Multiparticle Systems Research Articles

Absorption properties of identical atoms

Emission rates and other optical properties of multi-particle systems in collective and entangled states differ from those in product ones. We show the existence of similar effects in the absorption probabilities for (anti)symmetrized states of two identical atoms. The effects strongly depend on the overlapping between the atoms and differ for bosons and fermions. We propose a viable experimental verification of these ideas.

Relative locality in κ-Poincaré

We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum space leading to relative locality. We study the geometric properties of the momentum space described by κ-Poincaré and derive the consequences for particle propagation and energy–momentum conservation laws in interaction vertices, obtaining for the first time a coherent and fully workable model of the deformed relativistic kinematics implied by κ-Poincaré. We describe the action of boost transformations on multi-particle systems, showing that the covariance of the composed momenta requires a dependence of the rapidity parameter on the particle momenta themselves. Finally, we show that this particular form of the boost transformations keeps the validity of the relativity principle, demonstrating the invariance of the equations of motion under boost transformations.

BEST CONSTANTS AND POHOZAEV IDENTITY FOR HARDY–SOBOLEV-TYPE OPERATORS

This paper is threefold. Firstly, we reformulate the definition of the norm induced by the Hardy inequality (see [J. L. Vázquez and N. B. Zographopoulos, Functional aspects of the Hardy inequality. Appearance of a hidden energy, preprint (2011); http://arxiv. org/abs/1102.5661]) to more general elliptic and sub-elliptic Hardy–Sobolev-type operators. Secondly, we derive optimal inequalities (see [C. Cowan, Optimal inequalities for general elliptic operator with improvement, Commun. Pure Appl. Anal.9(1) (2010) 109–140; N. Ghoussoub and A. Moradifam, Bessel pairs and optimal Hardy and Hardy–Rellich inequalities, Math. Ann.349(1) (2010) 1–57 (electronic)]) for multiparticle systems in ℝN and Heisenberg group. In particular, we provide a direct proof of an optimal inequality with multipolar singularities shown in [R. Bossi, J. Dolbeault and M. J. Esteban, Estimates for the optimal constants in multipolar Hardy inequalities for Schrödinger and Dirac operators, Commun. Pure Appl. Anal.7(3) (2008) 533–562]. Finally, we prove an approximation lemma which allows to show that the domain of the Dirichlet–Laplace operator is dense in the domain of the corresponding Hardy operators. As a consequence, in some particular cases, we justify the Pohozaev-type identity for such operators.

PT -symmetric deformations of integrable models

We review recent results on new physical models constructed as -symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero–Moser–Sutherland type and nonlinear integrable field equations of Korteweg–de Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero–Moser–Sutherland models, we provide three alternative deformations: a complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real-valued field equations of nonlinear integrable systems; and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of Korteweg–de Vries type are studied with regard to different kinds of -symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.

Supergoop dynamics

We initiate a systematic study of the dynamics of multi-particle systems with supersymmetric Van der Waals and electron-monopole type interactions. The static interaction allows a complex continuum of ground state configurations, while the Lorentz interaction tends to counteract this configurational fluidity by magnetic trapping, thus producing an exotic low temperature phase of matter aptly named supergoop. Such systems arise naturally in $\mathcal{N}=2$ gauge theories as monopole-dyon mixtures, and in string theory as collections of particles or black holes obtained by wrapping D-branes on internal space cycles. After discussing the general system and its relation to quiver quantum mechanics, we focus on the case of three particles. We give an exhaustive enumeration of the classical and quantum ground states of a probe in an arbitrary background with two fixed centers. We uncover a hidden conserved charge and show that the dynamics of the probe is classically integrable. In contrast, the dynamics of one heavy and two light particles moving on a line shows a nontrivial transition to chaos, which we exhibit by studying the Poincar\'e sections. Finally we explore the complex dynamics of a probe particle in a background with a large number of centers, observing hints of ergodicity breaking. We conclude by discussing possible implications in a holographic context.

Direct Numerical Simulation of Fluid Flow and Mass Transfer in Dense Fluid–Particle Systems

In this paper, a novel simulation technique is presented to perform direct numerical simulation (DNS) of fluid flow and mass transfer in dense fluid–particle systems. The fluid–solid coupling is achieved via direct (i.e., implicit) incorporation of the boundary condition (with a second-order method) at the surface of the particles at the level of the discrete momentum and species conservation equations of the fluid. A fixed (Eulerian) grid is utilized to solve the Navier–Stokes equations for the entire computational domain. Dissipative particle–particle and/or particle–wall collisions are taken into account via a hard-sphere discrete particle (DP) approach, using a three-parameter particle–particle interaction model that accounts for normal and tangential restitution, as well as tangential friction. Following the verification of our method using well-known empirical expressions for the Sherwood number, we apply our method to study fluid–particle mass transfer in dense multiparticle systems involving rando...

