Particle-particle Correlations Research Articles

Nanopipette dynamic microscopy unveils nano coffee ring

Liquid-phase electron microscopy (LP-EM) imaging has revolutionized our understanding of nanosynthesis and assembly. However, the current closed geometry limits its application for open systems. The ubiquitous physical process of the coffee-ring phenomenon that underpins materials and engineering science remains elusive at the nanoscale due to the lack of experimental tools. We introduce a quartz nanopipette liquid cell with a tunable dimension that requires only standard microscopes. Depending on the imaging condition, the open geometry of the nanopipette allows the imaging of evaporation-induced pattern formation, but it can also function as an ordinary closed-geometry liquid cell where evaporation is negligible despite the nano opening. The nano coffee-ring phenomenon was observed by tracking individual nanoparticles in an evaporating nanodroplet created from a thin liquid film by interfacial instability. Nanoflows drive the assembly and disruption of a ring pattern with the absence of particle-particle correlations. With surface effects, nanoflows override thermal fluctuations at tens of nanometers, in which nanoparticles displayed a "drunken man trajectory" and performed work at a value much smaller than kBT.

Search for 22Na in novae supported by a novel method for measuring femtosecond nuclear lifetimes

Classical novae are thermonuclear explosions in stellar binary systems, and important sources of 26Al and 22Na. While γ rays from the decay of the former radioisotope have been observed throughout the Galaxy, 22Na remains untraceable. Its half-life (2.6 yr) would allow the observation of its 1.275 MeV γ-ray line from a cosmic source. However, the prediction of such an observation requires good knowledge of its nucleosynthesis. The 22Na(p, γ)23Mg reaction remains the only source of large uncertainty about the amount of 22Na ejected. Its rate is dominated by a single resonance on the short-lived state at 7785.0(7) keV in 23Mg. Here, we propose a combined analysis of particle-particle correlations and velocity-difference profiles to measure femtosecond nuclear lifetimes. The application of this method to the study of the 23Mg states, places strong limits on the amount of 22Na produced in novae and constrains its detectability with future space-borne observatories.

Extracting electronic many-body correlations from local measurements with artificial neural networks

The characterization of many-body correlations provides a powerful tool for analyzing correlated quantum materials. However, experimental extraction of quantum entanglement in correlated electronic systems remains an open problem in practice. In particular, the correlation entropy quantifies the strength of quantum correlations in interacting electronic systems, yet it requires measuring all the single-particle correlators of a macroscopic sample. To circumvent this bottleneck, we introduce a strategy to obtain the correlation entropy of electronic systems solely from a set of local measurements. We show that, by combining local particle-particle and density-density correlations with a neural-network algorithm, the correlation entropy can be predicted accurately. Specifically, we show that for a generalized interacting fermionic model, our algorithm yields an accurate prediction of the correlation entropy from a set of noisy local correlators. Our work shows that the correlation entropy in interacting electron systems can be reconstructed from local measurements, providing a starting point to experimentally extract many-body correlations with local probes.

Extracting electronic many-body correlations from local measurements with artificial neural networks

The characterization of many-body correlations provides a powerful tool for analyzing correlated quantum materials. However, experimental extraction of quantum entanglement in correlated electronic systems remains an open problem in practice. In particular, the correlation entropy quantifies the strength of quantum correlations in interacting electronic systems, yet it requires measuring all the single-particle correlators of a macroscopic sample. To circumvent this bottleneck, we introduce a strategy to obtain the correlation entropy of electronic systems solely from a set of local measurements. We demonstrate that by combining local particle-particle and density-density correlations with a neural-network algorithm, the correlation entropy can be predicted accurately. Specifically, we show that for a generalized interacting fermionic model, our algorithm yields an accurate prediction of the correlation entropy from a set of noisy local correlators. Our work demonstrates that the correlation entropy in interacting electron systems can be reconstructed from local measurements, providing a starting point to experimentally extract many-body correlations with local probes.

