Universal property of the information entropy in atoms,nuclei and atomic clusters

The position- and momentum-space information entropies of the electron distributions of atomic clusters are calculated using a Woods-Saxon single particle potential. The same entropies are also calculated for nuclear distributions according to the Skyrme parametrization of the nuclear mean field. It turns out that a similar functional form S = a + blnN for the entropy as function of the number of particles N holds approximately for atoms, nuclei and atomic clusters. It is conjectured that this is a universal property of a many-fermion system in a mean field.     

Vacuum mass spectra for SU(N) self-dual Chern-Simons-Higgs systems

We study the SU(N) self-dual Chem-Simons-Higgs systems with adjoint matter coupling, and show that the sixth-order self-dual potential has p(N) gauge inequivalent degenerate minima, where p(N) is the number of partitions of N. We compute the masses of the gauge and scalar excitations in these different vacua, revealing an intricate mass structure which reflects the self-dual nature of the model.     

Renormalization and phase transition in the quantum ofCPN−1 model (D=2,3)

We prove in the framework of the 1/N expansion the ultraviolet renormalizibility of the ofCP^N?1 model when D = 2, 3. It is shown that when D = 2 the model gains infrared divergences in higher orders of 1/N. When D = 3, the phase transition of second order occurs: above the critical points there exist N massive scalar charged particles and one particle corresponding to the massless isoscalar vector field, but below it there exist only N ? 1 massless particles.     

Isotopic features of the N p N n function for even-even isotope chains of Ni and Zn

Low-energy (0.04–3.0 MeV) neutron data for even-even ^58–64Ni and ^64–70Zn isotopes are analyzed in terms of the coupled channel optical model (CCOM) as a function of N _p N _n, where N _p(N _n) are the numbers of valent nucleons (particles or holes), and consider the relationship between the diffuseness parameter obtained from CCOM calculations and the value of the N _p N _n function. Considering the Ni and Zn isotope chains with the traditional magic number Z = 28 and the nontraditional N = 38 proves the existence of N = 28–38 subshells. The results from our analysis indicate the possible existence of the nontraditional magic nucleus ₃₀ ⁶⁸ Zn₃₈.     

Mesoscopic Casimir forces in quantum vacuum

Traditionally, it is assumed that the Casimir vacuum pressure does not depend on the ultraviolet cutoff. There are, however, some arguments that the effect actually depends on the regularization procedure and thus on trans-Planckian physics. We provide the condensed matter example where the Casimir forces do explicitly depend on microscopic (correspondingly trans-Planckian) physics due to the mesoscopic finite-N effects, where N is the number of bare particles in condensed matter (or correspondingly the number of elements comprising the quantum vacuum). The finite-N effects lead to mesoscopic fluctuations of the vacuum pressure. The amplitude of the mesoscopic fluctuations of the Casimir force in a system with linear dimension L is a factor of N ^1/3～L/a _p larger than the traditional value of the Casimir force given by effective theory, where a _p =?/p _p is the interatomic distance which plays the role of the Planck length.     

Ground States of the 2D Sticky Disc Model: Fine Properties and N 3/4 Law for the Deviation from the Asymptotic Wulff Shape

We investigate ground state configurations for a general finite number N of particles of the Heitmann-Radin sticky disc pair potential model in two dimensions. Exact energy minimizers are shown to exhibit large microscopic fluctuations about the asymptotic Wulff shape which is a regular hexagon: There are arbitrarily large N with ground state configurations deviating from the nearest regular hexagon by a number of ～N ^3/4 particles. We also prove that for any N and any ground state configuration this deviation is bounded above by ～N ^3/4. As a consequence we obtain an exact scaling law for the fluctuations about the asymptotic Wulff shape. In particular, our results give a sharp rate of convergence to the limiting Wulff shape.     

Thermodynamic and scaling behaviour in finite diffusion-limited aggregation

Rényi's entropies for diffusion-limited aggregates are studied as a function of the number N of particles contained in the aggregates. It is found that Rényi's values increase with log N in a linear fashion, and that the aggregates exhibit multifractal behaviour for finite values of N. When N → ∞, the aggregate has a monofractal structure. Rényi's entropies depend on the fractal dimension of the aggregate. When the fractal dimension increases, the values of K_q decrease for q ? 1> and increase for q > 1.     

An exactly solvable many-body problem in one dimension and the short-range Dyson model

For N impenetrable particles in one dimension with upto next-to-nearest neighbours interaction, we obtain the exact ground state.We establish a mapping between these N-body problems and the short-range Dyson model introduced recently to model intermediate spectral statistics. We prove the absence of long-range order and off-diagonal long-range order in the corresponding many-body theory.     