Particle-fluid mass transfer in multiparticle systems at low Reynolds numbers

The problem of mass transfer between active solid particles and a fluid in multiparticle systems is examined with a focus on the stagnant and the low Reynolds number cases. This problem has attracted significant attention with regard to operation of fixed and fluidized beds. It is recognized that different Sherwood numbers can be defined depending on the choice of the reference concentration difference (driving force). An effective Sh has often been used to analyze experimental data based on an overall concentration difference across the bed. A local Sh can also be introduced based on a concentration difference close to the active particle. However, the use of these two different Sherwood numbers implies a different implementation of the mass balance equations.The mass balance equations are here analytically solved both under stagnant and non-stagnant conditions in a multiparticle system under suitable simplifying assumptions. Equations for the effective and local Sherwood numbers are derived for the general case and for the asymptotic limits. Allowance is given for the variation of bed voidage and volume fraction of active particles in the bed. It is shown that the local Sh only depends on geometrical and fluid-dynamics considerations and accordingly has a general validity. On the contrary, the effective Sh also depends on the assumptions made in deriving the mass balance equations across the bed (e.g., fluid plug flow). The use of the local Sh is therefore suggested.Results show that for Re→0 the limiting value of the local Sh is always a finite number, while the effective Sh tends to zero linearly with Re. It is shown that this result is simply a consequence of the plug flow assumption made in the bed mass balance. The general expressions derived here compare very well to experimental trends for the cases of large Reynolds numbers and of few isolated active spheres immersed in a bed of inert particles, where most of the reported experimental data gather. Unfortunately, for the most controversial case of very low Re in beds made entirely of active particles no reliable data appears to be available to check the accuracy of the expressions.

Effects of relative density on microwave heating of various carbon powder compacts microwave-metallic multi-particle coupling using spatially separated magnetic fields

We have investigated the microwave heating characteristics of non-magnetic conductive multi-particle systems using spatially separated electric and magnetic fields (Emax and Hmax, respectively) to determine the effects of the multi-particle structure on microwave heating. Pure carbon, carbon black, and artificial graphite multi-particle systems exhibited peak microwave absorption at specific relative densities only under Hmax. These absorptions can be categorized into two types: one originates from coupling between metal spheres, while the other originates from a heterogeneous distribution of particles.

Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem

A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of the standard pairing problem is established based on the Heine-Stieltjes correspondence. For $k$ pairs of valence nucleons on $n$ different single-particle levels, it is found that solutions of the Bethe ansatz equations can be obtained from one $(k+1)\ifmmode\times\else\texttimes\fi{}(k+1)$ and one $(n\ensuremath{-}1)\ifmmode\times\else\texttimes\fi{}(k+1)$ matrices, which are associated with the extended Heine-Stieltjes and Van Vleck polynomials, respectively. Since the coefficients in these polynomials are free from divergence with variations in contrast to the original Bethe ansatz equations, the approach provides an efficient and systematic way to solve the problem, which by extension, can also be used to solve a large class of Gaudin-type quantum many-body problems, including an efficient angular momentum projection method for multiparticle systems.

Multi-fragment vector correlation imaging. A search for hidden dynamical symmetries in many-particle molecular fragmentation processes

State-of-the-art multi-fragment imaging techniques like the COLTRIMS reaction microscope unveil the complete momentum pattern in low-energy atomic and molecular many-particle fragmentation processes much like the bubble chamber in high-energy particle physics. The excellent momentum resolution far below 1 m e a 0 E h/ħ (1 a.u.) and the high multi-fragment detection efficiency of the COLTRIMS technique reveal the dynamic correlation of bound many-particle systems as they are fragmented into the continuum. For the fragmentation process of carbon monoxide following carbon K-shell ionization using 306 eV photons (right and left circularly polarized) hν + CO → ephoto + O+ + C+ + eK-Auger, the vector correlations between all fragments were measured in coincidence for each event. According to the common view of this process, the photoelectron and Auger electron emission probe different aspects of the time-dependent fragmentation process, i.e. the ‘time evolution’ of fragmentation. Based on measured vectors and vector combinations (e.g. vector products) of (1) the absorbed photon, (2) the emitted photoelectron and (3) ions, the Auger electron emission can be investigated with respect to the axes and planes defined by these vector combinations for each event in order to explore dynamical symmetries in multi-particle systems.