Laughlin topology on fractal lattices without area law entanglement

Laughlin states have recently been constructed on fractal lattices, and the charge and braiding statistics of the quasiholes were used to confirm that these states have Laughlin type topology. Here, we investigate density, correlation, and entanglement properties of the states on a fractal lattice derived from a Sierpinski triangle with the purpose of identifying similarities and differences compared to two-dimensional systems and with the purpose of investigating whether various probes of topology work for fractal lattices. Similarly to two-dimensional systems, we find that the connected particle-particle correlation function decays roughly exponentially with the distance between the lattice sites measured in the two-dimensional plane, but the values also depend on the local environment. Contrary to two-dimensional systems, we find that the entanglement entropy does not follow the area law if one defines the area to be the number of nearest neighbor bonds that cross the edge of the selected subsystem. Considering bipartitions with two bonds crossing the edge, we find a close to logarithmic scaling of the entanglement entropy with the number of sites in the subsystem. This also means that the topological entanglement entropy cannot be extracted using the Kitaev-Preskill or the Levin-Wen methods. Studying the entanglement spectrum for different bipartitions, we find that the number of states below the entanglement gap is robust and the same as for Laughlin states on two-dimensional lattices.

Multiperipheral final states in crowded twin-jet events at the LHC

The 13 TeV run of the LHC has provided a unique opportunity to explore multi-jet final states with unprecedented accuracy. An interesting region for study is that of events where one jet is tagged in the forward direction and another one in the backward direction and a plethora of low energy mini-jets populate the possibly large rapidity span in between them. Since the number of these events is very high, it is possible to introduce stringent constraints on the transverse momentum of the two leading jets which can be kept in small windows not very different from each other, defining what we call “twin jets”. The associated “crowd” of mini-jets can also have a restricted span in transverse momentum. The study of these events for a fixed multiplicity is an ideal playground to investigate different models of multi-particle production in hadron-hadron collisions. We set up an exploratory analysis by using an ancient model of Chew and Pignotti to describe the gross features one can expect for the structure of single and double differential-in-rapidity cross sections and for particle-particle rapidity correlations when the longitudinal phase space completely decouples from the transverse degrees of freedom.

Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles.

We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component V_{R} for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D_{2}. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011)PLEEE81539-375510.1103/PhysRevE.84.045304; J. Turbul. 15, 34 (2014)1468-524810.1080/14685248.2013.875188] that the scale invariant part of the distribution has two asymptotic regimes: (1) |V_{R}|≪R, where the distribution depends solely on R, and (2) |V_{R}|≫R, where the distribution is a function of |V_{R}| alone. The probability distributions in these two regimes are matched along a straight line: |V_{R}|=z^{*}R. Our simulations confirm that this is indeed correct. We further obtain D_{2} and z^{*} as a function of the Stokes number, St. The former depends nonmonotonically on St with a minimum at about St≈0.7 and the latter has only a weak dependence on St.

Bosonic particle-correlated states: A nonperturbative treatment beyond mean field

Many useful properties of dilute Bose gases at ultra-low temperature are predicted precisely by the (mean-field) product-state Ansatz, in which all particles are in the same quantum state. Yet, in situations where particle-particle correlations become important, the product Ansatz fails. To include correlations nonperturbatively, we consider a new set of states: the particle-correlated state of $N=l\times n$ bosons is derived by symmetrizing the $n$-fold product of an $l$-particle quantum state. The particle-correlated states can be simulated efficiently for large $N$, because their parameter spaces, which depend on $l$, do not grow with $n$. Here we formulate and develop in great detail the pure-state case for $l=2$, where the many-body state is constructed from a two-particle pure state. These paired wave functions, which we call pair-correlated states (PCS), were introduced by A. J. Leggett [Rev. Mod. Phys. ${\bf 73}$, 307 (2001)] as a particle-number-conserving version of the Bogoliubov approximation. We present an iterative algorithm that solves for the reduced (marginal) density matrices (RDMs), i.e., the correlation functions, associated with PCS in time $O(N)$. The RDMs can also be derived from the normalization factor of PCS, which is derived analytically in the large-$N$ limit. To test the efficacy of PCS, we analyze the ground state of the two-site Bose-Hubbard model by minimizing the energy of the PCS~state, both in its exact form and in its large-$N$ approximate form, and comparing with the exact ground state. For $N=1\,000$, the relative errors of the ground-state energy for both cases are within $10^{-5}$ over the entire parameter region from a single condensate to a Mott insulator. We present numerical results that suggest that PCS might be useful for describing the dynamics in the strongly interacting regime.