The production of charginos of theSU(N, 1) minimal sugra model ine + e − annihilation andp \bar p collider experiments

We present cross sections for the charged lepton production from the lightest charged superpartner particles predicted by theSU(N, 1) Minimal SUGRA model, either the superpartners of the r.h. charged leptons or the Wino/Higgsino. At least one of these should appear in the decay of theZ, which is produced ine ⁺ e ^?-annihilation-presumably soon at the SLC — or inp \(\bar p\) collider experiments. A large missing mass and strong deviations from back to back production of lepton pairs (and possibly ae-μ final state) would indicate such charged massive intermediate particles.     

Dynamic simulation using a multipolar model of particles under dielectrophoretic force

This article presents the simulation of an electrorheological (ER) fluid system by using a multipole model that includes multipolar interactions between particles. The model uses the multipole re-expansion and the method of images for calculating electric field and force. The highest order of multipoles (N_mp) and the number of iterations (N_iter) used in the method of images can be chosen for the accuracy of the force approximation and the simulation time required. Study of a two-particle configuration shows that the force does not increase linearly with increasing N_mp and N_iter. The specific case N_mp=4 and N_iter=2 is chosen for dynamic simulation. We have performed the simulation of a system of 20 particles, and compared the formulation of particle chains with that obtained using the dipole model. The results imply that the response time for the change in viscosity of real-ER fluids is significantly shorter than that predicted by the dipole model.     

Transfer Matrix Functional Relations for the Generalized τ2 (t q ) Model

The N-state chiral Potts model in lattice statistical mechanics can be obtained as a “descendant” of the six-vertex model, via an intermediate “Q” or “τ₂ (t _q )” model. Here we generalize this to obtain a column-inhomogeneous τ₂ (t _q ) model, and derive the functional relations satisfied by its row-to-row transfer matrix. We do not need the usual chiral Potts relations between the Nth powers of the rapidity parameters a _p , b _p , c _p , d _p of each column. This enables us to readily consider the case of fixed-spin boundary conditions on the left and right-most columns. We thereby re-derive the simple direct product structure of the transfer matrix eigenvalues of this model, which is closely related to the superintegrable chiral Potts model with fixed-spin boundary conditions.     

Formation of η′(958) Meson Bound States and Chiral Symmetry In-Medium

We theoretically discuss the feasibility to observe the η′(958)-mesic nuclei by using the missing mass spectroscopy. We evaluate the η′-nucleus optical potential including the contribution of lowest order in density together with the second order terms account for η′ absorption by two nucleons, based on a recent model of the η′N interaction. We show the calculated formation cross section of the η′ bound states from (π, N) reaction with pion beam momentum p _π = 1.8 GeV/c and (p, d) reaction with proton kinetic energy T _p = 2.5 GeV.     

Rényi entropy and quantum phase transition in the Dicke model

The Rényi entropies of the Dicke model are presented. This quantum-optical model describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. There is a quantum phase transition in the N→∞ limit. It is shown that there is an abrupt change in the Rényi entropy of order β at the transition point. Around the critical value of the coupling strength λc the Rényi entropy is proportional to the logarithm of the characteristic length and diverges as ln|λc−λ| for any order β. The pseudocapacity defined here in analogy with the heat capacity exhibits the phase transition. The critical exponent for the Dicke model is found to be 1 for any value of the parameter β.     

Last Passage Percolation and Traveling Fronts

We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida (Phys. Rev. E 70:016106, 2004). The particles can be interpreted as last passage times in directed percolation on {1,…,N} of mean-field type. The particles remain grouped and move like a traveling front, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. As shown in Brunet and Derrida (Phys. Rev. E 70:016106, 2004), the model with Gumbel distributed jumps has a simple structure. We establish that the scaling limit is a Lévy process in this case. We study other jump distributions. We prove a result showing that the limit for large N is stable under small perturbations of the Gumbel. In the opposite case of bounded jumps, a completely different behavior is found, where finite-size corrections are extremely small.     

Fast convergence of path integrals for many-body systems

We generalize a recently developed method for accelerated Monte Carlo calculation of path integrals to the physically relevant case of generic many-body systems. This is done by developing an analytic procedure for constructing a hierarchy of effective actions leading to improvements in convergence of N-fold discretized many-body path integral expressions from 1/N to 1/Np for generic p. In this Letter we present explicit solutions within this hierarchy up to level p=5. Using this we calculate the low lying energy levels of a two particle model with quartic interactions for several values of coupling and demonstrate agreement with analytical results governing the increase in efficiency of the new method. The applicability of the developed scheme is further extended to the calculation of energy expectation values through the construction of associated energy estimators exhibiting the same speedup in convergence.     

