Single-particle Density Research Articles

Solitary waves explore the quantum-to-classical transition

How the classical appearance of our environment arises from the underlying quantum many-body theory is an open fundamental question. We propose that phenomena involved in the quantum-to-classical transition can be probed in collisions of bright solitary waves in Bose-Einstein condensates, where thousands of atoms form a large compound object at ultra cold temperatures. For the experimentally most relevant quasi-1D regime, where integrability is broken through effective three-body interactions, we find that ensembles of solitary waves exhibit complex interplay between phase coherence and entanglement generation in beyond mean-field simulations using the truncated Wigner method: An initial state of two solitons with a well-defined relative phase looses that phase coherence in the ensemble, with its single-particle two-mode density matrix exhibiting similar dynamics as a decohering two-mode superposition. This apparent decoherence is a prerequisite for the formation of entangled superpositions of different atom numbers in a subsequent soliton collision. The necessity for the solitons to first decohere is explained based on the underlying phase-space of the quintic mean-field equation. We show elsewhere that superpositions of different atom numbers later further evolve into spatially entangled solitons. Loss of ensemble phase coherence followed by system internal entanglement generation appear in an unusual order in this closed system, compared to a typical open quantum system.

Black hole scattering and partition functions

When computing the ideal gas thermal canonical partition function for a scalar outside a black hole horizon, one encounters the divergent single-particle density of states (DOS) due to the continuous nature of the normal mode spectrum. Recasting the Lorentzian field equation into an effective 1D scattering problem, we argue that the scattering phases encode non-trivial information about the DOS and can be extracted by “renormalizing” the DOS with respect to a reference. This defines a renormalized free energy up to an arbitrary additive constant. Interestingly, we discover that the 1-loop Euclidean path integral, as computed by the Denef-Hartnoll-Sachdev formula, fixes the reference free energy to be that on a Rindler-like region, and the renormalized DOS captures the quasinormal modes for the scalar. We support these claims with the examples of scalars on static BTZ, Nariai black holes and the de Sitter static patch. For black holes in asymptotically flat space, the renormalized DOS is captured by the phase of the transmission coefficient whose magnitude squared is the greybody factor. We comment on possible connections with recent works from an algebraic point of view.

Simulating realistic screening clouds around quantum impurities: Role of spatial anisotropy and disorder

Dynamical quantum impurities in metals induce electronic correlations in real space that are difficult to simulate due to their multi-scale nature, so that only s-wave scattering in clean metallic hosts has been investigated so far. However, screening clouds should show anisotropy due to lack of full rotational invariance in two- and three-dimensional lattices, while inherent disorder will also induce spatial inhomogeneities. To tackle these challenges, we present an efficient and robust algorithm based on the recursive generation of natural orbitals defined as eigenvectors of the truncated single-particle density matrix. This method provides well-converged many-body wave functions on lattices with up to tens of thousands of sites, bypassing some limitations of other approaches. The algorithm is put to the test by investigating the charge screening cloud around an interacting resonant level, both on clean and disordered lattices, achieving accurate spatial resolution from short to long distances. We thus demonstrate strong anisotropy of spatial correlations around an adatom in the half-filled square lattice. Taking advantage of the efficiency of the algorithm, we further compute the disorder-induced distribution of Kondo temperatures over several thousands of random realizations, at the same time gaining access to the full spatial profile of the screening cloud in each sample. While the charge screening cloud is typically shortened due to the polarization of the impurity by the disorder potential, we surprisingly find that rare disorder configurations preserve the long range nature of Kondo correlations in the electronic bath.