Effective Interactions and Colloidal Stability of Bovine γ-Globulin in Solution.

Interactions and phase behavior of γ-globulins are of fundamental interest in biophysical and pharmaceutical research, as these are among the most abundant proteins in blood plasma. In this work, we report the characterization of the oligomeric state of bovine γ-globulin, the effective protein-protein interactions, and the colloidal stability in aqueous solution as a function of protein concentration and ionic strength. Classical biochemical techniques, such as size exclusion chromatography (SEC) and gel electrophoresis, together with small-angle X-ray and neutron scattering (SAXS/SANS), were employed for this study. The results show that bovine γ-globulin solutions are dominated by monomer and idiotype anti-idiotype dimer. Despite the flexibility and highly nonspherical shape of the protein, a simple model with a disk-type form factor and a structure factor of a square-well potential provide a satisfying description of the scattering data. The overall interactions are attractive and the strength decreases with increasing protein concentration, or adding buffer or salts. For higher protein volume fraction (>7%), the model would imply a strong particle-particle correlation which does not appear in the experimental data. This mismatch is most likely due to the smearing effect of the conformation change of proteins in solution. The stability of γ-globulin solutions is highly sensitive to protein concentration, ionic strength, and the type of added salts, such as NaCl, Na2SO4, and NaSCN. For solutions below 50 mg/mL and at low ionic strengths (<0.1 M), protein aggregation is most likely due to subpopulations of IgG molecules with attractive patches of complementary surface charge. This effect is reduced for higher protein concentration due to self-buffering effects. For high ionic strength (>1 M), typical salting-in (with NaSCN) and salting-out effects (with NaCl and Na2SO4) are observed. Results are further discussed in comparison with current studies in the literature on monoclonal antibodies.

Interactions, Structure, and Dynamics of Polymer-Tethered Nanoparticle Blends.

We report on the structure, jamming, and dynamics of blends of self-suspended hairy silica nanoparticles grafted with poly(ethylene glycol) (PEG) and poly(methyl methacrylate) (PMMA). We find that favorable enthalpic attraction between tethered PEG and PMMA chains augment previously reported entropic attractions between tethered polymer chains in self-suspended suspensions to enhance particle-particle correlations, increase jamming, and slow down chain dynamics. As with their single-component counterparts, the hairy SiO2-PEG/SiO2-PMMA nanoparticle blends exhibit soft glassy rheological behavior and both the energy dissipated at yielding and the plateau elastic modulus display strong maxima in the symmetric case. A comparison of the small angle X-ray scattering (SAXS) measurements with theoretical analysis from density functional theory (DFT) reveals that the addition of SiO2-PMMA to a self-suspended SiO2-PEG suspension initially leads to a higher degree of stretching of the corona chains, which produces stronger interdigitation of the tethered chains, enhanced jamming, and slower polymer relaxation than observed in the single-component materials. By means of an analysis of the heat of mixing released upon blending tethered and untethered PEG and PMMA chains, we find that the strong enthalpic attraction between the grafted polymer chains enhances entropic attractive forces produced by the space-filling constraint on tethered ligands in self-suspended suspensions to produce entangled-polymer-like physical properties in polymers with molecular weights below the thresholds normally associated with the transition to an entangled state.

General continuum approach for dissipative systems of repulsive particles.

