Decay Of Correlation Function Research Articles

Hyperuniformity in mass transport processes with center-of-mass conservation: some exact results

Abstract We characterize the steady-state static and dynamic properties in a broad class of mass transport processes on a periodic hypercubic lattice of volume Ld , where both the mass and center-of-mass (CoM) remain conserved and the detailed balance is violated in the bulk; we specifically consider the models in the d = 1 and 2 dimensions. Using a microscopic approach, we exactly determine the decay (or growth) exponents for various dynamic and static correlation functions. We show that despite constrained dynamics due to CoM conservation (CoMC), the density relaxation is indeed diffusive. However, the fluctuation properties are strikingly different from those in diffusive systems with a single (mass) conservation law as dynamic and static fluctuations are more suppressed in systems with CoMC, resulting in an extreme (‘class-I’) hyperuniformity in certain cases. In the thermodynamic limit, the steady-state variance ⟨ Q 2 ( T ) ⟩ c of time-integrated bond current Q ( T ) across a bond in the time interval T exhibits the following long-time behavior: ⟨ Q 2 ( T ) ⟩ c ≃ A 1 T + A 2 + A 3 T − d / 2 . The exponents governing the small-frequency behavior of the power spectra S J ( f ) ≃ A 1 + Const . f ψ J for bond current are exactly determined as ψ J = 3 / 2 and 2 in d = 1 and 2 dimensions, respectively; the corresponding unequal-time current-current correlation function decay as t − 5 / 2 and t −3 as a function of time t in d = 1 and 2 dimensions, respectively. Remarkably, depending on the dimensions and microscopic details, the prefactor A 1 can vanish, causing the variance to eventually saturate, implying a class-I ‘dynamic hyperuniformity’. We also compute the static structure factor S(q), which varies as the square of the wave number q in the small-q limit, i.e. S ( q ) ∼ q 2 , implying a class-I spatial hyperuniformity.

Hierarchical Cubes: Gibbs Measures and Decay of Correlations

We study a hierarchical model of non-overlapping cubes of sidelengths 2j\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^j$$\\end{document}, j∈Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j\\in {\\mathbb {Z}}$$\\end{document}. The model allows for cubes of arbitrarily small size and the activities need not be translationally invariant. It can also be recast as a spin system on a tree with a long-range hard-core interaction. We prove necessary and sufficient conditions for the existence and uniqueness of Gibbs measures, discuss fragmentation and condensation, and prove bounds on the decay of two-point correlation functions.

Momentum-dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems.

We study Ruelle-Pollicott resonances in translationally invariant quantum many-body lattice systems via spectra of a momentum-resolved operator propagator on infinite systems. Momentum dependence gives insight into the decay of correlation functions, showing that, depending on their symmetries, different correlation functions in general decay with different rates. Focusing on the kicked Ising model, the spectrum seems to be typically composed of an annular random matrix-like ring whose size we theoretically predict, and few isolated resonances. We identify several interesting regimes, including a mixing regime with a power-law decay of correlation functions. In that regime, we also observe a huge difference in timescales of different correlation functions due to an almost conserved operator. An exact expression for the singular values of the operator propagator is conjectured, showing that it becomes singular at a special point.

Revisiting Brownian SYK and its possible relations to de Sitter

We revisit Brownian Sachdev-Ye-Kitaev model and argue that it has emergent energy conservation overlooked in the literature before. We solve this model in the double-scaled regime and demonstrate hyperfast scrambling, exponential decay of correlation functions, bounded spectrum and unexpected factorization of higher-point functions. We comment on how these results are related to de Sitter holography.

Vibrational frequency fluctuations of poly(N,N-diethylacrylamide) in the vicinity of coil-to-globule transition studied by two-dimensional infrared spectroscopy and molecular dynamics simulations.