Bubble nuclei: Single-particle versus Coulomb interaction effects

The detailed investigation of microscopic mechanisms leading to the formation of bubble structures in nuclei is performed in the framework of covariant density functional theory. The main emphasis of this study is on the role of single-particle degrees of freedom and Coulomb interaction. In general, the formation of bubbles lowers the Coulomb energy. However, in nuclei this trend is counteracted by the quantum nature of the single-particle states: only specific single-particle states with specific density profiles can be occupied with increasing proton and neutron numbers. A significant role of the central classically forbidden region at the bottom of the wine bottle potentials in the formation of nuclear bubbles (via primarily the reduction of the densities of the $s$ states at $r=0$) is revealed for the first time. Their formation also depends on the availability of low-$l$ single-particle states for occupation since single-particle densities represent the basic building blocks of total densities. Nucleonic potentials disfavor the occupation of such states in hyperheavy nuclei and this contributes to the formation of bubbles in such nuclei. Existing bubble indicators are strongly affected by single-particle properties and thus they cannot be reliable measures of bulk properties (such as the Coulomb interaction). An additivity rule for densities is proposed for the first time. It was shown that the differences in the densities of bubble and flat density nuclei follow this rule in the $A\ensuremath{\approx}40$ mass region and in superheavy nuclei with comparable accuracy. This strongly suggests the same mechanism of the formation of central depression in bubble nuclei of these two mass regions. Nuclear saturation mechanisms and self-consistency effects also affect the formation of bubble structures. The detailed analysis of different aspects of bubble physics strongly suggests that the formation of bubble structures in superheavy nuclei is dominated by single-particle effects. The role of the Coulomb interaction increases in hyperheavy nuclei but even for such systems we do not find strong arguments that the formation of bubble structures is dominated by it.

Nanoelectrochemistry Reveals Selective Interactions of Perfluoroalkyl Substances (PFASs) with Silver Nanoparticles

AbstractNanoelectrochemistry allows for the investigation of the interaction of per‐ and polyfluoroalkyl substances (PFASs) with silver nanoparticles (AgNPs) and the elucidation of the binding behaviour of PFASs to nanoscale surfaces with high sensitivity. Mechanistic studies supported by single particle collision electrochemistry (SPCE), spectroscopic and density functional theory (DFT) calculations indicate the capability of polyfluorooctane sulfonic acid (PFOS), a representative PFAS, to selectively bind and induce aggregation of AgNPs. Single‐particle measurements provide identification of the “discrete” AgNPs agglomeration (e.g. 2–3 NPs) formed through the inter‐particles F−F interactions and the selective replacement of the citrate stabilizer by the sulfonate of the PFOS. Such interactions are characteristic only for long chain PFAS (‐SO3−) providing a means to selectively identify these substances down to ppt levels. Measuring and understanding the interactions of PFAS at nanoscale surfaces are crucial for designing ultrasensitive methods for detection and for modelling and predicting their interaction in the environment.

Nanoelectrochemistry Reveals Selective Interactions of Perfluoroalkyl Substances (PFASs) with Silver Nanoparticles.

Nanoelectrochemistry allows for the investigation of the interaction of per- and polyfluoroalkyl substances (PFASs) with silver nanoparticles (AgNPs) and the elucidation of the binding behaviour of PFASs to nanoscale surfaces with high sensitivity. Mechanistic studies supported by single particle collision electrochemistry (SPCE), spectroscopic and density functional theory (DFT) calculations indicate the capability of polyfluorooctane sulfonic acid (PFOS), a representative PFAS, to selectively bind and induce aggregation of AgNPs. Single-particle measurements provide identification of the "discrete" AgNPs agglomeration (e.g. 2-3 NPs) formed through the inter-particles F-F interactions and the selective replacement of the citrate stabilizer by the sulfonate of the PFOS. Such interactions are characteristic only for long chain PFAS (-SO3 - ) providing a means to selectively identify these substances down to ppt levels. Measuring and understanding the interactions of PFAS at nanoscale surfaces are crucial for designing ultrasensitive methods for detection and for modelling and predicting their interaction in the environment.

