Identical Particles Research Articles

Water layer and radiation damage effects on the orientation recovery of proteins in single-particle imaging at an X-ray free-electron laser

The noise caused by sample heterogeneity (including sample solvent) has been identified as one of the determinant factors for a successful X-ray single-particle imaging experiment. It influences both the radiation damage process that occurs during illumination as well as the scattering patterns captured by the detector. Here, we investigate the impact of water layer thickness and radiation damage on orientation recovery from diffraction patterns of the nitrogenase iron protein. Orientation recovery is a critical step for single-particle imaging. It enables to sort a set of diffraction patterns scattered by identical particles placed at unknown orientations and assemble them into a 3D reciprocal space volume. The recovery quality is characterized by a “disconcurrence” metric. Our results show that while a water layer mitigates protein damage, the noise generated by the scattering from it can introduce challenges for orientation recovery and is anticipated to cause problems in the phase retrieval process to extract the desired protein structure. Compared to these disadvantageous effects due to the thick water layer, the effects of radiation damage on the orientation recovery are relatively small. Therefore, minimizing the amount of residual sample solvent should be considered a crucial step in improving the fidelity and resolution of X-ray single-particle imaging experiments.

A universal mechanism for the development of self-ordering processes in systems of identical particles

A universal mechanism for the development of self-ordering processes in systems of identical particles

Back Cover: Robust Engineering of Maximally Entangled States by Identical Particle Interferometry (Adv. Quantum Technol. 9/2023)

Back Cover: Robust Engineering of Maximally Entangled States by Identical Particle Interferometry (Adv. Quantum Technol. 9/2023)

The quantum harmonic oscillator with icosahedral symmetry and some explicit wavefunctions

The Dunkl Laplacian is used to define the Hamiltonian of a modified quantum harmonic oscillator, associated with any finite reflection group. The potential is a sum of the inverse squares of the linear functions whose zero sets are the mirrors of the group’s reflections. The symmetric group version of this is known as the Calogero-Moser model of N identical particles on a line. This paper focuses on the group of symmetries of the regular icosahedron, associated to the root system of type H3. Special wavefunctions are defined by a generating function arising from the vertices of the icosahedron and have the key property of allowing easy calculation of the effect of the Dunkl Laplacian. The ground state is the product of a Gaussian function with powers of linear functions coming from the root system. Two types of wavefunctions are considered, inhomogeneous polynomials with specified top-degree part, and homogeneous harmonic polynomials. The squared norms for both types are explicitly calculated. Symmetrization is applied to produce the invariant polynomials of both types, as well as their squared norms. The action of the angular momentum square on the harmonic homogeneous polynomials is determined. There is also a sixth-order operator commuting with the Hamiltonian and the group action.

Particle fusion of super-resolution data reveals the unit structure of Nup96 in Nuclear Pore Complex

Single molecule localization microscopy offers resolution nearly down to the molecular level with specific molecular labelling, and is thereby a promising tool for structural biology. In practice, however, the actual value to this field is limited primarily by incomplete fluorescent labelling of the structure. This missing information can be completed by merging information from many structurally identical particles in a particle fusion approach similar to cryo-EM single-particle analysis. In this paper, we present a data analysis of particle fusion results of fluorescently labelled Nup96 nucleoporins in the Nuclear Pore Complex to show that Nup96 occurs in a spatial arrangement of two rings of 8 units with two Nup96 copies per unit giving a total of 32 Nup96 copies per pore. We use Artificial Intelligence assisted modeling in Alphafold to extend the existing cryo-EM model of Nup96 to accurately pinpoint the positions of the fluorescent labels and show the accuracy of the match between fluorescent and cryo-EM data to be better than 3 nm in-plane and 5 nm out-of-plane.

Hyper-entangling mesoscopic bound states

We predict hyper-entanglement generation by binary scattering of mesoscopic bound states, considering solitary waves in Bose–Einstein condensates containing thousands of identical Bosons. For it to occur, the underlying many-body Hamiltonian must not be integrable, and the pre-collision quantum state of the solitons needs to be fragmented. Under these conditions, we show that the post-collision state will be hyper-entangled in spatial degrees of freedom and atom number within solitons, for realistic parameters. The effect links aspects of non-linear systems and quantum-coherence and the entangled post-collision state challenges present entanglement criteria for identical particles. Our results are based on simulations of colliding quantum solitons in a quintic interaction model beyond the mean-field, using the truncated Wigner approximation.

