\left({\vec r}\right)$. Several examples in 1D and 2D are presented for well-known pdfs and for the hydrogen atom in momentum space.

quant-ph↗

arXiv2019

Comparison of D-Wave Quantum Annealing and Classical Simulated Annealing for Local Minima Determination

Restricted Boltzmann Machines trained with different numbers of iterations were used to provide a diverse set of energy functions each containing many local valleys (LVs) with different energies, widths, escape barrier heights, etc. They were used to verify the previously reported possibility of using the D-Wave quantum annealer (QA) to find potentially important LVs in the energy functions of Ising spin glasses that may be missed by classical searches. For classical search, extensive simulated annealing (SA) was conducted to find as many LVs as possible regardless of the computational cost. SA was conducted long enough to ensure that the number of SA-found LVs approaches that and eventually significantly exceeds the number of the LVs found by a single call submitted to the D-Wave. Even after a prohibitively long SA search, as many as 30-50% of the D-Wave-found LVs remained not found by the SA. In order to establish if LVs found only by the D-Wave represent potentially important regions of the configuration space, they were compared to those that were found by both techniques. While the LVs found by the D-Wave but missed by SA predominantly had higher energies and lower escape barriers, there was a significant fraction having intermediate values of the energy and barrier height. With respect to most other important LV parameters, the LVs found only by the D-Wave were distributed in a wide range of the parameters' values. It was established that for large or small, shallow or deep, wide or narrow LVs, the LVs found only by the D-Wave are distinguished by a few-times smaller size of the LV basin of attraction (BoA). Apparently, the size of the BoA is not or at least is less important for QA search compared to the classical search, allowing QA to easily find many potentially important (e.g., wide and deep) LVs missed by even prohibitively lengthy classical searches.

quant-ph↗

arXiv2019

Towards Sampling from Nondirected Probabilistic Graphical models using a D-Wave Quantum Annealer

A D-Wave quantum annealer (QA) having a 2048 qubit lattice, with no missing qubits and couplings, allowed embedding of a complete graph of a Restricted Boltzmann Machine (RBM). A handwritten digit OptDigits data set having 8x7 pixels of visible units was used to train the RBM using a classical Contrastive Divergence. Embedding of the classically-trained RBM into the D-Wave lattice was used to demonstrate that the QA offers a high-efficiency alternative to the classical Markov Chain Monte Carlo (MCMC) for reconstructing missing labels of the test images as well as a generative model. At any training iteration, the D-Wave-based classification had classification error more than two times lower than MCMC. The main goal of this study was to investigate the quality of the sample from the RBM model distribution and its comparison to a classical MCMC sample. For the OptDigits dataset, the states in the D-Wave sample belonged to about two times more local valleys compared to the MCMC sample. All the lowest-energy (the highest joint probability) local minima in the MCMC sample were also found by the D-Wave. The D-Wave missed many of the higher-energy local valleys, while finding many "new" local valleys consistently missed by the MCMC. It was established that the "new" local valleys that the D-Wave finds are important for the model distribution in terms of the energy of the corresponding local minima, the width of the local valleys, and the height of the escape barrier.

cs.LG↗

arXiv2018

A small-world search for quantum speedup: How small-world interactions can lead to improved quantum annealer designs

There are many factors that influence the design of quantum annealing processing units. Here we address the issue of improving quantum annealing processing unit designs from the point of view of the critical behavior of spin glasses. It has been argued [Phys. Rev. X 4, 021008 (2014)] that among the most difficult Ising spin-glass ground-state problems are those related to lattices which exhibit a finite-temperature spin-glass transition. Here, we show that adding small-world couplers between qubits (spins) to the native quasi-planar quantum processing unit graph results in a topology where a disordered Ising system can undergo a finite-temperature spin-glass transition, even when an Ising spin glass on the quasi-planar native graph does not display a transition into a glassy phase at any finite temperature. To ensure that these systems can be engineered with current fabrication techniques, using large-scale Monte Carlo simulations we demonstrate that highly-constrained systems restricted to a few fabrication layers and with fixed coupler angles can also exhibit a finite-temperature spin-glass transition. This indicates that these systems might be mean-field-like, which also means that embedding highly-nonplanar problems might be simplified when compared to the underlying native topology. Our results are illustrated using the quasi-planar Chimera topology currently used in the D-Wave Systems Inc. quantum annealing machines, as well as standard two-dimensional square lattices. The presented approach can be generalized to other topologies.

quant-ph↗

arXiv2017

Quantum Dragon Solutions for Electron Transport through Nanostructures based on Rectangular Graphs