We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle correlations is incorporated to the overall balance of energy, and a nonlinear diffusion equation is obtained to represent the overdamped dynamics. In particular, when the repulsive interaction potential is a short-ranged power law, our approach reveals a distinctive correspondence between particle-particle energy and the generalized thermostatistics of Tsallis for any nonpositive value of the entropic index q. Our methodology can also be applied to microscopic models of superconducting vortices and complex plasma, where particle-particle correlations are pronounced at low concentrations. The resulting continuum descriptions provide elucidating and useful insights on the microdynamical behavior of these physical systems. The consistency of our approach is demonstrated by comparison with molecular dynamics simulations.

On the single-lane TASEP with generalized update and open boundary conditions

We report on numerical simulation results for the stationary properties of the totally asymmetric simple exclusion process (TASEP) with generalized update (GU) on a simple chain with open boundary conditions (OBC). We note that the application of TASEP to biomolecular processes can be traced back to [1], see also [2,3], where the model was used to describe directed motion of molecular motors along twisted filaments. The model with generalized update, suggested and studied on a ring in [4,5], includes interaction between nearest-neighbor particles. The implementation of OBC leads to a variety of stationary properties of the TASEP with GU, which cannot be observed on a ring. We introduce here a modified left boundary condition which controls the input of particles in the chain, which allows for a smooth transition from the standard updates to the extreme case of particles gluing in stable clusters. The density distribution of particles along the chain, nearest-neighbor particle-particle correlations, and the fundamental relationship between particle current and density were studied at different values of the parameters. Our numerical simulations reveal broad and quite unexpected modes of behavior of the system. Simple analytical models for the description of some of the unusual types of behavior are suggested. Finally, the possibilities for different applications are mentioned. [1] C. T. MacDonald, J. H. Gibbs, and A. C. Pipkin, Biopolymers 6, 1 (1968). [2] Y.-M. Yuan et al., J. Phys. A 40, 12351 (2007). [3] A. E. Derbyshev et al, J. Stat. Mech., 2012, P05014 (2012); Phys. Rev. E 91, 022125 (2015).

Development of the Multicomponent Coupled-Cluster Theory for Investigation of Multiexcitonic Interactions.

Multicomponent systems are defined as chemical systems that require a quantum mechanical description of two or more different types of particles. Non-Born-Oppenheimer electron-nuclear interactions in molecules, electron-hole interactions in electronically excited nanoparticles, and electron-positron interactions are examples of physical systems that require a multicomponent quantum mechanical formalism. The central challenge in the theoretical treatment of multicomponent systems is capturing the many-body correlation effects that exist not only between particles of identical types (electron-electron) but also between particles of different types (electron-nuclear and electron-hole). In this work, the development and implementation of multicomponent coupled-cluster (mcCC) theory for treating particle-particle correlation in multicomponent systems are presented. This method provides a balanced treatment of many-particle correlation effects in a general multicomponent system while maintaining a size-consistent and size-extensive formalism. The coupled-cluster ansatz presented here is an extension of the electronic structure CCSD formulation for multicomponent systems and is defined as |ΨmcCC⟩ = eT1I+T2I+T1II+T2II+T11I,II+T12I,II+T21I,II+T22I,II|0I0II⟩. The cluster amplitudes in the mcCC wave function were obtained by projecting the mcCC Schrödinger equation onto a direct product space of singly and doubly excited states of type I and II particles and then solving the resulting mcCC equations iteratively. These equations were derived using an automated application of the generalized Wick’s theorem and were implemented using a computer-assisted source code generation approach. The applicability of the mcCC method was demonstrated by calculating ground state energies of multicomponent Hooke's atom and positronium hydride systems as well as by calculating exciton and biexciton binding energies in multiexcitonic systems. For each case, the mcCC results were benchmarked against full configuration interaction (FCI) calculations and were found to be in excellent agreement with the FCI results. The effect of neglecting certain classes of multicomponent connected excitation terms from the mcCC wave function was also investigated. The results from this study demonstrate that connected cluster operators that generate simultaneous excitation in type I and type II space are critical for capturing electron-hole correlation in multiexcitonic systems.

