Finite Size Effects Research Articles

Condensate and superfluid fraction of homogeneous Bose gases in a self-consistent Popov approximation

We study the condensate and superfluid fraction of a homogeneous gas of weakly interacting bosons in three spatial dimensions by adopting a self-consistent Popov approximation, comparing this approach with other theoretical schemes. Differently from the superfluid fraction, we find that at finite temperature the condensate fraction is a non-monotonic function of the interaction strength, presenting a global maximum at a characteristic value of the gas parameter, which grows as the temperature increases. This non-monotonic behavior has not yet been observed, but could be tested with the available experimental setups of ultracold bosonic atoms confined in a box potential. We clearly identify the region of parameter space that is of experimental interest to look for this behavior and provide explicit expressions for the relevant observables. Finite size effects are also discussed within a semiclassical approximation.

Effects of finite counterion size and nonhomogeneous permittivity and viscosity of the solution on the electrokinetics of a concentrated salt-free colloid.

In the present work, a general model of the electrokinetics and dielectric response of a concentrated salt-free colloid is developed which includes consideration of the finite size of the counterions released by the particles to the solution, a nonhomogeneous permittivity of the solution, the existence of Born and dielectrophoretic forces acting on the counterions, and especially the fact that the solution viscosity and diffusion counterion coefficient are allowed to be functions of the local counterion concentration. These effects have recently been discussed by J. J. López-García etal. [Phys. Rev. Fluids 4, 103702 (2019)10.1103/PhysRevFluids.4.103702] in the case of dilute colloids in general electrolyte solutions. The objective of this work is to explore the new effects and their influence on the electrokinetic response of concentrated salt-free systems. Present results confirm previous findings regarding the important increases of the dc electrophoretic mobility and dc electrical conductivity, as well as huge increments of the dynamic electrophoretic mobilities at high frequencies when finite-ion-size effects were taken into account. In addition, consideration of the viscosity of the solution and of the counterion diffusion coefficient as functions of the local counterion concentration leads to a decrease of the magnitude of the previous electrokinetic results. The theory incorporates a more convenient hard-sphere hydrodynamic model to account for the nonhomogeneous viscosity of the solution than others proposed in previous works in the literature. A comparison is elaborated on between electrokinetic and dielectric responses with different levels of complexity of the theoretical model, starting from the case of pointlike counterions and following with the inclusion in sequence of additional aspects such as finite counterion size, nonhomogeneous electrical permittivity with associated Born and dielectrophoretic effects, and, finally, position-dependent viscosity and diffusion counterion coefficient, and clearly shows the influence of individual effects on the general electrokinetic response and especially the relevant role the nonhomogeneous viscosity on the dc and ac electrokientic behavior of salt-free colloids.

Gbps key rate passive-state-preparation continuous-variable quantum key distribution within an access-network area

The conventional Gaussian-modulated coherent-state quantum key distribution (QKD) protocol requires the sender to perform active modulations based on a true random number generator. Compared with it, the passive-state-preparation (PSP) continuous-variable quantum key distribution (CVQKD) equivalently performs modulations passively by exploring the intrinsic field fluctuations of a thermal source, which offers the prospect of chip integration QKD with low cost. In this paper, we propose and experimentally demonstrate a high-rate PSP-CVQKD scheme within an access-network area using high-bandwidth detectors in a continuous wave encoding and decoding way. By proposing effective methods for suppressing the noises during the PSP process and polarization multiplexing to decrease the photon leakage noises, we realize the high-intensity local oscillator transmission, thereby achieving coherent detection with high efficiency, low noise, and high bandwidth. The secure key rates over transmission distance of 5.005 km with and without consideration of the finite-size effect are 273.25 Mbps and 1.09 Gbps. The use of the PSP method boosts the asymptotic secret key rate of CVQKD to Gbps level for the first time, to our knowledge, within the range of the access network, which provides an effective and secure key distribution strategy for high-speed quantum cryptography access communication.

Random Field Ising Model Criticality in a Complex Binary Liquid System.