Electron transport through nanodevices of atoms in a single-layer rectangular arrangement with free (open) boundary conditions parallel to the direction of the current flow is studied within the single-band tight binding model. The Landauer formula gives the electrical conductance to be a function of the electron transmission probability, ${\cal T}(E)$, as a function of the energy $E$ of the incoming electron. A quantum dragon nanodevice is one which has a perfectly conducting channel, namely ${\cal T}(E)=1$ for all energies which are transmitted by the external leads even though there may be arbitrarily strong electron scattering. The rectangular single-layer systems are shown to be able to be quantum dragon devices, both for uniform leads and for dimerized leads. The quantum dragon condition requires appropriate lead-device connections and correlated randomness in the device.

cond-mat.mes-hall↗

arXiv2016

Site and bond percolation thresholds in $K_{n,n}$-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies

We estimate the critical thresholds of bond and site percolation on nonplanar, effectively two-dimensional graphs with chimera like topology. The building blocks of these graphs are complete and symmetric bipartite subgraphs of size $2n$, referred to as $K_{n,n}$ graphs. For the numerical simulations we use an efficient union-find based algorithm and employ a finite-size scaling analysis to obtain the critical properties for both bond and site percolation. We report the respective percolation thresholds for different sizes of the bipartite subgraph and verify that the associated universality class is that of standard two-dimensional percolation. For the canonical chimera graph used in the D-Wave Systems Inc.~quantum annealer ($n = 4$), we discuss device failure in terms of network vulnerability, i.e., we determine the critical fraction of qubits and couplers that can be absent due to random failures prior to losing large-scale connectivity throughout the device.

cond-mat.dis-nn↗

arXiv2015

How ubiquitous are dragon segments in quantum transmission?

Quantum dragon segments are nanodevices that have energy-independent total transmission of electrons. At the level of the single-band tight-binding model a nanodevice is viewed as a weighted undirected graph, with a vertex weight given by the on-site energy and the edge weight given by the tight-binding hopping parameter. A quantum dragon is a weighted undirected graph which when connected to idealized semi-infinite input and output leads, has the electron transmission probability ${\cal T}(E)$$=$$1$ for all electron energies $E$. The probability ${\cal T}(E)$ is obtained from the solution of the time-independent Schrödinger equation. A graph must have finely tuned tight-binding parameters in order to have ${\cal T}(E)$$=$$1$. This paper addresses classes of weighted graphs which can be tuned, by adjusting a small fraction of the total weights, to be a quantum dragon. We prove that with proper tuning any nanodevice can be a quantum dragon. Three prescriptions are presented to tune a weighted graph into a quantum dragon nanodevice. The implications of the prescriptions for physical nanodevices is discussed.

cond-mat.mes-hall↗

arXiv2015

Quantum Decoherence at Finite Temperatures

We study measures of decoherence and thermalization of a quantum system $S$ in the presence of a quantum environment (bath) $E$. The whole system is prepared in a canonical thermal state at a finite temperature. Applying perturbation theory with respect to the system-environment coupling strength, we find that under common Hamiltonian symmetries, up to first order in the coupling strength it is sufficient to consider the uncoupled system to predict decoherence and thermalization measures of $S$. This decoupling allows closed form expressions for perturbative expansions for the measures of decoherence and thermalization in terms of the free energies of $S$ and of $E$. Numerical results for both coupled and decoupled systems with up to 40 quantum spins validate these findings.

cond-mat.stat-mech↗

arXiv2015

Nonuniversal effects in mixing correlated-growth processes with randomness: Interplay between bulk morphology and surface roughening

To construct continuum stochastic growth equations for competitive nonequilibrium surface-growth processes of the type RD+X that mixes random deposition (RD) with a correlated-growth process X, we use a simplex decomposition of the height field. A distinction between growth processes X that do and do not create voids in the bulk leads to the definition of the {\it effective probability} $p_{\mathrm{eff}}$ of the process X that is a measurable property of the bulk morphology and depends on the {\it activation probability} $p$ of X in the competitive process RD+X. The bulk morphology is reflected in the surface roughening via {\it nonuniversal} prefactors in the universal scaling of the surface width that scales in $p_{\mathrm{eff}}$. The equation and the resulting scaling are derived for X in either a Kardar-Parisi-Zhang or Edwards-Wilkinson universality class in $(1+1)$ dimensions, and illustrated by an example of X being a ballistic deposition. We obtain full data collapse on its corresponding universal scaling function for all $p \in (0;1]$. We outline the generalizations to $(1+n)$ dimensions and to many-component competitive growth processes.

cond-mat.stat-mech↗

arXiv2010

A New Charging Method for Li-ion Batteries: Dependence of the charging time on the Direction of an Additional Oscillating Field

