Systems Of Identical Particles Research Articles

Topology-induced quantum transition in multiparticle systems in vicinity of a black hole

The qualitative change of the type of particle trajectory homotopy in close vicinity of general-relativistic gravitational singularity affects quantum statistics in systems of identical indistinguishable particles at passing the photon sphere rim of a Schwarzschild black hole. This causes a local departure from the Pauli exclusion principle, which results in some high energy effects manifesting themselves when the matter is falling into a black hole. The release of the energy can take place at the rim of the photon sphere of a black hole due to the decay of Fermi spheres in highly compressed fermion systems entering this region. The effect is observable at activity of quasars or at collapses of neutron star mergers. The related supplementation to conventional models of the accretion disc luminosity by additional radiation from close vicinity of the event horizon of a massive black hole powering super-luminous quasar is proposed and compared with observations. The source of short-lasting gamma-ray bursts has been also identified at collapses of unstable neutron star mergers due to the decay of Fermi sphere of neutrons. The duration and spectrum of the related e-m radiation bursts estimated by the Fermi golden rule for the Fermi sphere decay agree with observations. The quantum statistics effect contributes also to the radiation of transients of micro-quasars and short lasting brightening episodes in closer active galactic nuclei. The proposed quantum effect changes the premises for the current discussion of the information paradox and hypothesis of the black hole firewall.

Modeling the structure and thermodynamics of multicomponent and polydisperse hard-sphere dispersions with continuous potentials.

A model system of identical particles interacting via a hard-sphere potential is essential in condensed matter physics; it helps to understand in and out of equilibrium phenomena in complex fluids, such as colloidal dispersions. Yet, most of the fixed time-step algorithms to study the transport properties of those systems have drawbacks due to the mathematical nature of the interparticle potential. Because of this, mapping a hard-sphere potential onto a soft potential has been recently proposed [Báez et al., J. Chem. Phys. 149, 164907 (2018)]. More specifically, using the second virial coefficient criterion, one can set a route to estimate the parameters of the soft potential that accurately reproduces the thermodynamic properties of a monocomponent hard-sphere system. However, real colloidal dispersions are multicomponent or polydisperse, making it important to find an efficient way to extend the potential model for dealing with such kind of many-body systems. In this paper, we report on the extension and applicability of the second virial coefficient criterion to build a description that correctly captures the phenomenology of both multicomponent and polydisperse hard-sphere dispersions. To assess the accuracy of the continuous potentials, we compare the structure of soft polydisperse systems with their hard-core counterpart. We also contrast the structural and thermodynamic properties of soft binary mixtures with those obtained through mean-field approximations and the Ornstein-Zernike equation for the two-component hard-sphere dispersion.

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

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'.

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'.

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.

Symmetry of Identical Particles, Modern Achievements in the Pauli Exclusion Principle, in Superconductivity and in Some Other Phenomena

In this review, the modern achievements in studies of the Pauli exclusion principle (PEP) and the properties of the identical particle systems when PEP is not fulfilled are discussed. The validity of conception of the spin in the framework of density functional theory (DFT) approaches is analyzed. The modern state of the recently discovered Fe-based superconductors is discussed in detail. These materials belong to the paramagnetic semimetal family and become superconductors upon doping. Recently, in 2020, room-temperature superconductivity was realized. However, from the following discussion in the SC community, it was not evident that the results of room-temperature superconductivity have been repeated by other laboratories. Thus, the question “is room temperature really achieved?” is still open. In the concluding remarks, we present the explanation of why the PEP limitations on the symmetry of identical particles system exist in nature, and following from it, some important consequences.