While Ising criticality in classical liquids has been firmly established both theoretically and experimentally, much less is known about criticality in liquids in which the growth of the correlation length is frustrated by finite-size effects. A theoretical approach for dealing with this issue is the random-field Ising model (RFIM). While experimental critical-exponent values have been reported for magnetic samples (here, we consider γ, ν and η), little experimental information is available for critical fluctuations in corresponding liquid systems. In this paper, we present a study on a binary liquid consisting of 3-methyl pyridine and heavy water in a very light-weight porous gel. We find that the experimental results are in agreement with the theoretical predictions from the RFIM.

Designing edge states from fractional polarization insulators

We theoretically investigated disconnected dispersive edge states in an anisotropic honeycomb lattice without chiral symmetry. When both mirror and chiral symmetries are present, this system is defined by a topological quantity known as fractional polarization (FP) term and exhibits a bulk band gap, classifying it as an FP insulator. While the FP insulator accommodates robust, flat topological edge states (TES), it also offers the potential to engineer these edge states by deliberately disrupting a critical symmetry that safeguards the underlying topology. These symmetry-breaking terms allow the edge states to become dispersive and generate differing configurations along the open boundaries. Furthermore, disconnected helical-like and chiral-like edge states analogous to TES seen in quantum spin and anomalous hall effect are achieved by the finite size effect, not possible from the symmetry-breaking terms alone. The demonstration of manipulating these edge states from a FP insulator can open up new avenues in constructing devices that utilize topological domain walls.

Fractional quantum Hall states with variational projected entangled-pair states: A study of the bosonic Harper-Hofstadter model

An important class of model Hamiltonians for investigation of topological phases of matter consists of mobile, interacting particles on a lattice subject to a semiclassical gauge field, as exemplified by the bosonic Harper-Hofstadter model. A unique method for investigations of two-dimensional quantum systems are the infinite projected-entangled pair states, as they avoid spurious finite-size effects that can alter the phase structure. However, due to no-go theorems in related cases, this was often conjectured to be impossible in the past. In this Letter, we show that upon variational optimization, the infinite projected-entangled pair states can be used to this end by identifying fractional Hall states in the bosonic Harper-Hofstadter model. The obtained states are characterized by showing exponential decay of bulk correlations, as dictated by a bulk gap, as well as chiral edge modes via the entanglement spectrum. Published by the American Physical Society 2024

Improved composable key rates for CV-QKD

Modern security proofs of quantum key distribution (QKD) must take finite-size effects and composable aspects into consideration. This is also the case for continuous-variable (CV) protocols, which are based on the transmission and detection of bosonic coherent states. In this paper, we refine and advance the previous theory in this area providing a more rigorous formulation for the composable key rate of a generic CV-QKD protocol. Thanks to these theoretical refinements, our general formulas allow us to prove more optimistic key rates with respect to previous literature. Published by the American Physical Society 2024

Unveiling chiral states in the XXZ chain: finite-size scaling probing symmetry-enriched c = 1 conformal field theories

We study the low-energy properties of the one-dimensional spin-1/2 XXZ chain with time-reversal symmetry-breaking pseudo-scalar chiral interaction and propose a phase diagram for the model. In the integrable case of the isotropic Heisenberg model with the chiral interaction, we employ the thermodynamic Bethe ansatz to find “chiralization”, the response of the ground state versus the strength of the pseudo-scalar chiral interaction of a chiral Heisenberg chain. Unlike the magnetization case, the chirality of the ground state remains zero until the transition point corresponding to critical coupling αc = 2J/π with J being the antiferromagnetic spin-exchange interaction. The central-charge c = 1 conformal field theories (CFTs) describe the two phases with zero and finite chirality. We show for this particular case and conjecture more generally for similar phase transitions that the difference between two emergent CFTs with identical central charges lies in the symmetry of their ground state (lightest weight) primary fields, i.e., the two phases are symmetry-enriched CFTs. At finite but small temperatures, the non-chiral Heisenberg phase acquires a finite chirality that scales with the temperature quadratically. We show that the finite-size effect around the transition point probes the transition.

Contrasting Views of the Electric Double Layer in Electrochemical CO2 Reduction: Continuum Models vs Molecular Dynamics.