Generating indistinguishability within identical particle systems: spatial deformations as quantum resource activators.

Identical quantum subsystems can possess a property which does not have any classical counterpart: indistinguishability. As a long-debated phenomenon, identical particles' indistinguishability has been shown to be at the heart of various fundamental physical results. When concerned with the spatial degree of freedom, identical constituents can be made indistinguishable by overlapping their spatial wave functions via appropriately defined spatial deformations. By the laws of quantum mechanics, any measurement designed to resolve a quantity which depends on the spatial degree of freedom only and performed on the regions of overlap is not able to assign the measured outcome to one specific particle within the system. The result is an entangled state where the measured property is shared between the identical constituents. In this work, we present a coherent formalization of the concept of deformation in a general [Formula: see text]-particle scenario, together with a suitable measure of the degree of indistinguishability. We highlight the basic differences with non-identical particles scenarios and discuss the inherent role of spatial deformations as entanglement activators within the spatially localized operations and classical communication operational framework. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Indistinguishable entangled fermions: basics and future challenges.

The study of entanglement in systems composed of identical particles raises interesting challenges with far-reaching implications in both, our fundamental understanding of the physics of composite quantum systems, and our capability of exploiting quantum indistinguishability as a resource in quantum information theory. Impressive theoretical and experimental advances have been made in the last decades that bring us closer to a deeper comprehension and to a better control of entanglement. Yet, when it involves composites of indistinguishable quantum systems, the very meaning of entanglement, and hence its characterization, still finds controversy and lacks a widely accepted definition. The aim of the present paper is to introduce, within an accessible and self-contained exposition, the basic ideas behind one of the approaches advanced towards the construction of a coherent definition of entanglement in systems of indistinguishable particles, with focus on fermionic systems. We also inquire whether the corresponding tools developed for studying entanglement in identical-fermion systems can be exploited when analysing correlations in distinguishable-party systems, in which the complete information of the individual parts is not available. Further, we open the discussion on the broader problem of constructing a suitable framework that accommodates entanglement in the presence of generalized statistics. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Entanglement and indistinguishability: facing some challenges from a new perspective.

While entanglement in the case of distinguishable particles is clearly understood, in the case of indistinguishable particles, there is still a wide debate regarding basic conceptual issues. Here, I will address two such issues. First, the debate almost always rests on a differentiated treatment of the cases of distinguishability and indistinguishability, even with respect to the definition of the concept of entanglement. Second, the fact that symmetrized and antisymmetrized states of indistinguishable particles are non-factorizable leads to certain perplexities about the very nature of entanglement. In the present work, both issues will be addressed from the perspective of an ontology of properties, which finds its natural expression in the algebraic formalism of quantum mechanics. The final goal will be to show that the proposed ontology allows a unified treatment of entanglement in the distinguishability and indistinguishability cases and offers a straightforward way out to perplexities. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Entanglement and discernibility of identical particles.

This article follows an unorthodox approach to the individuation of quantum particles of the same type. According to this approach, individuation of the components of a composite system of identical particles is done not with the help of unphysical labels (indices) but physically meaningful projection operators. This unorthodox conception requires a modification of the standard notion of entanglement, in order to exclude states whose non-factorizability arises merely from the (anti)symmetrization of a product state. I will report several facts regarding the connections of the modified concept of entanglement with the issue of discernibility. I will also discuss recent experiments involving measurement-induced entanglement, and I will point out that they do not threaten the cogency of the new concept of entanglement. The statistical correlations observed in these experiments are explainable not by the entanglement of the initial state but by the creation of a new, genuinely entangled state by means of a pre-measurement selection. Finally, I will identify and discuss a genuine difference between non-entangled but non-factorizable states of identical particles and ordinary product states, which is that the former but not the latter admits an infinity of alternative and incompatible individuations by single-particle properties. This phenomenon can be accounted for using the concept of emergent particles proposed by Dennis Dieks. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Interaction of Nanoparticles in Electrolyte Solutions.