Strongly correlated zero-bias anomaly in double quantum dot measurements

Experiments in doped transition metal oxides often show suppression in the single-particle density of states at the Fermi level, but disorder-induced zero-bias anomalies in strongly correlated systems remain poorly understood. Numerical studies of the Anderson-Hubbard model have identified a zero-bias anomaly that is unique to strongly correlated materials, with a width proportional to the intersite hopping amplitude t [S. Chiesa, P. B. Chakraborty, W. E. Pickett, and R. T. Scalettar, Phys. Rev. Lett. 101, 086401 (2008)]. In ensembles of two-site systems, a zero-bias anomaly with the same parameter dependence also occurs, suggesting a similar physical origin [R. Wortis and W. A. Atkinson, Phys. Rev. B 82, 073107 (2010)]. We describe how this kinetic-energy-driven zero-bias anomaly in ensembles of two-site systems may be seen in a mesoscopic realization based on double quantum dots. Moreover, the double-quantum-dot measurements provide access not only to the ensemble-average density of states but also to the details of the transitions which give rise to the zero-bias anomaly.

Impurity bands in magnetic superconductors with spin density wave

Magnetic superconductors define a broad class of strongly correlated materials in which superconductivity may coexist with either localized or itinerant long-range magnetic order. In this work we consider a multiband model of a disordered magnetic superconductor which realizes coexistence of unconventional superconductivity and a spin-density-wave. We derive an exact T-matrix and compute a single particle density of states in this system. In a purely superconducting state the interband scattering potential leads to an appearance of the localized Yu–Shiba–Rusinov bound states. Our main finding is that in the fairly broad swath of the coexistence region superconductivity remains fully gapped despite the presence of the impurity bands. We also discuss the effects of spatial inhomogeneities on the density of states in strongly contaminated superconductors.

A probabilistic framework for particle-based reaction–diffusion dynamics using classical Fock space representations

The modeling and simulation of stochastic reaction–diffusion processes is a topic of steady interest that is approached with a wide range of methods. At the level of particle-resolved descriptions, where chemical reactions are coupled to the spatial diffusion of individual particles, there exist comprehensive numerical simulation schemes, while the corresponding mathematical formalization is relatively underdeveloped. The aim of this paper is to provide a framework to systematically formulate the probabilistic evolution equation, termed chemical diffusion master equation (CDME), that governs particle-based stochastic reaction–diffusion processes. To account for the non-conserved and unbounded particle number of this type of open systems, we employ a classical analogue of the quantum mechanical Fock space that contains the symmetrized probability densities of the many-particle configurations in space. Following field-theoretical ideas of second quantization, we introduce creation and annihilation operators that act on single-particle densities and provide natural representations of symmetrized probability densities as well as of reaction and diffusion operators. These operators allow us to consistently and systematically formulate the CDME for arbitrary reaction schemes. The resulting form of the CDME further serves as the foundation to derive more coarse-grained descriptions of reaction–diffusion dynamics. In this regard, we show that a discretization of the evolution equation by projection onto a Fock subspace generated by a finite set of single-particle densities leads to a generalized form of the well-known reaction–diffusion master equation, which supports non-local reactions between grid cells and which converges properly in the continuum limit.

DC and optical signatures of the reconstructed Fermi surface for electrons with parabolic band

We study the main intra-band and inter-band transport properties at zero temperature of free electron-like system undergoing a topological reconstruction of the Fermi surface for the two-dimensional and three-dimensional case. The calculated intra-band properties include the single-particle density of states, the total and the effective concentrations of electrons and the thermopower. As for the inter-band case, the real part of the conductivity has been calculated within the vanishing inter-band relaxation approximation as a function of the incident photon energy. Within this approach, it is shown that the optical conductivity has a nonvanishing component parallel to the reconstruction wave vector and the shape which depends on the value of the Fermi energy. Each dimensionality has its particular features in the transport quantities presented in the paper, which are discussed and compared with those in the free electron scenario. Finally, we identify the signature of the topological reconstruction of the Fermi surface in the intra-band and inter-band transport functions.