We have recently proposed a new method for charging Li-ion batteries based on large-scale molecular dynamics studies (I. Abou Hamad et al, Phys. Chem. Chem. Phys., 12, 2740 (2010)). Applying an additional oscillating electric field in the direction perpendicular to the graphite sheets of the anode showed an exponential decrease in charging time with increasing amplitude of the applied oscillating field. Here we present new results exploring the effect on the charging time of changing the orientation of the oscillating field. Results for oscillating fields in three orthogonal directions are compared.

physics.chem-ph↗

arXiv2010

Quantum Transport through Hierarchical Structures

The transport of quantum electrons through hierarchical lattices is of interest because such lattices have some properties of both regular lattices and random systems. We calculate the electron transmission as a function of energy in the tight binding approximation for two related Hanoi networks. HN3 is a Hanoi network with every site having three bonds. HN5 has additional bonds added to HN3 to make the average number of bonds per site equal to five. We present a renormalization group approach to solve the matrix equation involved in this quantum transport calculation. We observe band gaps in HN3, while no such band gaps are observed in linear networks or in HN5.

cond-mat.dis-nn↗

arXiv2010

Mapping the dynamics of complex multi-dimensional systems onto a discrete set of states conserving mean first passage times: a Projective Dynamics approach

We consider any dynamical system that starts from a given ensemble of configurations and evolves in time until the system reaches a certain fixed stopping criterion, with the mean first-passage time the quantity of interest. We present a general method, Projective Dynamics, which maps the multi-dimensional dynamics of the system onto an arbitrary discrete set of states ${ζ_k}$, subject only to the constraint that the dynamics is restricted to transitions not further than the neighboring states $ζ_{k\pm 1}$. We prove that with this imposed condition there exists a master equation with nearest-neighbor coupling with the same mean first-passage time as the original dynamical system. We show applications of the method for Brownian motion of particles in one and two dimensional potential energy landscapes and the folding process of small bio-polymers. We compare results for the mean first passage time and the mean folding time obtained with the Projective Dynamics method with those obtained by a direct measurement, and where possible with a semi-analytical solution.

cond-mat.stat-mech↗

arXiv2010

A new battery-charging method suggested by molecular dynamics simulations

Based on large-scale molecular dynamics simulations, we propose a new charging method that should be capable of charging a Lithium-ion battery in a fraction of the time needed when using traditional methods. This charging method uses an additional applied oscillatory electric field. Our simulation results show that this charging method offers a great reduction in the average intercalation time for Li+ ions, which dominates the charging time. The oscillating field not only increases the diffusion rate of Li+ ions in the electrolyte but, more importantly, also enhances intercalation by lowering the corresponding overall energy barrier.

physics.chem-ph↗

arXiv2009

Applications of Computer Simulations and Statistical Mechanics in Surface Electrochemistry

We present a brief survey of methods that utilize computer simulations and quantum and statistical mechanics in the analysis of electrochemical systems. The methods, Molecular Dynamics and Monte Carlo simulations and quantum-mechanical density-functional theory, are illustrated with examples from simulations of lithium-battery charging and electrochemical adsorption of bromine on single-crystal silver electrodes.

physics.chem-ph↗

arXiv2009

Comment on "Dynamic properties in a family of competitive growing models"

The article [Phys. Rev. E {\bf 73}, 031111 (2006)] by Horowitz and Albano reports on simulations of competitive surface-growth models RD+X that combine random deposition (RD) with another deposition X that occurs with probability $p$. The claim is made that at saturation the surface width $w(p)$ obeys a power-law scaling $w(p) \propto 1/p^δ$, where $δ$ is only either $δ=1/2$ or $δ=1$, which is illustrated by the models where X is ballistic deposition and where X is RD with surface relaxation. Another claim is that in the limit $p \to 0^+$, for any lattice size $L$, the time evolution of $w(t)$ generally obeys the scaling $w(p,t) \propto (L^α/p^δ) F(p^{2δ}t/L^z)$, where $F$ is Family-Vicsek universal scaling function. We show that these claims are incorrect.

cond-mat.stat-mech↗

arXiv2008

Efficiency of Rejection-Free Methods for Dynamic Monte Carlo Studies of Off-lattice Interacting Particles

We calculate the efficiency of a rejection-free dynamic Monte Carlo method for $d$-dimensional off-lattice homogeneous particles interacting through a repulsive power-law potential $r^{-p}$. Theoretically we find the algorithmic efficiency in the limit of low temperatures and/or high densities is asymptotically proportional to $ρ^{\tfrac{p+2}{2}}T^{-\tfrac{d}{2}}$ with the particle density $ρ$ and the temperature $T$. Dynamic Monte Carlo simulations are performed in 1-, 2- and 3-dimensional systems with different powers $p$, and the results agree with the theoretical predictions.

cond-mat.stat-mech↗