arXiv subjects

Eric J. Heller

Publications and source records attributed to Eric J. Heller.

At least 19 recordsLinked to original sources

arXiv2026

Quantum birthmarks: Ergodicity breaking beyond scarring

A hallmark of classical ergodicity is the complete loss of memory of the initial conditions due to eventual uniform covering of {\it a priori} available phase space. In quantum counterparts of such systems, however, this classical ergodic ideal is fundamentally limited: Here, we introduce the concept of a \emph{quantum birthmark}, a permanent signature left by the initial state and its early-time evolution in a general quantum system, which gives rise to non-ergodic behavior persisting even in the infinite-time limit. We present a birthmark framework outlining a ubiquitous memory effect for an arbitrary, non-stationary state composed of two factors conspiring together: the universal and the revival-enhancement. The former sets the minimal amplification carried by the time evolution of a quantum state based on global symmetries, whereas the latter incorporates the further enhancement stemming from the early dynamics, particularly prominent in the presence of recurrences that occur before the Heisenberg time. As a concrete example, we identify quantum birthmarks in the venerable stadium billiard, where they can be significantly enhanced by quantum scars. Finally, we discuss the broader implications of quantum birthmarks, including their role as a natural extension of all types of scarring theories to generic non-stationary quantum systems and prospects for experimental observation. Generally, our work opens an unexplored avenue for understanding the elusive quantum nature of ergodicity.

quant-ph↗

arXiv2026

Path-Integral Approach to Quantum Acoustics

A path-integral approach to quantum acoustics is developed here. In contrast to the commonly utilized particle perspective, this emerging field brings forth a long neglected but essential wave paradigm for lattice vibrations. Within the coherent state picture, we formulate a non-Markovian, stochastic master equation that captures the exact dynamics of any system with coupling linear in the bath coordinates and nonlinear in the system coordinates. We further demonstrate the capability of the presented master equation by applying the corresponding procedure to the eminent Fröhlich model. In general, we establish a solid foundation for quantum acoustics as a kindred framework to quantum optics, while paving the way for deeper first-principle explorations of non-perturbative system dynamics driven by lattice vibrations.

quant-ph↗

arXiv2026

Shaping chaos in bilayer graphene cavities

Bilayer graphene cavities where electrons are confined within finite graphene flakes provide an alluring platform not only for the future nanoelectronic devices owing to the tunable energy gap but also for investigating the quantum nature of chaos due to the trigonal warping of their Fermi surface. Here we demonstrate that rotating the cavity boundary relative to the underlying lattice structure drives a quantum transition from nearly integrable dynamics to chaotic regime, observed as a concomitant crossover of eigenvalue statistics and eigenstate profiles. Complementing the full quantum treatment, we examine the classical backbone of this onset of chaos by employing semiclassical ray dynamics. Our results position bilayer graphene cavities as a promising venue for investigating and engineering quantum-chaotic behavior in graphene-based devices.

cond-mat.mes-hall↗

arXiv2026

Elastic, Quasielastic, and Superelastic Electron Scattering from Thermal Lattice Distortions in Perfect Crystals

In standard treatments of electron transport, momentum relaxation in a perfect, defect-free crystal is linked with phonon creation or annihilation. In this work, we reconsider this problem for a finite, isolated crystal, retaining the lattice center-of-mass (recoil) degree of freedom and enforcing conservation of total mechanical momentum together with discrete crystal pseudomomentum. Starting from the density-density form of the electron-lattice interaction, we show that an electron in the interior of a perfect crystal admits elastic momentum-transfer channels in which total momentum is conserved by recoil of the lattice background without phonon excitation. These elastic channels can provide the leading contribution to momentum relaxation. We further identify mixed quasi-elastic and superelastic processes in which phonon occupations change but do not account entirely for the electron's momentum transfer. The elastic channels arise within the standard microscopic Hamiltonian and do not require additional disorder or defects. The resulting framework provides a complementary microscopic perspective on momentum relaxation in clean crystals and is consistent with experimental phenomena such as weak localization, quantum oscillations, ultrasonic attenuation, and the observed separation of momentum and energy relaxation times.