RTGW2020: An efficient implementation of the multi-orbital Gutzwiller method with general local interactions

In the present paper, we propose an efficient numerical scheme for Gutzwiller method for multi-band Hubbard models with general onsite Coulomb interaction. Following the basic idea of Deng et al. (2009) [26] and extensions by Lanata et al. (2012) [28], the ground state is variationally determined through optimizing the total energy with respect to the variational single particle density matrix (n0), which is called “outer loop”. In the corresponding “inner loop” where n0 is fixed, the non-interacting wave function and the parameters contained in the Gutzwiller projector are determined by a two-step iterative approach. All derivatives of the implementation process have been analytically derived, which allows us to apply some advanced minimization or root-searching algorithms for both the inner and outer loops leading to the highly efficient convergence. In addition, an atomic diagonalization method taking the point group symmetry into account has been developed for the customized design of the Gutzwiller projector, making it convenient to explore many interesting orders at a lower cost of computation. As benchmarks, several different types of correlated models have been studied utilizing the proposed method, which are in perfect agreement with the previous results by DMFT and multi-orbital slave-boson mean field method. Compared with the linear mixing method, Newton's method with analytical derivatives shows much faster convergence for the inner loop. As for the outer loop, the minimization using analytical derivatives also shows much better stability and efficiency compared with that using numerical derivatives.

High Harmonic Generation in Triangular Graphene Quantum Dots

Higher harmonic generation in plane graphene quantum dots initiated by intense coherent radiation is investigated using dynamical Hartree–Fock mean-field theory. A microscopic theory describing the extreme nonlinear optical response of plane graphene quantum dots is developed. The closed set of differential equations for the single-particle density matrix at the multiphoton interaction of graphene quantum dots and strong laser field is solved numerically. The obtained solutions indicate the significance of the type of edge and lateral size and the band gap and laser field strength in the process of high harmonic generation in the triangular graphene quantum dot.

Free-energy profiles from single-molecule cryo-electron microscopy

Cryo-electron microscopy (cryo-EM) extracts single-particle density projections of individual biolmolecules. Although cryo-EM is widely used for 3D reconstruction, due to its single-particle nature, it has the potential to provide information about a biomolecule's conformational variability and underlying free energy landscape. However, treating cryo-EM as a single molecule technique is challenging because of the low signal-to-noise ratio in the individual particles. In this work, we developed the cryo-BIFE method, a Bayesian framework that uses a path collective variable to extract free energy profiles and their uncertainties from cryo-EM images.

Dissipative dynamics in the free massive boson limit of the sine-Gordon model

We study the dissipative dynamics of one-dimensional fermions, described in terms of the sine-Gordon model in its free massive boson or semi-classical limit, while keeping track of forward scattering processes. The system is prepared in the gapped ground state, and then coupled to environment through local currents within the Lindblad formalism. The heating dynamics of the system is followed using bosonization. The single particle density matrix exhibits correlations between the left and right moving particles. While the density matrix of right movers and left movers is translationally invariant, the left-right sector is not, corresponding to a translational symmetry breaking charge density wave state. Asymptotically, the single particle density matrix decays exponentially with exponent proportional to -\gamma t|x|\Delta^2−γt|x|Δ2 where \gammaγ and \DeltaΔ are the dissipative coupling and the gap, respectively. The charge density wave order parameter decays exponentially in time with an interaction independent decay rate. The second R'enyi entropy grows linearly with time and is essentially insensitive to the presence of the gap.