Forbidden trajectories for path integrals

The problem of the availability of trajectories for the Feynman path integral is considered. Forbidden trajectories for single-particle integrals are featured in the case of quantum tunneling across barriers. In the case of multiparticle systems of indistinguishable identical particles, some limits for the availability of cyclotron braid trajectories are demonstrated, which leads to the explanation of statistics and correlation in quantum Hall systems of interacting 2D electrons. The homotopy-type restrictions for trajectories close to general-relativity singularities are discussed with indication of quantum properties of black holes manifesting themselves at quasar luminosity or at neutron star merger collapses. The related supplementation to conventional models of accretion disk luminosity in the close vicinity of the event horizon of a supermassive black hole is proposed and compared with observations.

Quantum indistinguishability through exchangeability

Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrisation postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.

Quantum Statistics of Identical Particles

The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical behaviors are excluded a priori. A more general approach is to ask what other many-particle statistics are consistent with the indistinguishability of identical particles. This strategy offers a way to discuss possible violations of the Pauli Exclusion Principle, and it leads to some interesting issues related to preparation of states and a superselection rule arising from invariance under the permutation group.

Investigating and improving student understanding of the basics for a system of identical particles

We discuss an investigation of students' difficulties with systems of non-interacting identical particles. The investigation was carried out in advanced quantum mechanics courses at both the undergraduate and graduate levels by administering free-response and multiple-choice questions and conducting individual interviews with students. This research on student difficulties was used as a guide to develop and evaluate a Quantum Interactive Learning Tutorial (QuILT) that helps students develop a functional understanding of the concepts necessary for determining the many-particle Hamiltonian and stationary state wavefunctions for a system of non-interacting identical particles.

Witnessing pairing correlations in identical-particle systems

Quantum correlations and entanglement in identical-particle systems have been a puzzling question which has attracted vast interest and widely different approaches. Witness formalism developed first for entanglement measurement can be adopted to other kind of correlations. An approach is introduced by Kraus \emph{et al.}, [Phys. Rev. A \textbf{79}, 012306 (2009)] based on pairing correlations in fermionic systems and the use of witness formalism to detect pairing. In this contribution, a two-particle-annihilation operator is used for constructing a two-particle observable as a candidate witness for pairing correlations of both fermionic and bosonic systems. The corresponding separability bounds are also obtained. Two different types of separability definition are introduced for bosonic systems and the separability bounds associated with each type are discussed.

Toward a relativistic microscopic substantiation of thermodynamics: classical relativistic many-particle dynamics

An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The law of variation of the energy of a system of particles in terms of the microscopic distribution function is obtained.

Path-integral approach to the thermodynamics of bosons with memory: Partition function and specific heat

For a system of bosons that interact through a class of general memory kernels, a recurrence relation for the partition function is derived within the path-integral formalism. This approach provides a generalization to previously known treatments in the literature of harmonically coupled systems of identical particles. As an example the result is applied to the specific heat of a simplified model of an open quantum system of bosons, harmonically coupled to a reservoir of distinguishable fictitious masses.

Entanglement and Non-Locality in Quantum Protocols with Identical Particles.

We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism, whereby it is the entanglement of the modes that can be populated by the particles that really matters and not the particles themselves. Indeed, by means of a metrological and of a teleportation protocol, we show that inconsistencies arise in formulations that force entanglement and non-locality to be properties of the identical particles rather than of the modes they can occupy. The reason resides in the fact that orthogonal modes can always be addressed while identical particles cannot.

Distinguishing noisy boson sampling from classical simulations

Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise. Recently found classical algorithms can efficiently approximate, to any small error, the output of boson sampling with finite-amplitude noise. In this work it is shown analytically and confirmed by numerical simulations that one can efficiently distinguish the output distribution of such a noisy boson sampling from the approximations accounting for low-order quantum multiboson interferences, what includes the mentioned classical algorithms. The number of samples required to tell apart the quantum and classical output distributions is strongly affected by the previously unexplored parameter: density of bosons, i.e., the ratio of total number of interfering bosons to number of input ports of interferometer. Such critical dependence is strikingly reminiscent of the quantum-to-classical transition in systems of identical particles, which sets in when the system size scales up while density of particles vanishes.