cond-mat.other↗

arXiv2026

Mobility Crossover in Two-Dimensional Berry Crystals

A Berry crystal is a random superposition of N plane waves of equal amplitude and fixed wavevector magnitude, propagating in different directions. Using numerical simulations of wavepacket dynamics, spectral analysis based on autocorrelation functions, and scaling of Inverse Participation Ratio, the nature of eigenstates across the energy spectrum of a two-dimensional Berry crystal is characterized. It exhibits Anderson localization and critical (extended but non-ergodic) states, reminiscent of quasicrystals, which sit in the middle ground between periodic and disordered systems and can host critical states. However, in contrast to quasicrystals that display sharp mobility edges separating extended and localized phases, the Berry crystal exhibits an extended regimes of critical states. We name this a "mobility crossover". At weak potential strength, low-energy states are extended while higher-energy states near the backscattering momentum are critical. As the potential strength increases to become comparable with the recoil energy, these critical states evolve into localized states, yielding a transition from extended non-ergodic to localized behavior near the backscattering momentum. An estimate for the boundaries of ergodic extended regimes is given by the mapping onto an effective Anderson model on a Bethe Lattice. The results shed light on the relation between backscattering and Anderson localization in continuous two-dimensional aperiodic systems.

cond-mat.dis-nn↗

arXiv2026

Universal Quantum Birthmark: Ghost of the quantum past

Quantum dynamics retains a permanent and universal memory of its initial conditions, even in systems whose spectra display fully chaotic, random-matrix behavior. This effect, known as the quantum birthmark, appears as an enhancement of the long-time return probability of any non-stationary state compared to the overlap with a typical ergodic state. In this work, we develop the full theoretical foundation for this universal contribution that depends only on the global symmetry class and accessible Hilbert-space dimension, not on the microscopic dynamics. Our findings reveal that quantum evolution preserves an unavoidable, symmetry-controlled imprint of its origin, a quantum effect calling into question classical expectations of ergodicity and the resulting thermalization scenarios.

quant-ph↗

arXiv2026

Musical Molecules: Sonifying the IR Spectra and Modeling Intramolecular Vibrational Energy Redistribution of Small Molecules

This work explores how small molecules sound. Infrared (IR) spectra of HCl, H2O, NH3, and acetone are mapped into the audible range using a simple anharmonic oscillator model and NIST vibrational data. Comparing harmonic and anharmonic sonifications reveals systematic pitch flattening, beating, and the emergence of combination bands, which are analyzed with spectrograms and autocorrelation functions. A time-dependent model of intramolecular vibrational energy redistribution (IVR) in acetone, implemented by "plucking" a single mode, produces evolving sound textures that mirror energy flow through the molecule. These results suggest that sonified IR spectra can provide an intuitive, pedagogical window into anharmonicity, mode coupling, and IVR.

physics.chem-ph↗

arXiv2025

Adiabaticity Crossover: From Anderson Localization to Planckian Diffusion

We investigate electron transport in one dimension from the quantum-acoustic perspective, where the coherent-state representation of lattice vibrations results in a time-dependent deformation potential whose rate is set by the sound speed, fluctuation spectrum is set by the temperature, and overall amplitude is set by the electron-lattice coupling strength. We introduce an acceleration-based adiabatic criterion, consistent with the adiabatic theorem and Landau-Zener theory, that separates adiabatic and diabatic dynamics across the $(T,v)$ plane. The discrete classification agrees with a continuous mean-squared acceleration scale and correlates with a coherence measure given by the ratio of coherence length to the initial packet width $L_ϕ(t)/σ_0$. We identify a broad Planckian domain in which the dimensionless diffusivity $α\!=\!Dm/\hbar$ is of order unity and only weakly depends on the parameters. This domain is more prevalent in diabatic regions and in areas of reduced phase coherence, indicating a dephasing driven crossover from Anderson localization to Planckian diffusion. Using the Einstein relation together with nearly constant $α$, we directly obtain a low temperature tendency $1/τ_{\rm tr}\propto T$, offering a insight to $T$-linear resistivity in strange metals. These results provide a unified picture that links adiabaticity, dephasing, and Planckian diffusion in dynamically disordered quantum-acoustics.

quant-ph↗

arXiv2025

Influence of string register locations on vibratos among violoncellists

This study analyzes how vibrato changes with finger position along the cello string. Examining 94 excerpts, we found moving the finger toward the bridge strongly increases acoustic vibrato depth ($ρ=0.6902$, $p=1.408\cdot 10^{-14}$). However, the performer's physical finger amplitude simultaneously decreases ($ρ=-0.6391$, $p=4.172\cdot 10^{-12}$). This shows players reduce finger motion in higher positions, but not enough to counteract the greater pitch deviation there, revealing both the presence and limits of compensatory vibrato behavior.

