arXiv subjects

David K. Campbell

Publications and source records attributed to David K. Campbell.

At least 19 recordsLinked to original sources

arXiv2025

Gradient of the Adiabatic Gauge Potential in Classical Systems

The adiabatic gauge potential (AGP) is the generator of unitary transformations which preserve the eigenbasis of a quantum Hamiltonian under parametric variation. While its usefulness in quantum mechanics has been thoroughly demonstrated in recent years, less attention has been given to its behavior in classical systems, where the AGP is a phase space function and its gradient defines special canonical transformations. In this paper we propose an efficient method to compute the gradient of the AGP as a classical function. We demonstrate that the obtained canonical transformation reproduces expected results for simple orbits and integrable systems for which the adiabatic limit is well-defined. In chaotic systems the gradient diverges in a way that is related to Lyapunov times.

nlin.CD↗

arXiv2024

Seeking the Casimir Energy

Since its first description in 1948, the Casimir effect has been studied extensively. Standard arguments for its existence hinge on the elimination of certain modes of the electromagnetic field because of the boundary conditions in the Casimir cavity. As such, it has been suggested that the ground state energy of the vacuum within the cavity may be reduced compared to the value outside. Could this have an effect on physical phenomena within the cavity? We study this Casimir energy and probe whether the critical temperature $T_c$ of a superconductor is altered when it is placed in the cavity. We do not detect any change in $T_c$ larger than 12 microKelvin, but theoretically expect a change on the order of 0.025 microKelvin, roughly 1000 times lower than our achieved sensitivity.

quant-ph↗

arXiv2024

Zeptonewton and Attotesla per Centimeter Metrology With Coupled Oscillators

We present the coupled oscillator: a new mechanism for signal amplification with widespread application in metrology. We introduce the mechanical theory of this framework, and support it by way of simulations. We present a particular implementation of coupled oscillators: a microelectromechanical system (MEMS) that uses one large (~100mm) N52 magnet coupled magnetically to a small (~0.25mm), oscillating N52 magnet, providing a force resolution of 200zN measured over 1s in a noiseless environment. We show that the same system is able to resolve magnetic gradients of 130aT/cm at a single point (within 500um). This technology therefore has the potential to revolutionize force and magnetic gradient sensing, including high-impact areas such cardiac and brain imaging.

physics.app-ph↗

arXiv2023

Application of Generalized Periodic Anderson Hamiltonians to the Superconducting Nickelates

We study the extent to which a three-dimensional dispersing Periodic Anderson Model (PAM) can explain the emergence of novel superconductivity in the Infinite-Layer Nickelate compounds. By going beyond frequently used 2D models, the 3D dispersing PAM allows us to incorporate effects of finite out-of-plane hopping and orbital hybridization in describing these systems. Using an unbiased functional Renormalization Group (fRG) approach, we show that $d_{x^2-y^2}$ superconductivity arises in a series of 3D {\it {ab-initio}} models of the Nickelates ({\it {e.g.}}$\mathrm{RNiO_2}$), where R is a rare earth element. We the study the impact of going beyond the Ni-d orbital by including the R-$d_{z^2}$ and the interstitial-$s$ as hybridizing conducting bands. We explore the dependence of the models on key parameters, including the local Hubbard coupling, doping and temperature. We find the hybridization with the interstitial-$s$ band driving a 3D $d_{z^2-r^2}$-type superconductivity while out of plane hopping primarily enhances an $s$-wave superconducting order.

cond-mat.str-el↗

arXiv2022

Phonon Induced Instabilities in Correlated Electron Hamiltonians

Studies of Hamiltonians modeling the coupling between electrons as well as to local phonon excitations have been fundamental in capturing the novel ordering seen in many quasi-one dimensional condensed matter systems. Extending studies of such Hamiltonians to quasi-two dimensional systems is of great current interest, as electron-phonon couplings are predicted to play a major role in the stabilization or enhancement of novel phases in 2D material systems. In this work, we study model systems that describe the interplay between the Hubbard coupling and the phonon modes in the Holstein (H) and Su-Schrieffer-Heeger (SSH) Hamiltonians using the functional renormalization group (fRG). For both types of electron phonon couplings, we find the predicted charge density wave phases in competition with anti-ferromagnetic ($AF$) ordering. As the system is doped, the transition shifts, with both orders showing incommensurate peaks. We compare the evolution of the quasiparticle weight for the Holstein model with that of the SSH model as the systems transition from antiferromagnetic to charge-ordered ground states. Finally, we calculate the self-energy of the phonon and capture the impact of charge ordering on the phonon modes.