Binding energies of exciton complexes in transition metal dichalcogenide monolayers and effect of dielectric environment

Excitons, trions, biexcitons, and exciton-trion complexes in two-dimensional transition metal dichalcogenide sheets of MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$ and WSe$_2$ are studied by means of density functional theory and path integral Monte Carlo method in order to accurately account for the particle-particle correlations. In addition, the effect of dielectric environment on the properties of these exciton complexes is studied by modifying the effective interaction potential between particles. Calculated exciton and trion binding energies are consistent with previous experimental and computational studies, and larger systems such as biexciton and exciton-trion complex are found highly stable. Binding energies of biexcitons are similar or higher than those of trions, but the binding energy of the trion depends significantly stronger on the dielectric environment than that of biexciton. Therefore, as a function of an increasing dielectric constant of the environment the exciton-trion complex "dissociates" to a biexciton rather than to an exciton and a trion.

Evaluation of the theoretical nuclear matrix elements forββdecay ofGe76

The nuclear matrix elements for two-neutrino double-$\ensuremath{\beta}$ and zero-neutrino double-$\ensuremath{\beta}$ decay of $^{76}\mathrm{Ge}$ are evaluated in terms of the configuration-interaction (CI), quasiparticle random-phase approximation (QRPA), and interacting boson model methods. We point out deficiencies in all of these models and suggest ways that some of them can be corrected. The final results are obtained from the CI method corrected for configuration admixtures involving orbitals outside of the CI configuration space by using results from QRPA, many-body-perturbation theory, and the connections to related observables. The CI two-neutrino matrix element is reduced due to the inclusion of spin-orbit partners and to many-body correlations connected with Gamow-Teller $\ensuremath{\beta}$ decay. The CI zero-neutrino matrix element for the heavy neutrino is enhanced due to particle-particle correlations that are connected with the odd-even oscillations in the nuclear masses. The CI zero-neutrino matrix element for the light neutrino contains both types of correlations that approximately cancel each other. The uncertainty from short-range correlations is also considered.

Dissipation-induced first-order decoherence phase transition in a noninteracting fermionic system

We consider a quantum wire connected to the leads and subjected to dissipation along its length. The dissipation manifests as tunneling into (out of) the chain from (to) a memoryless environment. The evolution of the system is described by the Lindblad equation. Already infinitesimally small dissipation along the chain induces a quantum phase transition (QPT). This is a decoherence QPT: the reduced density matrix of a subsystem in the nonequilibrium steady state (far from the ends of the chain) can be represented as the tensor product of single-site density matrices. The QPT is identified from the jump of the current and the entropy per site as the dissipation becomes nonzero. We also explore the properties of the boundaries of the chain close to the transition point and observe that the boundaries behave as if they undergo a second-order phase transition as a function of the dissipation strength: the particle-particle correlation functions and the response to the electric field exhibit a power-law divergence. Disorder is known to localize one-dimensional systems, but the coupling to the memoryless environment pushes the system back into the delocalized state even in the presence of disorder. Interestingly, we observe a similar transition in the classical dissipative counterflow model: the current has a jump at the ends of the chain introducing an infinitely small dissipation.

Fluid approach to evaluate sound velocity in Yukawa systems and complex plasmas.

The conventional fluid description of multicomponent plasma, supplemented by an appropriate equation of state for the macroparticle component, is used to evaluate the longitudinal sound velocity of Yukawa fluids. The obtained results are in very good agreement with those obtained earlier employing the quasilocalized charge approximation and molecular dynamics simulations in a rather broad parameter regime. Thus, a simple yet accurate tool to estimate the sound velocity across coupling regimes is proposed, which can be particularly helpful in estimating the dust-acoustic velocity in strongly coupled dusty (complex) plasmas. It is shown that, within the present approach, the sound velocity is completely determined by particle-particle correlations and the neutralizing medium (plasma), apart from providing screening of the Coulomb interaction, has no other effect on the sound propagation. The ratio of the actual sound velocity to its "ideal gas" (weak coupling) scale only weakly depends on the coupling strength in the fluid regime but exhibits a pronounced decrease with the increase of the screening strength. The limitations of the present approach in applications to real complex plasmas are briefly discussed.