Effect of Internal Insect Infestation on Single Kernel Mass and Particle Density of Corn and Wheat

HighlightsSingle kernel mass and particle density were not significantly affected by the number of rice weevils feeding within a corn kernel and lesser grain borers feeding within a wheat kernel.In both corn and wheat, single kernel mass decreased after the larval stage of internally feeding insects.Particle density increased linearly with insect age for both rice weevils in corn and lesser grain borer in wheat.The increasing particle density while the kernel mass was being eroded indicates that the kernel internal void was detected by the gas pycnometer employed for measurement of the true volume of grain kernels.Abstract. To model the dynamics of insect infestation in a grain handling system using the discrete element method (DEM), physical properties of the infested kernels compared to their sound counterparts are needed, specifically particle density and single kernel mass of infested kernels. Thus, the objective of this study was to determine the particle density and single kernel mass of internally infested kernels as affected by insect age. Corn and wheat were infested with internal feeders: rice weevil (RW), Sitophilus oryzae (L.), in corn and lesser grain borer (LGB), Rhyzopertha dominica (F.), in wheat. The internal feeders were allowed to grow and mature inside the kernels and properties were measured for representative samples selected using X-ray imaging approximately 14, 28, 35, and 42 days after the end of a 4-day oviposition period. The measured kernel physical properties were not affected by the number of internal insects per kernel. In both corn and wheat, single kernel mass decreased after the larval stage of internally feeding insects. Single kernel mass decreased from 374 mg in sound corn to 346 mg in corn with pre-emerged RW adults and from 31.4 mg in sound wheat to 25.9 mg in wheat with pre-emerged LGB adults. Particle density increased with insect age for both RW in corn and LGB in wheat with a linear trend. The increasing particle density while the kernel mass eroded indicates that kernel internal void was detected by the gas pycnometer employed for measurement of the true volume of grain kernels. Data obtained from this study enables effective DEM modeling of grain commingling of insect-infested and sound grain kernels in grain handling systems. Keywords: Corn, Insect age, Internal feeders, Insect infestation, Lesser grain borer, Particle density, Rice weevil, Single kernel mass, Wheat.

In-gap band in the one-dimensional two-orbital Kanamori-Hubbard model with interorbital Coulomb interaction

We study the electronic spectral properties at zero temperature of the one-dimensional (1D) version of the degenerate two-orbital Kanamori Hubbard model (KHM), one of the well established frameworks to study transition metal compounds, using state-of-the-art numerical techniques based on the Density Matrix Renormalization Group. While the system is Mott insulating for the half-filled case, as expected for an interacting 1D system, we find interesting and rich structures in the single-particle density of states (DOS) for the hole-doped system. In particular, we find the existence of in-gap states which are pulled down to lower energies from the upper Hubbard band (UHB) with increasing the inter-orbital Coulomb interaction $V$. We analyze the composition of the DOS by projecting it onto different local excitations and we observe that for large dopings these in-gap excitations are formed mainly by inter-orbital holon-doublon (HD) states and their energies follow approximately the HD states in the atomic limit. We observe that the Hund interaction $J$ increases the width of the in-gap band, as expected from the two-particle fluctuations in the Hamiltonian. The observation of a finite density of states within the gap between the Hubbard bands for this extended 1D model indicates that these systems present a rich excitation spectra which could help us understand the microscopic physics behind multi-orbital compounds.

Theory of spin–charge-coupled transport in proximitized graphene: an SO(5) algebraic approach

Establishing the conditions under which orbital, spin and lattice-pseudospin degrees of freedom are mutually coupled in realistic nonequilibrium conditions is a major goal in the emergent field of graphene spintronics. Here, we use linear-response theory to obtain a unified microscopic description of spin dynamics and coupled spin–charge transport in graphene with an interface-induced Bychkov–Rashba effect. Our method makes use of an SO(5) extension of the familiar inverse-diffuson approach to obtain a quantum kinetic equation for the single-particle density matrix that treats spin and pseudospin on equal footing and is valid for arbitrary external perturbations. As an application of the formalism, we derive a complete set of drift–diffusion equations for proximitized graphene with scalar impurities in the presence of electric and spin-injection fields which vary slowly in space and time. Our approach is amenable to a wide variety of generalizations, including the study of coupled spin–charge dynamics in layered materials with strong spin–valley coupling and spin–orbit torques in van der Waals heterostructures.