cond-mat.str-el↗

arXiv2022

Counter-diabatic driving in the classical $β$-Fermi-Pasta-Ulam-Tsingou chain

Shortcuts to adiabaticity (STAs) have been used to make rapid changes to a system while eliminating or minimizing excitations in the system's state. In quantum systems, these shortcuts allow us to minimize inefficiencies and heating in experiments and quantum computing protocols, but the theory of STAs can also be generalized to classical systems. We focus on one such STA, approximate counter-diabatic (ACD) driving, and numerically compare its performance in two classical systems: a quartic anharmonic oscillator and the $β$ Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. In particular, we modify an existing variational technique to optimize the approximate driving and then develop classical figures of merit to quantify the performance of the driving. We find that relatively simple forms for the ACD driving can dramatically suppress excitations regardless of system size. ACD driving in classical nonlinear oscillators could have many applications, from minimizing heating in bosonic gases to finding optimal local dressing protocols in interacting field theories.

quant-ph↗

arXiv2021

Analysis of a Casimir-driven Parametric Amplifier with Resilience to Casimir Pull-in for MEMS Single-Point Magnetic Gradiometry

The Casimir Force, a quantum mechanical effect, has been observed in several microelectromechanical systems (MEMS) platforms. Due to its extreme sensitivity to the separation of two objects, the Casimir Force has been proposed as an excellent avenue for quantum metrology. Practical application, however, is challenging due to attractive forces leading to stiction and failure of the device, called Casimir pull-in. In this work, we design and simulate a Casimir-driven metrology platform, where a time-delay based parametric amplification technique is developed to achieve a steady state and avoid pull-in. We apply the design to the detection of weak, low frequency, gradient magnetic fields, similar to those emanating from ionic currents in the heart and brain. Simulation parameters are selected from recent experimental platforms developed for Casimir metrology and magnetic gradiometry, both on MEMS platforms. While MEMS offer many advantages to such an application, the detected signal must typically be at the resonant frequency of the device, with diminished sensitivity in the low frequency regime of biomagnetic fields. Using a Casimir-drive parametric amplifier, we report a 10,000 fold improvement in the best-case resolution of MEMS single-point gradiometers, with a maximum sensitivity of 6 Hz/(pT/cm) at 1 Hz. The development of the proposed design has the potential to revolutionize metrology, and specifically may enable unshielded monitoring of biomagnetic fields in ambient conditions.

quant-ph↗

arXiv2020

Frequency Dependent Functional Renormalization Group for Interacting Fermionic Systems

We derive an expansion of the functional renormalization (fRG) equations that treats the frequency and momentum dependencies of the vertices in a systematic manner. The scheme extends the channel-decomposed fRG equations to the frequency domain and reformulates them as a series of linear integral equations in the particle-particle, particle-hole and particle-hole exchange channels. We show that the linearity of the equations offers numerous computational advantages and leads to converged, stable solutions for a variety of Hamiltonians. As the expansion is in the coupling between channels, the truncations that are necessary to making the scheme computationally viable still lead to equations that treat contributions from all channels equally. As a first benchmark we apply the two-loop fRG equations to the single impurity Anderson model. We consider the sources of error within the fRG, the computational cost associated with each, and how the choice of regulator affects the flow of the fRG. We then use the optimal truncation scheme to study the Extended Hubbard Hamiltonian in one and two dimensions. We find that in many cases of interest the fRG flow converges to a stable vertex and self-energy from which we can extract the various correlation functions and susceptibilities of interest.

cond-mat.str-el↗

arXiv2020

Forward and Inverse Design of Kirigami via Supervised Autoencoder

Machine learning (ML) methods have recently been used as forward solvers to predict the mechanical properties of composite materials. Here, we use a supervised-autoencoder (sAE) to perform inverse design of graphene kirigami, where predicting the ultimate stress or strain under tensile loading is known to be difficult due to nonlinear effects arising from the out-of-plane buckling. Unlike the standard autoencoder, our sAE is able not only to reconstruct cut configurations but also to predict mechanical properties of graphene kirigami and classify the kirigami witheither parallel or orthogonal cuts. By interpolating in the latent space of kirigami structures, the sAE is able to generate novel designs that mix parallel and orthogonal cuts, despite being trained independently on parallel or orthogonal cuts. Our method allows us to both identify novel designs and predict, with reasonable accuracy, their mechanical properties, which is crucial for expanding the search space for materials design.

cond-mat.mtrl-sci↗

arXiv2020

Adiabatic eigenstate deformations as a sensitive probe for quantum chaos

In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypothesis. Standard measures of chaos in quantum many-body systems are level statistics and the spectral form factor. In this work, we show that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from non-ergodic to ergodic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability-breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size.