The interaction between nanoparticles includes several components; however, the most frequently used are electrostatic, caused by overlapping double electrical layers, and London-van der Waals interactions, caused by quantum and thermodynamic fluctuations of electromagnetic fields. Only these two kinds of interaction are considered below. The electrostatic interaction is calculated based on the linearized Poisson-Boltzmann equation for particles with constant electrical potential of the surfaces (constant ζ potentials). An exact solution of the problem is obtained for both identical particles and particles of different sizes. For the London-van der Waals interaction, the screening of static fluctuations and the retardation of electromagnetic fields for the dispersive part of the interaction are taken into account. The total interaction energy for two particles was calculated for a range of possible nanoparticle sizes from 1 to 103 nm and electrolyte concentration from 10-2 to 10-6 mol/L. The predominance of the London-van der Waals force over the shielded electrostatic repulsion force was found at high electrolyte concentrations in the range from 10-2 to 10-3 mol/L at large interparticle distances.

Robust Engineering of Maximally Entangled States by Identical Particle Interferometry

AbstractThis study proposes a procedure for the robust preparation of maximally entangled states of identical fermionic qubits, studying the role played by particle statistics in the process. The protocol exploits externally activated noisy channels to reset the system to a known state. The subsequent interference effects generated at a beam splitter result in a mixture of maximally entangled Bell states and NOON states. It also discusses how every maximally entangled state of two fermionic qubits distributed over two spatial modes can be obtained from one another by fermionic passive optical transformations. Using a pseudospin‐insensitive, non‐absorbing, parity check detector, the proposed technique is thus shown to deterministically prepare any arbitrary maximally entangled state of two identical fermions. These results extend recent findings related to bosonic qubits. Finally, it analyzes the performance of the protocol for both bosons and fermions when the externally activated noisy channels are not used and the two qubits undergo standard types of noise. The results supply further insights toward viable strategies for noise‐protected entanglement exploitable in quantum‐enhanced technologies.

A generalized scattering theory in quantum mechanics

In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of particle. In laboratory frame, a generalized Lippmann-Schwinger scattering equation is derived. We emphasized that the derivation is rigorous, even for treating infinitesimals. No manual operation such as analytical continuation is allowed. In the case that before scattering N particles are plane waves and after the scattering they are new plane waves, the transition amplitude and transition probability are given and the generalized S matrix is presented. It is proved that the transition probability from a set of plane waves to a new set of plane waves of the N particles equal to that of the reciprocal process. The generalized theory is applied to the cases of one- and two-particle scattering as two examples. When applied to single-particle scattering problems, our generalized formalism degrades to that usually seen in the literature. When our generalized theory is applied to two-particle scattering problems, the formula of the transition probability of two-particle collision is given. It is shown that the transition probability of the scattering of two free particles is identical to that of the reciprocal process. This transition probability and the identity are needed in deriving Boltzmann transport equation in statistical mechanics. The case of identical particles is also discussed.

Boson bunching is not maximized by indistinguishable particles

Boson bunching is among the most remarkable features of quantum physics. A celebrated example in optics is the Hong–Ou–Mandel effect, where the bunching of two photons arises from a destructive quantum interference between the trajectories where they both either cross a beamsplitter or are reflected. This effect takes its roots in the indistinguishability of identical photons. Hence, it is generally admitted—and experimentally verified—that bunching vanishes as soon as photons can be distinguished, for example, when they occupy distinct time bins or have different polarizations. Here we disprove this alleged straightforward link between indistinguishability and bunching by exploiting a recent finding in the theory of matrix permanents. We exhibit a family of optical circuits such that the bunching of photons into two modes can be substantially boosted by making them partially distinguishable via an appropriate polarization pattern. This boosting effect is already visible in a seven-photon interferometric process, making the observation of this phenomenon within reach of current photonic technology. This unexpected behaviour questions our understanding of multiparticle interference in the grey zone between indistinguishable bosons and classical particles. A common belief about boson bunching—fully indistinguishable bosons exhibit the utmost bunching—is theoretically disproved with seven photons of distinct polarization in a seven-mode interferometric process. Enhanced bunching could thus be observed with partially distinguishable photons.