High-order harmonic generation from twisted bilayer graphene driven by a midinfrared laser field

Theoretical calculations of high-harmonic generation (HHG) from commensurate twisted bilayer graphene (tBLG) under intense laser fields are performed. The nonlinear electron dynamics in tBLG is considered by solving the Liouville--von Neumann equation for a single-particle density matrix, which combines the full energy bands and momentum matrix elements within the framework of tight-binding approximation. We show that the pump intensity determines the relative magnitude of two components of the harmonic spectrum parallel and perpendicular to driving polarization. The important dependence of HHG on twisted angles and crystal orientations is also presented. Especially in the absence of the relaxation process, the harmonic emission for twisted angles around 10 \ifmmode^\circ\else\textdegree\fi{} exhibits an evident decrease in efficiency per layer compared to monolayer graphene (MLG), which can be interpreted according to Fermi velocity modification. Our calculation also shows that the relative emission efficiency of different harmonic orders between tBLG and MLG contains redundant information on both the dephasing time and an empirical parameter characterizing the decay of the interlayer electron hopping, thus suggesting an all-optical method for the reconstruction of the two parameters. The reconstruction feasibility is successfully demonstrated by a simple optimization algorithm even if considering the possible experimental uncertainty of both driving pulse parameters and high-harmonic signals. Our results show that HHG spectroscopic characteristics in tBLG might serve as a fingerprint to identify the geometric stacking angle and the electronic interaction between adjacent layers, as well as the strong-field laser induced ultrafast dephasing process.

Green’s function approach to the Bose–Hubbard model with disorder

We analyse the distinction between the three different ground states presented by a system of spinless bosons with short-range interactions submitted to a random potential using the disordered Bose–Hubbard model. The criteria for identifying the superfluid, the Mott-insulator, and the Bose-glass phases at finite temperatures are discussed for small values of the kinetic energy associated with the tunnelling of particles between potential wells. Field theoretical considerations are applied in order to construct a diagrammatic hopping expansion to the finite-temperature Green’s function. By performing a summation of subsets of diagrams we are able to find the condition to the long-range correlations which leads to the phase boundary between superfluid and insulating phases. The perturbative expression to the local correlations allows us to calculate an approximation to the single-particle density of states of low-energy excitations in the presence of small hopping, which characterizes unambiguously the distinction between the Mott-insulator and the Bose-glass phases. We obtain the phase diagram for bounded on-site disorder. It is demonstrated that our analysis is capable of going beyond the mean-field theory results for the classification of these different ground states.

A Bayesian approach to extracting free-energy profiles from cryo-electron microscopy experiments

Cryo-electron microscopy (cryo-EM) extracts single-particle density projections of individual biomolecules. Although cryo-EM is widely used for 3D reconstruction, due to its single-particle nature it has the potential to provide information about a biomolecule’s conformational variability and underlying free-energy landscape. However, treating cryo-EM as a single-molecule technique is challenging because of the low signal-to-noise ratio (SNR) in individual particles. In this work, we propose the cryo-BIFE method (cryo-EM Bayesian Inference of Free-Energy profiles), which uses a path collective variable to extract free-energy profiles and their uncertainties from cryo-EM images. We test the framework on several synthetic systems where the imaging parameters and conditions were controlled. We found that for realistic cryo-EM environments and relevant biomolecular systems, it is possible to recover the underlying free energy, with the pose accuracy and SNR as crucial determinants. We then use the method to study the conformational transitions of a calcium-activated channel with real cryo-EM particles. Interestingly, we recover not only the most probable conformation (used to generate a high-resolution reconstruction of the calcium-bound state) but also a metastable state that corresponds to the calcium-unbound conformation. As expected for turnover transitions within the same sample, the activation barriers are on the order of k_BT. We expect our tool for extracting free-energy profiles from cryo-EM images to enable more complete characterization of the thermodynamic ensemble of biomolecules.