Poly(N,N-diethylacrylamide) (PdEA), one of the thermoresponsive polymers, in aqueous solutions has attracted much attention because of its characteristic properties, such as coil-to-globule (CG) transition. We performed two-dimensional infrared spectroscopy and molecular dynamics (MD) simulations to understand the hydration dynamics in the vicinity of the CG transition at the molecular level via vibrational frequency fluctuations of the carbonyl stretching modes in the side chains of PdEA. Furthermore, N,N-diethylpropionamide, a repeating monomer unit of PdEA, is also investigated for comparison. From decays of the frequency-frequency time correlation functions (FFTCFs) of the carbonyl stretching modes, we consider that inhomogeneity of the hydration environments originates from various backbone configurations of PdEA. The degree of the inhomogeneity depends on temperature. Hydration water molecules near the carbonyl groups are influenced by the confinements of the polymers. The restricted reorientation of the embedded water, the local torsions of the backbone, and the rearrangement of the whole structure contribute to the slow spectral diffusion. By performing MD simulations, we calculated the FFTCFs and dynamical quantities, such as fluctuations of the dihedral angles of the backbone and the orientation of the hydration water molecules. The simulated FFTCFs match well with the experimental results, indicating that the retarded water reorientations via the excluded volume effect play an important role in the vibrational frequency fluctuations of the carbonyl stretching mode. It is also found the embedded water molecules are influenced by the local torsions of the backbone structure within the time scales of the spectral diffusion.

Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions

AbstractWe present two approaches to establish the exponential decay of correlation functions of Euclidean quantum field theories (EQFTs) via stochastic quantization (SQ). In particular we consider the elliptic stochastic quantization of the Høegh–Krohn (or $$\exp (\alpha \phi )_2$$ exp ( α ϕ ) 2 ) EQFT in two dimensions. The first method is based on a path-wise coupling argument and PDE apriori estimates, while the second on estimates of the Malliavin derivative of the solution to the SQ equation.

A Deterministic Chaos-Model-Based Gaussian Noise Generator

The abilities of quantitative description of noise are restricted due to its origin, and only statistical and spectral analysis methods can be applied, while an exact time evolution cannot be defined or predicted. This emphasizes the challenges faced in many applications, including communication systems, where noise can play, on the one hand, a vital role in impacting the signal-to-noise ratio, but possesses, on the other hand, unique properties such as an infinite entropy (infinite information capacity), an exponentially decaying correlation function, and so on. Despite the deterministic nature of chaotic systems, the predictability of chaotic signals is limited for a short time window, putting them close to random noise. In this article, we propose and experimentally verify an approach to achieve Gaussian-distributed chaotic signals by processing the outputs of chaotic systems. The mathematical criterion on which the main idea of this study is based on is the central limit theorem, which states that the sum of a large number of independent random variables with similar variances approaches a Gaussian distribution. This study involves more than 40 mostly three-dimensional continuous-time chaotic systems (Chua’s, Lorenz’s, Sprott’s, memristor-based, etc.), whose output signals are analyzed according to criteria that encompass the probability density functions of the chaotic signal itself, its envelope, and its phase and statistical and entropy-based metrics such as skewness, kurtosis, and entropy power. We found that two chaotic signals of Chua’s and Lorenz’s systems exhibited superior performance across the chosen metrics. Furthermore, our focus extended to determining the minimum number of independent chaotic signals necessary to yield a Gaussian-distributed combined signal. Thus, a statistical-characteristic-based algorithm, which includes a series of tests, was developed for a Gaussian-like signal assessment. Following the algorithm, the analytic and experimental results indicate that the sum of at least three non-Gaussian chaotic signals closely approximates a Gaussian distribution. This allows for the generation of reproducible Gaussian-distributed deterministic chaos by modeling simple chaotic systems.

Decay of Multi-point Correlation Functions in Zd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}^d$$\\end{document}

We prove multi-point correlation bounds in Zd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}^d$$\\end{document} for arbitrary d≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\ge 1$$\\end{document} with symmetrized distances, answering open questions proposed by Sims–Warzel (Commun Math Phys 347(3):903–931, 2016) and Aza–Bru–Siqueira Pedra (Commun Math Phys 360(2):715–726, 2018). As applications, we prove multi-point correlation bounds for the Ising model on Zd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}^d$$\\end{document}, and multi-point dynamical localization in expectation for uniformly localized disordered systems, which provides the first examples of this conjectured phenomenon by Bravyi–König (Commun Math Phys 316(3):641–692, 2012) .

Exponential vs Gaussian Correlation Functions in the Characterization of Block Copolymer Grain Structure by Depolarized Light Scattering.