cs.SD↗

arXiv2025

Quantum Acoustics Demystifies the Strange Metals

Phonons have long been thought to be incapable of explaining key phenomena in strange metals, including linear-in-\textit{T} Planckian resistivity from high to very low temperatures. We argue that these conclusions were based on static, perturbative approaches that overlooked essential time-dependent and nonperturbative electron-lattice physics. In fact ``phonons'' are not the best target for discussion, just like ``photons'' are not the best way to think about Maxwell's equations. Quantum optics connects photons and electromagnetism, as developed 60 years ago by Glauber and others. We have been developing the parallel world of quantum acoustics. Far from being only of academic interest, the new tools are rapidly exposing the secrets of the strange metals, revealing strong vibronic (vibration-electronic) interactions playing a crucial role forming polarons and charge density waves, linear-in-$T$ resistivity at the Planckian rate over thousands of degrees, resolution of the Drude peak infrared anomaly, and the absence of a $T^4$ low-temperature resistivity rise in 2D systems, and of a Mott-Ioffe-Regel resistivity saturation. We derive Planckian transport, polarons, CDWs, and pseudogaps from the Fröhlich model. The ``new physics'' has been hiding in this model all along, in the right parameter regime, if it is treated nonperturbatively. In the course of this work we have uncovered the generalization of Anderson localization to dynamic media: a universal Planckian diffusion emerges, a ``ghost'' of Anderson localization. Planckian diffusion is clearly defined and is more fundamental than the popular but elusive, model dependent concept of ``Planckian speed limit''.

cond-mat.str-el↗

arXiv2025

Antiscarring from eigenstate stacking in a chaotic spinor condensate

We reveal a feature of quantum scarring in systems with many particles: Quantum scars, living densely near an unstable periodic orbit, must be compensated by corresponding antiscarred states suppressed there to establish the uniformity of the whole. The uniformity of the underlying phase space is linked to early-time dynamics -- a regime beyond the predictions of random matrix theory and encapsulated in the eigenstate stacking theorem. By extending the domain of the stacking theorem, we apply our theory to a chaotic spinor Bose-Einstein condensate, whose quantum scar dynamics have recently been observed in the laboratory. Our work uncovers how scarring of some eigenstates affects the rest of the chaotic and thermal spectrum in quantum systems with many particles.

quant-ph↗

arXiv2025

Polaron catastrophe within quantum acoustics

The quantum acoustic framework has recently emerged as a non-perturbative, coherent approach to electron-lattice interactions, uncovering rich physics often obscured by perturbative methods with incoherent scattering events. Here, we model the strongly coupled dynamics of electrons and acoustic lattice vibrations within this framework, representing lattice vibrations as coherent states and electrons as quantum wavepackets, in a manner distinctively different from tight-binding or discrete hopping-based approaches. We derive and numerically implement electron backaction on the lattice, providing both visual and quantitative insights into electron wavepacket evolution and the formation of acoustic polarons. We investigate polaron binding energies across varying material parameters and compute key observables, including mean square displacement, kinetic energy, potential energy, and vibrational energy. over time. Our findings reveal the conditions that favor polaron formation, which is enhanced by low temperatures, high deformation potential constants, slow sound velocities, and high effective masses. Additionally, we explore the impact of external electric and magnetic fields, showing that while polaron formation remains robust under moderate fields, it is weakly suppressed at higher field strengths. These results deepen our understanding of polaron dynamics and pave the way for future studies into non-trivial transport behavior in quantum materials.

cond-mat.mes-hall↗

arXiv2024

Planckian Diffusion: The Ghost of Anderson Localization

We find that Anderson localization ceases to exist when a random medium begins to move, but another type of fundamental quantum effect, Planckian diffusion $D = α\hbar/m$, rises to replace it, with $α$ of order of unity. Planckian diffusion supercedes the Planckian speed limit $τ= α\hbar/k_B T,$ as it not only implies this relation in thermal systems but also applies more generally without requiring thermal equilibrium. Here we model a dynamic disordered system with thousands of itinerant impurities, having random initial positions and velocities. By incrementally increasing their speed from zero, we observe a transition from Anderson localization to Planckian diffusion, with $α$ falling within the range of $0.5$ to $2$. Furthermore, we relate the breakdown of Anderson localization to three additional, distinctly different confirming cases that also exhibit Planckian diffusion $D\sim \hbar/m$, including one experiment on solid hydrogen. Our finding suggests that Planckian diffusion in dynamic disordered systems is as universal as Anderson localization in static disordered systems, which may shed light on quantum transport studies.

quant-ph↗

arXiv2024

Direct Visualization of Relativistic Quantum Scars

Quantum scars refer to eigenstates with enhanced probability density along unstable classical periodic orbits (POs). First predicted 40 years ago, scars are special eigenstates that counterintuitively defy ergodicity in quantum systems whose classical counterpart is chaotic. Despite the importance and long history of scars, their direct visualization in quantum systems remains an open field. Here we demonstrate that, by using an in-situ graphene quantum dot (GQD) creation and wavefunction mapping technique, quantum scars are imaged for Dirac electrons with nanometer spatial resolution and meV energy resolution with a scanning tunneling microscope. Specifically, we find enhanced probability densities in the form of lemniscate-shaped and streak-like patterns within our stadium-shaped GQDs. Both features show equal energy interval recurrence, consistent with predictions for relativistic quantum scars. By combining classical and quantum simulations, we demonstrate that the observed patterns correspond to two unstable POs that exist in our stadium-shaped GQD, thus proving they are both quantum scars. In addition to providing the first unequivocal visual evidence of quantum scarring, our work offers insight into the quantum-classical correspondence in relativistic chaotic quantum systems and paves the way to experimental investigation of other recently proposed scarring species such as perturbation-induced scars, chiral scars, and antiscarring.