In the field of electrochemical CO2 reduction, both continuum models and molecular dynamics (MD) models have been used to understand the electric double layer (EDL). MD often focuses on the region within a few nm of the electrode, while continuum models can span up to the device level (cm). Still, both methods model the EDL, and for a cohesive picture of the CO2 electrolysis system, the two methods should agree in the regions where they overlap length scales. To this end, we make a direct comparison between state-of-the-art continuum models and classical MD simulations under the conditions of CO2 reduction on a Ag electrode. For continuum modeling, this includes the Poisson-Nernst-Planck formulation with steric (finite ion size) effects, and in MD the electrode is modeled with the constant potential method. The comparison yields numerous differences between the two modeling methods. MD shows cations forming two adsorbed layers, including a fully hydrated outer layer and a partial hydration layer closer to the electrode surface. The strength of the inner adsorbed layer increases with cation size (Li+ < Na+ < K+ < Cs+) and with more negative applied potentials. Continuum models that include steric effects predict CO2 to be mostly excluded within 1 nm of the cathode due to tightly packed cations, yet we find little evidence to support these predictions from the MD results. In fact, MD shows that the concentration of CO2 increases within a few Å of the cathode surface due to interactions with the Ag electrode, a factor not included in continuum models. The EDL capacitance is computed from the MD results, showing values in the range of 7-9 μF cm-2, irrespective of the electrolyte concentration, cation identity, or applied potential. The direct comparison between the two modeling methods is meant to show the areas of agreement and disagreement between the two views of the EDL, so as to improve and better align these models.

Classical and quantum computing of shear viscosity for (2+1)D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for (2+1)-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density ηs is consistent with a well-known holographic result 14π at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=12. We also find the ratio of the spectral function and frequency ρxy(ω)ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond jmax=12 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including jmax truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

The dance of neurons: Exploring nonlinear dynamics in brain networks

The brain is a complex, nonlinear system, exhibiting ever-evolving patterns of activities, whether in the presence or absence of external stimuli or task demands. Nonlinearity can notably obscure the link between structural constraints enforced on the interaction and its dynamical consequences. Suitable nonlinear dynamical models and their analysis serve as essential tools not only for bridging structural and functional understanding of the brain but also for predictably altering the complex dynamical organization of the brain. Here, starting from a large-scale network of threshold Hodgkin–Huxley style neurons, we formulate the average nonlinear dynamics implicitly following from the Wilson–Cowan assumptions. We investigate the influence of biophysical and structural properties on the complexity of neural dynamics at the microscale level and its relationship with the macroscopic Wilson–Cowan model. Incorporating the elements in the model can help identify more realistic regimes of activity and connect the mathematical prediction of increasing nonlinearity to physical manipulations. Our simulations of the temporal profiles reveal dependency on the binary state of interacting subpopulations and the random property of structural network at the transition points, when different synaptic weights are considered. For substantial configurations of stimulus intensity, our model provides further estimates of the neural population’s dynamics, ranging from simple-periodic to aperiodic patterns and phase transition regimes. This reflects the potential contribution of the microscopic nonlinear scheme to the mean-field approximation in studying the collective behaviour of individual neurons with particularly concentrating on the occurrence of critical phenomena. We show that finite-size effects kick the system in a state of irregular modes to evolve differently from predictions of the original Wilson–Cowan reference. Additionally, we report that the complexity and temporal diversity of neural dynamics, especially in terms of limit cycle trajectory, and synchronization can be induced by either small heterogeneity in the degree of various types of local excitatory connectivity or considerable diversity in the external drive to the excitatory pool.

Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles.