Direct numerical simulations of oscillatory boundary layers over rough walls

Numerical simulations of turbulent oscillatory flow over a bed made of fixed, identical spherical particles have been performed. Oscillations are imposed through a shear-driven forcing by means of an harmonic velocity boundary condition on the bed. A parametric study on the effect of the particle size and Reynolds number, spanning from the laminar to the fully-turbulent regimes, has been performed. Results show that the temporal evolution of the flow over the rough bed is modified compared to the classical Stokes’ solution for smooth-wall laminar boundary layers. In the turbulent cases, the phase shift in the velocity at various distances from the bed is reduced compared to the laminar case. The phase shift reduction seems predominantly dependent on the Reynolds number rather than the bed morphology, which suggests that a unique curve may exist for large enough values of the Reynolds number. Turbulence is observed during the deceleration phases of the cycle, with the presence of a logarithmic layer in the velocity profile, and “canonical” distribution of Reynolds shear stress and turbulent kinetic energy production. During the acceleration, the logarithmic region is suppressed and the Reynolds shear stress changes sign. Nevertheless, the turbulent kinetic energy production becomes only slightly negative, because the shear is also very small during these phases. A good correlation between Reynolds and shear stresses is also evidenced from the eddy viscosity profiles, which show the presence of plateau in the outer layers approximately constant across the phases of the cycle. Turbulence in the outer layers is related to structures which develop during previous cycles and propagate from the bed to the bulk of the channel. When the flow is fully developed, anisotropy maps show similar distributions to unidirectional wall-bounded flows, while departures from canonical distributions during the transient phases are mild, because the flow responds very rapidly to the time-varying forcing.

Identical Particle and Lepton Mass Effects in the Decay $$H\rightarrow Z^*(\rightarrow \tau ^+\tau ^-)+Z^*(\rightarrow \tau ^+\tau ^-)$$

We consider identical particle and lepton mass effects in the cascade decay $H\to Z^\ast(\to\tau^+\tau^-)+Z^\ast(\to\tau^+\tau^-)$. Since the scale of the problem is set by the off-shellness $p_a^2$ and $p_b^2$ of the respective gauge bosons in the limits ($4m_\tau^2\le p_a^2,p_b^2\le (m_H-2m_\tau)^2$) and not by $m_H^2$, lepton mass effects are nonnegligible in particular close to the threshold of the off-shell decays. We calculate the rates and single angle decay distributions and compare them with the corresponding rates and single angle decay distributions for the nonidentical particle decays $H\to Z^\ast(\to e^+e^-)+Z^\ast(\to\mu^+\mu^-)$ involving negligible lepton masses.

Computational investigation of flow characteristics and particle deposition patterns in a realistic human airway model under different breathing conditions

Airborne particle pollution causes a range of respiratory and cardiovascular disorders by entering the human respiratory system through the breathing process. The administration of pharmaceutical particles by inhalation is another effective way to treat pulmonary illnesses. Studying particle deposition in the respiratory system during human breathing is crucial to maintaining human health. This necessity served as the impetus for this work, which aims to investigate how the airflow and particles' deposition are influenced by constant inhalation and circulatory breathing, particle diameter, and changes in airflow rate. The focus of this paper is to compare the particle deposition results of circulatory respiration with constant respiration. Based on computed tomography (CT) scan pictures, a precise human airway model from the mouth cavity to the fifth-generation bronchi was created. Flow fields and particle deposition inside the respiratory tract were examined at varied breathing rates (30, 60, and 90 L/min of constant and circulatory breathing) and varying haled particle sizes (5 and 10 µm). The results showed that the oropharyngeal area is often where the majority of particles are deposited. The particle distribution fraction is more significant in the bronchial area than the oropharyngeal region due to lower inhalation velocities and smaller particle sizes. For particles with a diameter of 5 µm, constant respiration and circulatory respiration have virtually identical particle distribution fractions in each region. For particles with a diameter of 10 µm, the particle distribution fraction for circulatory respiration is slightly higher than for constant respiration in the bronchial region as the flow rate increases. For both constant and circulatory respiration, particles are deposited more in the right lung and less in the left. These results contribute to further research on respiratory diseases caused by inhaled particles and guide inhalation therapy for better treatment outcomes.