cond-mat.mes-hall↗

arXiv2024

Quantum acoustics unravels Planckian resistivity

Strange metals exhibit universal linear-in-temperature resistivity described by a Planckian scattering rate, the origin of which remains elusive. By employing a novel approach inspired by quantum optics, we arrive at the coherent state representation of lattice vibrations: quantum acoustics. Utilizing this nonperturbative framework, we demonstrate that lattice vibrations could serve as active drivers in the Planckian resistivity phenomenon, challenging prevailing theories. By treating charge carriers as quantum wave packets negotiating the dynamic acoustic field, we find that a competition ensues between localization and delocalization giving rise to the previously conjectured universal quantum bound of diffusion, $\hbar/m^{*}$, independent of temperature or any other material parameters. This leads to the enigmatic $T$-linear resistivity over hundreds of degrees, except at very low temperatures. Quantum diffusion also explains why strange metals have much higher electrical resistivity than typical metals. Our work elucidates the critical role of phonons in Planckian resistivity from a new perspective and reconsiders their significance in the transport properties of strange metals.

cond-mat.str-el↗

arXiv2024

Rise and Fall of Anderson Localization by Lattice Vibrations: A Time-Dependent Machine Learning Approach

The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fröhlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum acoustics, emphasizing the wave nature of lattice vibrations, has enabled the exploration of previously uncharted territories of electron-lattice interaction not accessible with conventional tools such as perturbation theory. In this context, our agenda here is two-fold. First, we showcase the application of machine learning methods to categorize various interaction regimes within the subtle interplay of electrons and the dynamical lattice landscape. Second, we shed light on a nebulous region of electron dynamics identified by the machine learning approach and then attribute it to transient localization, where strong lattice vibrations result in a momentary Anderson prison for electronic wavepackets, which are later released by the evolution of the lattice. Overall, our research illuminates the spectrum of dynamics within the Fröhlich model, such as transient localization, which has been suggested as a pivotal factor contributing to the mysteries surrounding strange metals. Furthermore, this paves the way for utilizing time-dependent perspectives in machine learning techniques for designing materials with tailored electron-lattice properties.

cond-mat.str-el↗

arXiv2024

Scattering model of scintillation arcs in pulsar secondary spectra

The dynamic spectra of pulsars frequently exhibit diverse interference patterns, often associated with parabolic arcs in the Fourier-transformed (secondary) spectra. Our approach differs from previous ones in two ways: first, we extend beyond the traditional Fresnel-Kirchhoff method by using the Green's function of the Helmholtz equation, i.e.\ we consider spherical waves originating from three dimensional space, not from a two dimensional screen. Secondly, the discrete structures observed in the secondary spectrum result from discrete scatterer configurations, namely plasma concentrations in the interstellar medium, and not from the selection of points by the stationary phase approximation. Through advanced numerical techniques, we model both the dynamic and secondary spectra, providing a comprehensive framework that describes all components of the latter spectra in terms of physical quantities. Additionally, we provide a thorough analytical explanation of the secondary spectrum.

astro-ph.HE↗

arXiv2022

Coherent charge carrier dynamics in the presence of thermal lattice vibrations

We develop the coherent state representation of lattice vibrations to describe their interactions with charge carriers. In direct analogy to quantum optics, the coherent state representation leads from quantized lattice vibrations (phonons) naturally to a quasiclassical field limit, i.e., the deformation potential. To an electron, the deformation field is a sea of hills and valleys, as ``real'' as any external field, morphing and propagating at the sound speed, and growing in magnitude with temperature. In this disordered potential landscape, the charge carrier dynamics is treated nonperturbatively, preserving their coherence beyond single collision events. We show the coherent state picture agrees exactly with the conventional Fock state picture in perturbation theory. Furthermore, it goes beyond by revealing aspects that the conventional theory could not explain: transient localization even at high temperatures by charge carrier coherence effects, and band tails in the density of states due to the self-generated disorder (deformation) potential in a pure crystal. The coherent state paradigm of lattice vibrations supplies tools for probing important questions in condensed matter physics as in quantum optics.

cond-mat.mes-hall↗