quant-ph↗

arXiv2020

Searching for the Casimir Energy

In this article, we present a nano-electromechanical system (NEMS) designed to detect changes in the Casimir Energy. The Casimir effect is a result of the appearance of quantum fluctuations in the electromagnetic vacuum. Previous experiments have used nano- or micro- scale parallel plate capacitors to detect the Casimir force by measuring the small attractive force these fluctuations exert between the two surfaces. In this new set of experiments, we aim to directly detect shifts in the Casimir $\textit{energy}$ in the vacuum due to the presence of metallic parallel plates, one of which is a superconductor. A change in the Casimir energy of this configuration is predicted to shift the superconducting transition temperature (T$_\textrm{c}$) because of an interaction between it and the superconducting condensation energy. The experiment we discuss consists of taking a superconducting film, carefully measuring its transition temperature, bringing a conducting plate close to the film, creating a Casimir cavity, and then measuring the transition temperature again. The expected shifts will be small, comparable to the normal shifts one sees in cycling superconducting films to cryogenic temperatures and so using a NEMS resonator and doing this in situ is the only practical way to obtain accurate, reproducible data. Using a thin Pb film and opposing Au surface, we observe no shift in T$_\textrm{c}$ greater than 12 $μ$K down to a minimum spacing of approximately 70 nm.

physics.app-ph↗

arXiv2020

Effect of mediated interactions on a Hubbard chain in mixed-dimensional fermionic cold atoms

Cold atom experiments can now realize mixtures where different components move in different spatial dimensions. We investigate a fermion mixture where one species is constrained to move along a one-dimensional lattice embedded in a two-dimensional lattice populated by another species of fermions, and where all bare interactions are contact interactions. By focusing on the one-dimensional fermions, we map this problem onto a model of fermions with non-local interactions on a chain. The effective interaction is mediated by the two-dimensional fermions and is both attractive and retarded, the form of which can be varied by changing the density of the two-dimensional fermions. By using the functional renormalization group in the weak-coupling and adiabatic limit, we show that the one-dimensional fermions can be controlled to be in various density-wave, or spin-singlet or triplet superconducting phases.

cond-mat.quant-gas↗

arXiv2019

Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

The electronic dispersions of the quasi-one-dimensional organic conductor TTF-TCNQ are studied by angle-resolved photoelectron spectroscopy (ARPES) with higher angular resolution and accordingly smaller step width than in previous studies. Our experimental results suggest that a refinement of the single-band 1D Hubbard model that includes finite-range interactions is needed to explain these photoemission data. To account for the effects of these finite-range interactions we employ a mobile quantum impurity scheme that describes the scattering of fractionalized particles at energies above the standard Tomonaga-Luttinger liquid limit. Our theoretical predictions agree quantitatively with the location in the $(k,ω)$ plane of the experimentally observed ARPES structures at these higher energies. The nonperturbative microscopic mechanisms that control the spectral properties are found to simplify in terms of the exotic scattering of the charge fractionalized particles. We find that the scattering occurs in the unitary limit of (minus) infinite scattering length, which limit occurs within neutron-neutron interactions in shells of neutron stars and in the scattering of ultracold atoms but not in perturbative electronic condensed-matter systems. Our results provide important physical information on the exotic processes involved in the finite-range electron interactions that control the high-energy spectral properties of TTF-TCNQ. Our results also apply to a wider class of 1D and quasi-1D materials and systems that are of theoretical and potential technological interest.

cond-mat.str-el↗

arXiv2019

Dynamical glass in weakly non-integrable Klein-Gordon chains

Integrable many-body systems are characterized by a complete set of preserved actions. Close to an integrable limit, a {\it nonintegrable} perturbation creates a coupling network in action space which can be short- or long-ranged. We analyze the dynamics of observables which turn into the conserved actions in the integrable limit. We compute distributions of their finite-time averages and obtain the ergodization time scale $T_E$ on which these distributions converge to $δ$-distributions. We relate $T_E \sim (σ_τ^+)^2/μ_τ^+$ to the statistics of fluctuation times of the observables, which acquire fat-tailed distributions with standard deviations $σ_τ^+$ dominating the means $μ_τ^+$. The Lyapunov time $T_Λ$ (the inverse of the largest Lyapunov exponent) is then compared to the above time scales. We use a simple Klein-Gordon chain to emulate long- and short-range coupling networks by tuning its energy density. For long-range coupling networks $T_Λ\approx σ_τ^+$, which indicates that the Lyapunov time sets the ergodization time, with chaos quickly diffusing through the coupling network. For short-range coupling networks we observe a {\it dynamical glass}, where $T_E$ grows dramatically by many orders of magnitude and greatly exceeds the Lyapunov time, which $T_Λ \lesssim μ_τ^+$. This is due to the formation of a highly fragmented inhomogeneous distributions of chaotic groups of actions, separated by growing volumes of non-chaotic regions. These structures persist up to the ergodization time $T_E$.