Taming identical particles for discerning the genuine non-locality

This work provides a comprehensive approach to analyze the entanglement between subsystems generated by identical particles, based on the symmetric/exterior algebra (SEA) and microcausality. Our method amends the no-labeling approach (NLA) to quantify any type of identical particles' entanglement, especially fermions with the parity superselection rule. We can analyze the non-local properties of identical particles' states in a fundamentally equivalent way to those for non-identical particles, which is achieved by the factorizability of the total Hilbert space of identical particles. This formal correspondence between identical and non-identical particle systems turns out to be useful for quantifying the non-locality generated by identical particles, such as the maximal CHSH inequality violation and the GHJW theorem of identical particles.

Role of mixed permutation symmetry sectors in the thermodynamic limit of critical three-level Lipkin-Meshkov-Glick atom models.

We introduce the notion of mixed symmetry quantum phase transition (MSQPT) as singularities in the transformation of the lowest-energy state properties of a system of identical particles inside each permutation symmetry sector μ, when some Hamiltonian control parameters λ are varied. We use a three-level Lipkin-Meshkov-Glick model, with U(3) dynamical symmetry, to exemplify our construction. After reviewing the construction of U(3) unitary irreducible representations using Young tableaux and the Gelfand basis, we first study the case of a finite number N of three-level atoms, showing that some precursors (fidelity susceptibility, level population, etc.) of MSQPTs appear in all permutation symmetry sectors. Using coherent (quasiclassical) states of U(3) as variational states, we compute the lowest-energy density for each sector μ in the thermodynamic N→∞ limit. Extending the control parameter space by μ, the phase diagram exhibits four distinct quantum phases in the λ-μ plane that coexist at a quadruple point. The ground state of the whole system belongs to the fully symmetric sector μ=1 and shows a fourfold degeneracy, due to the spontaneous breakdown of the parity symmetry of the Hamiltonian. The restoration of this discrete symmetry leads to the formation of four-component Schrödinger cat states.

Core-softened water-alcohol mixtures: the solute-size effects.

Water is the most anomalous material on Earth, with a long list of thermodynamic, dynamic and structural behaviors that deviate from what is expected. Recent studies have indicated that these anomalies may be related to a competition between two liquids, which means that water has a potential liquid-liquid phase transition (LLPT) that ends at a liquid-liquid critical point (LLCP). In a recent study [J. Mol. Liq., 2020, 320, 114420], using molecular dynamics simulations and a core-softened potential approach, we have shown that adding a simple solute such as methanol can "kill" the density-anomalous behavior as the LLCP is suppressed by spontaneous crystallization in a hexagonal close packing (HCP) crystal near the LLPT. Now, we extend this work to realize how longer-chain alcohols will affect the complex behavior of water-alcohol mixtures in the supercooled regime. Besides core-softened (CS) methanol, ethanol and 1-propanol were added to a system of identical particles that interact through the continuous shouldered well (CSW) potential. We observed that the density anomaly gradually decreases its extension in phase diagrams until it disappears with the growth of the non-polar chain and the alcohol concentration, different from the liquid-liquid phase transition (and the LLCP), which remained present in all analyzed mixtures, according to Nature, 2001, 409, 692. For our model, the longer non-polar chains and higher concentrations gradually impact the competition between the scales in the CS potential, leading to a gradual disappearing of the anomalies until the TMD total disappearance is observed when the first coordination shell structure is also affected: short-range ordering is favored, leading to less competition between short- and long-range ordering and, consequently, to the extinction of anomalies. Also, the non-polar chain size and concentration have an effect on the solid phases, favoring the hexagonal close packed (HCP) solid and the amorphous solid phase over the body-centered cubic (BCC) crystal. These findings help to elucidate the behavior of water solutions in the supercooled regime and indicate that the LLCP can be observed in systems without density-anomalous behavior.