Block copolymer (BCP) grain structure affects the mechanical, optical, and electrical properties of BCP materials, making the accurate characterization of this grain structure an important goal. In this study, improved BCP grain parameters were obtained by employing an exponentially decaying correlation function within the ellipsoidal grain model, instead of the Gaussian correlation function that was used in previous work. The exponential correlation function provides a better fit to the experimental depolarized light scattering data, which outweighs the disadvantage that it requires numerical integration to obtain the model scattered intensity.

High-fidelity realization of the AKLT state on a NISQ-era quantum processor

The AKLT state is the ground state of an isotropic quantum Heisenberg spin-1 model. It exhibits an excitation gap and an exponentially decaying correlation function, with fractionalized excitations at its boundaries. So far, the one-dimensional AKLT model has only been experimentally realized with trapped-ions as well as photonic systems. In this work, we successfully prepared the AKLT state on a noisy intermediate-scale quantum (NISQ) era quantum device. In particular, we developed a non-deterministic algorithm on the IBM quantum processor, where the non-unitary operator necessary for the AKLT state preparation is embedded in a unitary operator with an additional ancilla qubit for each pair of auxiliary spin-1/2’s. Such a unitary operator is effectively represented by a parametrized circuit composed of single-qubit and nearest-neighbor CX gates. Compared with the conventional operator decomposition method from Qiskit, our approach results in a much shallower circuit depth with only nearest-neighbor gates, while maintaining a fidelity in excess of 99.99% with the original operator. By simultaneously post-selecting each ancilla qubit such that it belongs to the subspace of spin-up |↑>, an AKLT state can be systematically obtained by evolving from an initial trivial product state of singlets plus ancilla qubits in spin-up on a quantum computer, and it is subsequently recorded by performing measurements on all the other physical qubits. We show how the accuracy of our implementation can be further improved on the IBM quantum processor with readout error mitigation.

2D-IR Spectroscopy of Nitrosyl Stretch of Sodium Nitroprusside Reveals the Elusive Two Anomalous Regions in the DMSO–Water Mixture

DMSO-water mixtures provide an intriguing hydrogen-bonding environment which has been a subject of various theoretical and experimental investigations. The structural dynamics of aqueous DMSO solutions has been investigated, using nitrosyl stretch of sodium nitroprusside (SNP, Na2[Fe(CN)5NO]) as a local vibrational probe, with the help of infrared (IR) absorption spectroscopy, vibrational pump-probe spectroscopy, and two-dimensional IR spectroscopy (2D-IR). Fourier transform infrared spectra of the nitrosyl stretch of SNP reveals that both the peak position and spectral broadening are very sensitive to the composition of the DMSO-water mixture and the subsequent structural changes occurring due to the addition of DMSO to water. The vibrational lifetime of the nitrosyl stretch displays two different linear variation regimes as a function of mole fraction of DMSO which has been assigned presumably to two different predominant structures at these compositions. However, the rotational depolarization measurements show that the reorientational times follow a bell-shaped profile, imitating the changes in the composition-dependent physical properties (viscosity) of DMSO-water solvent mixtures. To get a holistic picture of the system, 2D-IR spectroscopy of the NO stretch of SNP has been employed to study time scales of hydrogen-bond reorganization dynamics existing at different compositions. The analysis of frequency-frequency correlation function (FFCF) decay times reveal that the dynamics gets slower in intermediate DMSO concentrations than that of pure DMSO or pure water. A careful analysis reveals two anomalous regions of hydrogen-bond dynamics: XDMSO ∼0.2 and 0.4, which indicates that different hydrogen-bonded structures exist in these regions that can be effectively probed by SNP which has remained mostly elusive to previous vibrational probe-based investigations.

Slow dynamics of a mobile impurity interacting with an Anderson insulator

We investigate dynamics of a single mobile impurity immersed in a bath of Anderson localized particles and focus on the regime of relatively strong disorder and interactions. In that regime, the dynamics of the system is particularly slow, suggesting, at short times, an occurrence of many-body localization. Considering longer time scales, we show that the latter is a transient effect and that, eventually, the impurity spreads sub-diffusively and induces a gradual delocalization of the Anderson insulator. The phenomenology of the system in the considered regime of slow dynamics includes a sub-diffusive growth of mean square displacement of the impurity, power-law decay of density correlation functions of the Anderson insulator and a power-law growth of entanglement entropy in the system. We observe a similar regime of slow dynamics also when the disorder in the system is replaced by a sufficiently strong quasi-periodic potential.