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 105 structural models and 106 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable "shape envelope" among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

Emergent facilitation and glassy dynamics in supercooled liquids

In supercooled liquids, dynamical facilitation refers to a phenomenon where microscopic motion begets further motion nearby, resulting in spatially heterogeneous dynamics. This is central to the glassy relaxation dynamics of such liquids, which show super-Arrhenius growth of relaxation timescales with decreasing temperature. Despite the importance of dynamical facilitation, there is no theoretical understanding of how facilitation emerges and impacts relaxation dynamics. Here, we present a theory that explains the microscopic origins of dynamical facilitation. We show that dynamics proceeds by localized bond-exchange events, also known as excitations, resulting in the accumulation of elastic stresses with which new excitations can interact. At low temperatures, these elastic interactions dominate and facilitate the creation of new excitations near prior excitations. Using the theory of linear elasticity and Markov processes, we simulate a model, which reproduces multiple aspects of glassy dynamics observed in experiments and molecular simulations, including the stretched exponential decay of relaxation functions, the super-Arrhenius behavior of relaxation timescales as well as their two-dimensional finite-size effects. The model also predicts the subdiffusive behavior of the mean squared displacement (MSD) on short, intermediate timescales. Furthermore, we derive the phonon contributions to diffusion and relaxation, which when combined with the excitation contributions produce the two-step relaxation processes, and the ballistic-subdiffusive-diffusive crossover MSD behaviors commonly found in supercooled liquids.

Atomistic insights into argon clusters and nucleation dynamics

Accurate predictions of nucleation and atomic-level estimates of cluster properties in gas-phase chemical physics have proven challenging. These challenges arise from two primary sources: finite-size effects associated with nanoscopic particles and the emergence of non-standard thermodynamics, particularly at elevated temperatures. This study reexamines the formation of argon clusters using established methodologies such as atomistic simulations, configurational sampling, and statistical thermochemistry. To enhance the representation of condensed-phase argon, we employ an ab initio-based two-body potential, complemented by a three-body Axilrod–Teller potential. Additionally, we address the impact of anharmonicities on cluster stabilities using a recently developed extension to the standard statistical cluster model. The employed anharmonic model is rigorously benchmarked against molecular dynamics simulations. The subsequent analysis demonstrates a robust and consistent agreement between our model and experimental data. Our analysis covers nearly every experimental data point collected between 1971 and 2010, offering valuable insights into the predictive capabilities of the model. Moreover, in contrast to previous studies, our findings indicate that individual measurements are consistently in alignment with each other.

Linear Electro-Optic Effect in 2D Ferroelectric for Electrically Tunable Metalens.

The advent of 2D ferroelectrics, characterized by their spontaneous polarization states in layer-by-layer domains without the limitation of a finite size effect, brings enormous promise for applications in integrated optoelectronic devices. Comparing with semiconductor/insulator devices, ferroelectric devices show natural advantages such as non-volatility, low energy consumption and high response speed. Several 2D ferroelectric materials have been reported, however, the device implementation particularly for optoelectronic application remains largely hypothetical. Here, the linear electro-optic effect in 2D ferroelectrics is discovered and electrically tunable 2D ferroelectric metalens is demonstrated. The linear electric-field modulation of light is verified in 2D ferroelectric CuInP2S6. The in-plane phase retardation can be continuously tuned by a transverse DC electric field, yielding an effective electro-optic coefficient rc of 20.28 pm V-1. The CuInP2S6 crystal exhibits birefringence with the fast axis oriented along its (010) plane. The 2D ferroelectric Fresnel metalens shows efficacious focusing ability with an electrical modulation efficiency of the focusing exceeding 34%. The theoretical analysis uncovers the origin of the birefringence and unveil its ultralow light absorption across a wide wavelength range in this non-excitonic system. The van der Waals ferroelectrics enable room-temperature electrical modulation of light and offer the freedom of heterogeneous integration with silicon and another material system for highly compact and tunable photonics andmetaoptics.