Laser mapping of the inter-strip response in double sided silicon strip detectors for particle identification

Silicon microstrips are widely used in nuclear physics experiments when high granularity and high resolution is required (e.g. particle-particle correlation). In addition microstrip detectors are used in the field of X-ray detection for position resolved X-ray spectroscopy. In the framework of the construction of a novel Femtoscope ARray for Correlation and Spectroscopy, named FARCOS, we are performing a thorough characterization of the silicon detector layers in terms of the efficiency and charge collection properties as a function of the point of incidence and type of interaction. We have experimental evidence—as previously observed also in the literature for other strip detectors—that inter-strip incidence alters the signal shape not only for the trivial charge division but also affecting the shape of the induced signal on neighbor strips. The phenomenon can be more or less pronounced depending on the energy and ion type but it is always present. In order to surgically probe the response of the inter-strip region we tested the detector both in back and in front injection with an infrared pulsed laser at two different wavelengths (705 nm and 904 nm). Depending on the side of interaction, on the position of incidence and on the absorption length, the shapes of the induced signals are significantly altered and signals of opposite polarity or bipolar signals arise. In order to get a complete picture of the physical phenomena at the basis of the aforementioned behavior we performed detailed 3D device simulations with a custom semi-analytical code and compared the results with the experimental data. The paper focuses on the description of the experimental measurements and their exhaustive description and interpretation.

Pairing-induced speedup of nuclear spontaneous fission

Background: Collective inertia is strongly influenced at the level crossing at which the quantum system changes its microscopic configuration diabatically. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of these configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes.Purpose: To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of $^{264}\mathrm{Fm}$ and $^{240}\mathrm{Pu}$ using the state-of-the-art self-consistent framework.Methods: We employ the superfluid nuclear density functional theory with the Skyrme energy density functional ${\mathrm{SkM}}^{*}$ and a density-dependent pairing interaction. Along with shape variables, proton and neutron pairing correlations are taken as collective coordinates. The collective inertia tensor is calculated within the nonperturbative cranking approximation. The fission paths are obtained by using the least action principle in a four-dimensional collective space of shape and pairing coordinates.Results: Pairing correlations are enhanced along the minimum-action fission path. For the symmetric fission of $^{264}\mathrm{Fm}$, where the effect of triaxiality on the fission barrier is large, the geometry of the fission pathway in the space of the shape degrees of freedom is weakly impacted by pairing. This is not the case for $^{240}\mathrm{Pu}$, where pairing fluctuations restore the axial symmetry of the dynamic fission trajectory.Conclusions: The minimum-action fission path is strongly impacted by nucleonic pairing. In some cases, the dynamical coupling between shape and pairing degrees of freedom can lead to a dramatic departure from the static picture. Consequently, in the dynamical description of nuclear fission, particle-particle correlations should be considered on the same footing as those associated with shape degrees of freedom.

Two-point correlation function of an exclusion process with hole-dependent rates.

We consider an exclusion process on a ring in which a particle hops to an empty neighboring site with a rate that depends on the number of vacancies n in front of it. In the steady state, using the well-known mapping of this model to the zero-range process, we write down an exact formula for the partition function and the particle-particle correlation function in the canonical ensemble. In the thermodynamic limit, we find a simple analytical expression for the generating function of the correlation function. This result is applied to the hop rate u(n)=1+(b/n) for which a phase transition between high-density laminar phase and low-density jammed phase occurs for b>2. For these rates, we find that at the critical density, the correlation function decays algebraically with a continuously varying exponent b-2. We also calculate the two-point correlation function above the critical density and find that the correlation length diverges with a critical exponent ν=1/(b-2) for b<3 and 1 for b>3. These results are compared with those obtained using an exact series expansion for finite systems.