Transmission and reflection of energy at the boundary of a random two-component composite

A half-space x 2 > 0 is occupied by a two-component statistically uniform random composite with specified volume fractions and two-point correlation. It is bonded to a uniform half-space x 2 < 0 from which a plane wave is incident. The problem requires the specification of the properties of three media: those of the two constituents of the composite and those of the homogeneous half-space. The complexity of the problem is minimized by considering a model acoustic-wave problem in which the two media comprising the composite have the same modulus but different densities. The homogeneous half-space can have any chosen modulus and density. An approximate formulation based on a stochastic variational principle is formulated and solved explicitly in the particular case of an exponentially decaying correlation function, generalizing a previous solution in which the homogeneous medium had the same modulus as the composite. The main novelty of the present work is that the mean energy fluxes in the composite and reflected from the boundary are calculated, demonstrating explicitly the large backscatter associated with the mean-zero component of the reflected signal and the systematic transfer of energy from the decaying mean transmitted waves into the mean-zero disturbance as distance from the boundary increases.

Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with U(1) symmetry

We study a ($1+1$)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements, both of which conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition between a volume-law and an area-law entangled phase, we find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained by evolving an initial state with a definitive total charge exhibit critical scaling behaviors akin to Tomonaga-Luttinger-liquid theory for equilibrium critical quantum systems with $U(1)$ symmetry, such as logarithmic scaling of bipartite charge fluctuation, power-law decay of charge correlation functions, and logarithmic scaling of charge-resolved entanglement whose coefficient becomes a universal quadratic function in a flux parameter. These critical features, however, do not persist below the transition, in contrast to a recent prediction based on replica field theory and mapping to a classical statistical mechanical model.

Low-temperature behavior of the O(N) models below two dimensions.

We investigate the critical behavior and the nature of the low-temperature phase of the O(N) models treating the number of field components N and the dimension d as continuous variables with a focus on the d≤2 and N≤2 quadrant of the (d,N) plane. We precisely chart a region of the (d,N) plane where the low-temperature phase is characterized by an algebraic correlation function decay similar to that of the Kosterlitz-Thouless phase but with a temperature-independent anomalous dimension η. We revisit the Cardy-Hamber analysis leading to a prediction concerning the nonanalytic behavior of the O(N) models' critical exponents and emphasize the previously not broadly appreciated consequences of this approach in d<2. In particular, we discuss how this framework leads to destabilization of the long-range order in favor of the quasi-long-range order in systems with d<2 and N<2. Subsequently, within a scheme of the nonperturbative renormalization group we identify the low-temperature fixed points controlling the quasi-long-range ordered phase and demonstrate a collision between the critical and the low-temperature fixed points upon approaching the lower critical dimension. We evaluate the critical exponents η(d,N) and ν^{-1}(d,N) and demonstrate a very good agreement between the predictions of the Cardy-Hamber type analysis and the nonperturbative renormalization group in d<2.

Quantitative analysis of the blue-green single-photon emission from a quantum dot in a thick tapered nanowire

Quantum dots (QDs) acting as single-photon emitters in the blue-green range are fabricated and characterized at cryogenic temperature. They consist in CdSe dots inserted in (Zn,Mg)Se nanowires with a thick shell. Photoluminescence spectra, decay curves, and autocorrelation functions were measured under nonresonant continuous-wave and pulsed excitation. An analytical approach is applied simultaneously to the decay curves and correlation functions. It allows a quantitative description of how these two quantities are affected by the exciton rise due to biexciton feeding, the bright exciton decay, the effect of the dark exciton, and the reexcitation between two laser pulses. Linewidths at our limit of resolution (200 $\ensuremath{\mu}\mathrm{eV}$) are recorded. The reported correlation counts vary from a full control by reexcitation from traps, to a small contribution of reexcitation by mobile carriers or other QDs, as low as 5%.

Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems.