Quantum Dichotomies and Coherent Thermodynamics beyond First-Order Asymptotics

We address the problem of exact and approximate transformation of quantum dichotomies in the asymptotic regime, i.e., the existence of a quantum channel E mapping ρ1⊗n into ρ2⊗Rnn with an error ϵn (measured by trace distance) and σ1⊗n into σ2⊗Rnn exactly, for a large number n. We derive second-order asymptotic expressions for the optimal transformation rate Rn in the small-, moderate-, and large-deviation error regimes, as well as the zero-error regime, for an arbitrary pair (ρ1,σ1) of initial states and a commuting pair (ρ2,σ2) of final states. We also prove that for σ1 and σ2 given by thermal Gibbs states, the derived optimal transformation rates in the first three regimes can be attained by thermal operations. This allows us, for the first time, to study the second-order asymptotics of thermodynamic state interconversion with fully general initial states that may have coherence between different energy eigenspaces. Thus, we discuss the optimal performance of thermodynamic protocols with coherent inputs and describe three novel resonance phenomena allowing one to significantly reduce transformation errors induced by finite-size effects. What is more, our result on quantum dichotomies can also be used to obtain, up to second-order asymptotic terms, optimal conversion rates between pure bipartite entangled states under local operations and classical communication. Published by the American Physical Society 2024

Numerical tests of the large charge expansion

We perform Monte-Carlo measurements of two and three-point functions of charged operators in the critical O(2) model in 3 dimensions. Our results are compatible with the predictions of the large charge superfluid effective field theory. To obtain reliable measurements for large values of the charge, we improved the Worm algorithm and devised a measurement scheme which mitigates the uncertainties due to lattice and finite size effects.

Enhancement and suppression of nonsequential double ionization by spatially inhomogeneous fields

Using the three-dimensional classical ensemble approach, we theoretically investigate the nonsequential double ionization of argon atoms in an intense laser field enhanced by bowtie-nanotip. We observe an anomalous decrease in the double ionization yield as the laser intensity increases, along with a significant gap in the low momentum of photoelectrons. According to our theoretical analysis, the finite range of the induced field by the nanostructure is the fundamental cause of the decline in double ionization yield. Driven by the enhanced inhomogeneous field, energetic electrons can escape from the finite range of nanotips without returning. This reduces the possibility of re-scattering on the nucleus and imprints the finite size effect into the double ionization yield and momentum distribution of photoelectrons in the form of yield decline and a gap in the photoelectron-momentum distribution.

Novel barostat implementation for molecular dynamics.

We propose a novel implementation of the extended-dynamics equations for isothermal-isobaric ensemble in molecular dynamics, as the Martyna-Tobias-Klein thermostat and barostat. This method is suitable for systems with constraints and the Verlet-family integrators. Instead of iterations or the Trotter-expansion-based methods, both velocities and box sizes (scaling of bond lengths) are predicted. The algorithm begins with force calculation, requiring neither quarter nor half time steps, and necessitating iterations only inside SHAKE. Several tests demonstrate that the quality is comparable to other implementations. It is found that the formula relating the extended barostat mass to the characteristic time of volume fluctuations is inaccurate for condensed systems, which has consequences for the parameter setup. Emphasis is also put on the verification of the precise isothermal-isobaric ensemble and finite-size effects.

Microwave analogy of Förster resonance energy transfer and effect of finite antenna length

The near-field interaction between quantum emitters, governed by Förster resonance energy transfer (FRET), plays a pivotal role in nanoscale energy transfer mechanisms. However, FRET measurements in the optical regime are challenging as they require nanoscale control of the position and orientation of the emitters. To overcome these challenges, microwave measurements were proposed for enhanced spatial resolution and precise orientation control. However, unlike in optical systems for which the dipole can be taken to be infinitesimal in size, the finite size of microwave antennas can affect energy transfer measurements, especially at short distances. This highlights the necessity to consider the finite antenna length to obtain accurate results. In this study, we advance the understanding of dipole–dipole energy transfer in the microwave regime by developing an analytical model that explicitly considers finite antennas. Unlike previous works, our model calculates the mutual impedance of finite-length thin-wire dipole antennas without assuming a uniform current distribution. We validate our analytical model through experiments investigating energy transfer between antennas placed adjacent to a perfect electric conductor mirror. This allows us to provide clear guidelines for designing microwave experiments, distinguishing conditions where finite-size effects can be neglected and where they must be taken into account. Our study not only contributes to the fundamental physics of energy transfer but also opens avenues for microwave antenna impedance-based measurements to complement optical FRET experiments and quantitatively explore dipole–dipole energy transfer in a wider range of conditions.