A universal mechanism for the development of self-ordering processes in systems of identical particles

Based on the hypothesis of the existence of wave long-range action and its role in the development of self-ordering processes, expressed by us in previous works, we carried out a methodological analysis of the applicability of wave representations in systems of identical particles. The main attention in the analysis is paid to the practical application of de Broglie waves in systems of interacting particles. For this purpose, Bohr's theory of the hydrogen atom has been revised and inconsistencies that contradict modern ideas have been corrected. Two conclusions are made: wave representations of particles are of a material nature; the de Broglie wavelength should be determined in terms of the relative momentum of the interacting particles . Based on the materiality of wave representations, the features of the long-wave interaction of particles are determined. It is emphasized that in many manifestations this interaction has a resonant character. This interaction is the foundation for the universal mechanism for the development of self-ordering processes in systems of identical particles. The paper presents an algorithm for the emergence and functioning of a universal mechanism. The condition for the emergence is always any withdrawal of the system from the state of isotropic chaos and the formation of an initial subgroup of particles with the same magnitude and direction of momenta. The most common cause leading to the fulfillment of the condition is monoenergization of the spectrum of particles in the system. The causative agent of the mechanism is direct collisions of particles, in which the probability of long-wavelength representations is the highest. The development of the mechanism is limited only by the fulfillment of the percolation condition - overcoming the percolation threshold. The final stage of the mechanism is the formation of a superfluid component - a kind of macroparticle that does not interact with walls and other molecules. A characteristic wave feature of such a macroparticle is its coherence. Several final stages in the development of self-ordering processes for typical special phenomena in systems of identical particles are analyzed.

Many body density of states of a system of non interacting spinless fermions

The modeling of out-of-equilibrium many-body quantum systems requires to go beyond low-energy physics and single or few bodies densities of states. Many-body localization, presence or lack of thermalization and quantum chaos are examples of phenomena in which states at different energy scales, including highly excited ones, contribute to dynamics and therefore affect the system’s properties. Quantifying these contributions requires the many-body density of states (MBDoS), a function whose calculation becomes challenging even for non-interacting identical particles due to the difficulty to enumerate accessible states while enforcing the exchange symmetry. In the present work, we introduce a new approach to evaluate the MBDoS in the general case of non-interacting systems of identical quantum particles. The starting point of our method is the principal component analysis of a filling matrix F describing how N particles can be distributed into L single-particle energy levels. We show that the many body spectrum can be expanded as a weighted sum of singular vectors of the filling matrix. The weighting coefficients only involve renormalized energies obtained from the single body spectrum. We illustrate our method in two classes of problems that are mapped into spinless fermions : (i) non-interacting electrons in a homogeneous tight-binding model in 1D and 2D, and (ii) interacting spins in a chain under a transverse field.

Principles of Affinity Selection.

The most common application of phage-display technology is the discovery of peptides or proteins that specifically bind some molecule or other substance of interest-for example, antibodies that specifically bind an antigen. The discovery process starts with a library encompassing a very large array of proteins or peptides with a great diversity of binding specificities-for example, single-chain antibodies with a great diversity of antigen-binding sites. Each member of the array is displayed on the surface of hundreds to billions of identical virus particles (virions) belonging to a single-phage clone; the library as a whole comprises millions to billions of such clones, all mixed together in a single vessel. Affinity selection is the process by which a molecule or substance of interest-generically called the selector-is used to select very rare clones in the library displaying proteins or peptides that happen to bind the selector with high affinity and selectivity. Here, I explain general principles guiding a successful affinity-selection project-principles grounded in phage biology, kinetics of reversible binding, technological advances, and the practical experience of thousands of investigators around the globe.