Surface-plasmon-like modes of graphite powder compact in microwave heating

We determine the mechanism of rapid and selective heating of nonmagnetic conductive particles by the electric and magnetic fields of microwaves. We investigated the dependencies of the heating behaviors of carbon powders on the radius and electrical conductivity for various relative densities. In these experiments, strong microwave absorption was observed in magnetic field at certain radii and ratios of the crystallite size to the radius. Mie theory for a single particle could account for the high heating rates generated by the microwave magnetic field in sintering experiments. In the dependence of the heating behavior on the relative density, that H field exhibited the maximum absorption at certain relative densities of the graphite powders. These surface plasmon-like modes were observed in graphite, but were not observed when an E field was applied. Multiparticle systems such as graphite powder were found to have significantly different heating behaviors from a single particle. Microwave heating of metal particles is expected to be affected by the structure and shape of the particles.

Quasi-Classical Theory of Electronic Flux Density in Electronically Adiabatic Molecular Processes

The standard Born-Oppenheimer (BO) description of electronically adiabatic molecular processes predicts a vanishing electronic flux density (EFD). A previously proposed "coupled-channels" theory permits the extraction of the EFD from the BO wave function for one-electron diatomic systems, but attempts at generalization to many-electron polyatomic systems are frustrated by technical barriers. An alternative "quasi-classical" approach, which eliminates the explicit quantum dynamics of the electrons within a classical framework, yet retains the quantum character of the nuclear motion, appears capable of yielding EFDs for arbitrarily complex systems. Quasi-classical formulas for the EFD in simple systems agree with corresponding coupled-channels formulas. Results of the application of the new quasi-classical formula for the EFD to a model triatomic system indicate the potential of the quasi-classical scheme to elucidate the dynamical role of electrons in electronically adiabatic processes in more complex multiparticle systems.

Direct numerical simulation of flow and heat transfer in dense fluid–particle systems

In this paper a novel simulation technique is presented to perform Direct Numerical Simulation (DNS) of fluid flow and heat transfer in dense fluid–particle systems. The unique feature of our fluid–solid coupling technique is the direct (i.e., implicit) incorporation of the boundary condition (with a second-order method) at the surface of the particles at the level of the discrete momentum and thermal energy equations of the fluid. Contrary to lattice Boltzmann or other commonly used immersed boundary implementations, our method does not require using any effective diameter.A fixed (Eulerian) grid is utilized to solve the Navier–Stokes equations for the entire computational domain. Dissipative particle–particle and/or particle-wall collisions are accounted via a hard sphere discrete particle approach using a three-parameter particle–particle interaction model accounting for normal and tangential restitution and tangential friction. Following the detailed verification of the method several dense multi-particle systems are studied in detail involving stationary arrays of particles and fluidized particles.

Evaluation of Ranks of Real Space and Particle Entanglement Spectra for Large Systems

We devise a way to calculate the dimensions of symmetry sectors appearing in the particle entanglement spectrum (PES) and real space entanglement spectrum (RSES) of multiparticle systems from their real space wave functions. We first note that these ranks in the entanglement spectra equal the dimensions of spaces of wave functions with a number of particles fixed. This also yields equality of the multiplicities in the PES and the RSES. Our technique allows numerical calculations for much larger systems than were previously feasible. For somewhat smaller systems, we can find approximate entanglement energies as well as multiplicities. We illustrate the method with results on the RSES and PES multiplicities for integer quantum Hall states, Laughlin and Jain composite fermion states, and for the Moore-Read state at filling ν = 5/2 for system sizes up to 70 particles.

Similarity renormalization group and many-body effects in multiparticle systems

The similarity renormalization group (SRG), based on the simple one-body free harmonic oscillator Hamiltonian, is applied to various nucleon-nucleon realistic interactions to investigate the unitarity of the SRG transformations. Two-body and three-body contributions to the SRG-evolved Hamiltonian are studied in the framework of spectral distribution theory for reasonable SRG cutoffs and in multiparticle systems, with up through 28 particles considered. The outcome points to the first evidence for the overall importance of three-body SRG-induced interactions and especially, of its two-body effective content in multinucleon systems, without the need for large-scale shell model calculations for many light to heavier nuclei.