Drift velocity in the necklace model for reptation in a two-dimensional square lattice

We report the chain dynamics in the necklace model that mimics the reptation of a chain of N particles in a two-dimensional square lattice. We focus on the drift velocity under an applied static field. The characteristics of the model allow us to determine the effects of the forces on the chains and the resulting mechanisms that affect the drift velocity. Results obtained through Monte Carlo simulations were analyzed and discussed and distinct regimes as a function of the force strength and N were identified. We found that for small total applied forces, the drift velocity scales as 1/N. When the applied force to every particle is small but the total applied force is not, the tube deforms in such a way that the drift velocity does not depend on N. Large forces, applied to every particle, can straight chains such that the distance between the chain ends increases faster than the number of particles. Also, large forces can deform the chain within the tube what is directly related to a decrease of the drift velocity.     

Complexity Measures of Heart-Rate Variability in Amyotrophic Lateral Sclerosis with Alternative Pulmonary Capacities

Objective: the complexity of heart-rate variability (HRV) in amyotrophic lateral sclerosis (ALS) patients with different pulmonary capacities was evaluated. Methods: We set these according to their pulmonary capacity, and specifically forced vital capacity (FVC). We split the groups according to FVC (FVC > 50% (n = 29) and FVC < 50% (n = 28)). In ALS, the presence of an FVC below 50% is indicative of noninvasive ventilation with two pressure levels and with the absence of other respiratory symptoms. As the number of subjects per group was different, we applied the unbalanced one-way analysis of variance (uANOVA1) test after three tests of normality, and effect size by Cohen’s d to assess parameter significance. Results: with regard to chaotic global analysis, CFP4 (p < 0.001; d = 0.91), CFP5 (p = 0.0022; d = 0.85), and CFP6 (p = 0.0009; d = 0.92) were enlarged. All entropies significantly increased. Shannon (p = 0.0005; d = 0.98), Renyi (p = 0.0002; d = 1.02), Tsallis (p = 0.0004; d = 0.99), approximate (p = 0.0005; d = 0.97), and sample (p < 0.0001; d = 1.22). Detrended fluctuation analysis (DFA) (p = 0.0358) and Higuchi fractal dimension (HFD) (p = 0.15) were statistically inconsequential between the two groups. Conclusions: HRV complexity in ALS subjects with different pulmonary capacities increased via chaotic global analysis, especially CFP5 and 3 out of 5 entropies.     

Brunnian and Efimov N-Body States

The Efimov effect was originally formulated for three particles. The underlying principle of model independence is extended in this article in several directions. We present our definitions of the concepts of universality and scale independence. In this context we review briefly the scaling relations established for two- and three-body structures of nuclear halos. We emphasize the difference between the two extremes of weak binding named Efimov and Brunnian states. They arise respectively for two-body interactions at threshold of binding either two or N particles. We restrict the Hilbert space to include no more than two-body correlations, and discuss the derived excited N-body Efimov states both for zero- and finite-range two-body interactions. Then we investigate the relation between radius and binding energy extremely close to threshold of binding the Brunnian N-body system. Radii of both ground and first excited states for N?=?4, 5, 6 remain finite as the binding energy vanishes, and the distances between pairs of particles are substantially larger than the range of the two-body potential. The radii decrease with N and increase with excitation energy. The computed radii are larger for the complete than for the restricted Hilbert space. Model independence at the Brunnian threshold is strongly indicated.     

Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics

The Rényi entropies R_p [ ρ], p> 0,≠ 1 of the highly-excited quantum states of the D-dimensional isotropicharmonic oscillator are analytically determined by use of the strong asymptotics of theorthogonal polynomials which control the wavefunctions of these states, the Laguerrepolynomials. This Rydberg energetic region is where the transition from classical toquantum correspondence takes place. We first realize that these entropies are closelyconnected to the entropic moments of the quantum-mechanical probability ρ_n(r)density of the Rydberg wavefunctions Ψ_{n,l, { μ}}(r); so, to the?_p-norms of the associated Laguerrepolynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques ofapproximation theory based on the strong Laguerre asymptotics. Finally, we determine thedominant term of the Rényi entropies of the Rydberg states explicitly in terms of thehyperquantum numbers (n,l), the parameter order p and the universedimensionality D for all possible cases D ≥ 1. We find that (a) theRényi entropy power decreases monotonically as the order p is increasing and (b) thedisequilibrium (closely related to the second order Rényi entropy), which quantifies theseparation of the electron distribution from equiprobability, has a quasi-Gaussianbehavior in terms of D.