nlin.CD↗

arXiv2019

The $β$ Fermi-Pasta-Ulam-Tsingou Recurrence Problem

We perform a thorough investigation of the first FPUT recurrence in the $β$-FPUT chain for both positive and negative $β$. We show numerically that the rescaled FPUT recurrence time $T_{r}=t_{r}/(N+1)^{3}$ depends, for large $N$, only on the parameter $S\equiv Eβ(N+1)$. Our numerics also reveal that for small $\left|S\right|$, $T_{r}$ is linear in $S$ with positive slope for both positive and negative $β$. For large $\left|S\right|$, $T_{r}$ is proportional to $\left|S\right|^{-1/2}$ for both positive and negative $β$ but with different multiplicative constants. In the continuum limit, the $β$-FPUT chain approaches the modified Korteweg-de Vries (mKdV) equation, which we investigate numerically to better understand the FPUT recurrences on the lattice. In the continuum, the recurrence time closely follows the $|S|^{-1/2}$ scaling and can be interpreted in terms of solitons, as in the case of the KdV equation for the $α$ chain. The difference in the multiplicative factors between positive and negative $β$ arises from soliton-kink interactions which exist only in the negative $β$ case. We complement our numerical results with analytical considerations in the nearly linear regime (small $\left|S\right|$) and in the highly nonlinear regime (large $\left|S\right|$). For the former, we extend previous results using a shifted-frequency perturbation theory and find a closed form for $T_{r}$ which depends only on $S$. In the latter regime, we show that $T_{r}\propto\left| S\right|^{-1/2}$ is predicted by the soliton theory in the continuum limit. We end by discussing the striking differences in the amount of energy mixing as well as the existence of the FPUT recurrences between positive and negative $β$ and offer some remarks on the thermodynamic limit.

nlin.PS↗

arXiv2018

Floquet-engineered quantum state manipulation in a noisy qubit

Adiabatic evolution is a common strategy for manipulating quantum states and has been employed in diverse fields such as quantum simulation, computation and annealing. However, adiabatic evolution is inherently slow and therefore susceptible to decoherence. Existing methods for speeding up adiabatic evolution require complex many-body operators or are difficult to construct for multi-level systems. Using the tools of Floquet engineering, we design a scheme for high-fidelity quantum state manipulation, utilizing only the interactions available in the original Hamiltonian. We apply this approach to a qubit and experimentally demonstrate its performance with the electronic spin of a Nitrogen-vacancy center in diamond. Our Floquet-engineered protocol achieves state preparation fidelity of $0.994 \pm 0.004$, on the same level as the conventional fast-forward protocol, but is more robust to external noise acting on the qubit. Floquet engineering provides a powerful platform for high-fidelity quantum state manipulation in complex and noisy quantum systems.

quant-ph↗

arXiv2018

Behavior and Breakdown of Higher-Order Fermi-Pasta-Ulam-Tsingou Recurrences

We investigate numerically the existence and stability of higher-order recurrences (HoRs), including super-recurrences, super-super-recurrences, etc., in the alpha and beta Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial conditions in the fundamental normal mode. Our results represent a considerable extension of the pioneering work of Tuck and Menzel on super-recurrences. For fixed lattice sizes, we observe and study apparent singularities in the periods of these HoRs, speculated to be caused by nonlinear resonances. Interestingly, these singularities depend very sensitively on the initial energy and the respective nonlinear parameters. Furthermore, we compare the mechanisms by which the super-recurrences in the two model's breakdown as the initial energy and respective nonlinear parameters are increased. The breakdown of super-recurrences in the beta-FPUT lattice is associated with the destruction of the so-called metastable state and hence is associated with relaxation towards equilibrium. For the alpha-FPUT lattice, we find this is not the case and show that the super-recurrences break down while the lattice is still metastable. We close with comments on the generality of our results for different lattice sizes.

nlin.PS↗

arXiv2018

Accelerated search and design of stretchable graphene kirigami using machine learning

Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern. Our approach enables the rapid discovery of kirigami designs that yield extreme stretchability as verified by molecular dynamics (MD) simulations. We find that convolutional neural networks (CNN), commonly used for classification in vision tasks, can be applied for regression to achieve an accuracy close to the precision of the MD simulations. This approach can then be used to search for optimal designs that maximize elastic stretchability with only 1000 training samples in a large design space of $\sim 4\times10^6$ candidate designs. This example demonstrates the power and potential of ML in finding optimal kirigami designs at a fraction of iterations that would be required of a purely MD or experiment-based approach, where no prior knowledge of the governing physics is known or available.

physics.comp-ph↗