Non-Hermitian multi-particle systems from complex root spaces

We provide a general construction procedure for antilinearly invariant complex root spaces. The proposed method is generic and may be applied to any Weyl group allowing us to take any element of the group as a starting point for the construction. Worked-out examples for several specific Weyl groups are presented, focusing especially on those cases for which no solutions were found previously. When applied to the defining relations of models based on root systems, this usually leads to non-Hermitian models, which are nonetheless physically viable in a self-consistent sense as they are antilinearly invariant by construction. We discuss new types of Calogero models based on these complex roots. In addition, we propose an alternative construction leading to q-deformed roots. We employ the latter type of roots to formulate a new version of affine Toda field theories based on non-simply laced root systems. These models exhibit on the classical level a strong–weak duality in the coupling constant equivalent to a Lie algebraic duality, which is known for the quantum version of the undeformed case.

Entanglement and nonlocality in multi-particle systems

Entanglement, the Einstein-Podolsky-Rosen (EPR) paradox and Bell’s failure of local-hiddenvariable (LHV) theories are three historically famous forms of “quantum nonlocality”. We give experimental criteria for these three forms of nonlocality in multi-particle systems, with the aim of better understanding the transition from microscopic to macroscopic nonlocality. We examine the nonlocality of N separated spin J systems. First, we obtain multipartite Bell inequalities that address the correlation between spin values measured at each site, and then we review spin squeezing inequalities that address the degree of reduction in the variance of collective spins. The latter have been particularly useful as a tool for investigating entanglement in Bose-Einstein condensates (BEC). We present solutions for two topical quantum states: multi-qubit Greenberger-Horne-Zeilinger (GHZ) states, and the ground state of a two-well BEC.

Dynamical behaviour of multi-particle large-scale systems

Collective behaviours can be observed in both natural and man-made systems composed of a large number of elemental subsystems. Typically, each elemental subsystem has its own dynamics but, whenever interaction between individuals occurs, the individual behaviours tend to be relaxed, and collective behaviours emerge. In this paper, the collective behaviour of a large-scale system composed of several coupled elemental particles is analysed. The dynamics of the particles are governed by the same type of equations but having different parameter values and initial conditions. Coupling between particles is based on statistical feedback, which means that each particle is affected by the average behaviour of its neighbours. It is shown that the global system may unveil several types of collective behaviours, corresponding to partial synchronisation, characterised by the existence of several clusters of synchronised subsystems, and global synchronisation between particles, where all the elemental particles synchronise completely.

Analysis of pulsed laser plasmon-assisted photothermal heating and bubble generation at the nanoscale

A study is presented of photothermal effects associated with nanosecond-pulsed laser-illuminated subwavelength metallic nanoparticles in aqueous solutions. Computational electromagnetic and fluid analysis are used to model fundamental aspects of the photothermal process taking into account energy conversion within the nanoparticle at plasmon resonance, heat transfer to the fluid, homogeneous bubble nucleation, and the dynamic behaviour of the bubble and surrounding fluid. Various nanoparticle geometries are modelled including spheres, nanorods and tori. The analysis demonstrates that the laser intensity and pulse duration can be tuned to achieve controllable bubble generation without exceeding the melting temperature of the particle. The analysis also shows that the particle geometry can be tuned to optimize photothermal energy conversion for bubble generation at wavelengths that span the UV to NIR spectrum. Multiparticle systems are studied and a cooperative heating effect is demonstrated for particles that are within a few radii of each other. This provides more robust bubble generation using substantially reduced laser energy as compared to single-particle systems. The modelling approach is discussed in detail and should be of considerable use in the development of new photothermal applications.

On resonances in disordered multi-particle systems

We assess the probability of resonances between sufficiently distant states x=(x1,…,xN) and y=(y1,…,yN) in the configuration space of an N-particle disordered quantum system on the lattice Zd, d⩾1. This includes the cases where the transition x⇝y “shuffles” the particles in x, like the transition (a,a,b)⇝(a,b,b) in a 3-particle system. In presence of a random external potential V(⋅,ω) such pairs of configurations (x,y) give rise to strongly coupled random local Hamiltonians, so that eigenvalue concentration bounds are difficult to obtain (cf. Aizenman and Warzel (2009) [2]; Chulaevsky and Suhov (2009) [8]). This results in eigenfunction decay bounds weaker than expected. We show that more optimal bounds obtained so far only for 2-particle systems (Chulaevsky and Suhov (2008) [6]) can be extended to any N>2.