The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems. Its applicability has so far been limited to specific forms of spectral reservoir distributions and relatively elevated temperatures. Here we solve this problem and introduce an effective treatment of quantum noise in frequency space by systematically clustering higher order Matsubara poles, equivalent to an optimized rational decomposition. This leads to an elegant extension of the HEOM to arbitrary temperatures and very general reservoirs in combination with efficiency, high accuracy, and long-time stability. Moreover, the technique can directly be implemented in other approaches such as Green's function, stochastic, and pseudomode formulations. As one highly nontrivial application, for the subohmic spin-boson model at vanishing temperature the Shiba relation is quantitatively verified which predicts the long-time decay of correlation functions.

Simulating Chiral Spin Liquids with Projected Entangled-Pair States.

Doubts have been raised on the representation of chiral spin liquids exhibiting topological order in terms of projected entangled pair states (PEPSs). Here, starting from a simple spin-1/2 chiral frustrated Heisenberg model, we show that a faithful representation of the chiral spin liquid phase is in fact possible in terms of a generic PEPS upon variational optimization. We find a perfectly chiral gapless edge mode and a rapid decay of correlation functions at short distances consistent with a bulk gap, concomitant with a gossamer long-range tail originating from a PEPS bulk-edge correspondence. For increasing bond dimension, (i)the rapid decrease of spurious features-SU(2) symmetry breaking and long-range tails in correlations-together with (ii)a faster convergence of the ground state energy as compared to state-of-the-art cylinder matrix-product state simulations involving far more variational parameters, prove the fundamental relevance of the PEPS ansatz for simulating systems with chiral topological order.

Multiple Ensembles of the Hydrogen-bonded Network in Ethylammonium Nitrate versus Water from Vibrational Spectral Dynamics of SCN- Probe.

We performed classical molecular dynamics simulations to monitor the structural interactions and ultrafast dynamical and spectral response in the protic ionic liquid, ethylammonium nitrate (EAN) and water using the nitrile stretching mode of thiocyanate ion (SCN- ) as the vibrational probe. The normalized frequency distribution of the nitrile stretch in SCN- attains an asymmetric shape in EAN, indicating the existence of more than one hydrogen-bonding environment in EAN. Further, we computed the 2D IR spectrum from classical trajectories, applying the response function formalism. Spectral diffusion dynamics in EAN undergo an initial rattling of the SCN- inside the local ion-cage occurring at a timescale of 0.10 ps, followed by the breakup of the ion-cage activating molecular diffusion at 7.86 ps timescale. In contrast, the dynamics of structural reorganization occur at a timescale of 0.58 ps in H2 O. Hence, the time dependence of the frequency-frequency correlation function decay hints at the local molecular structure and ultrafast ion dynamics of the SCN- probe. The loss of frequency correlation read from the peak shape changes in the 2D correlation spectrum as a function of waiting time is faster in H2 O than in EAN due to the enhanced structural ordering and higher viscosity of the latter. We provide an atomic-level interpretation of the solvation environment around SCN- in EAN and water, which indicates multiple ensembles of the hydrogen bond network in EAN.

The hydrodynamic theory of dynamical correlation functions in the XX chain

By the hydrodynamic linear response theory, dynamical correlation functions decay as power laws along certain velocities, determined by the flux Jacobian. Such correlations are obtained by hydrodynamic projections, and physically, they are due to propagating ‘sound waves’ or generalisation thereof, transporting conserved quantities between the observables. However, some observables do not emit sound waves, such as order parameters associated to symmetry breaking. In these cases correlation functions decay exponentially everywhere, a behaviour not captured by the hydrodynamic linear response theory. Focussing on spin–spin correlation functions in the XX quantum chain, we first review how hydrodynamic linear response works, emphasising that the necessary fluid cell averaging washes out oscillatory effects. We then show how, beyond linear response, Euler hydrodynamics can still predict the exponential decay of correlation functions of order parameters. This is done by accounting for the large-scale fluctuations of domain walls, via the recently developed ballistic fluctuation theory. We use the framework of generalised hydrodynamics, which is particularly simple in this model due to its free fermion description. In particular, this reproduces, by elementary calculations, the exponential decay in the celebrated formulae by Its et al (1993) and by Jie (1998), which were originally obtained by intricate Fredholm determinant analysis; and gives a new formula in a parameter domain where no result was obtained before. We confirm the results by numerical simulations.