Persistence and financial markets

The persistence phenomenon is studied in a financial context by using a novel mapping of the time evolution of the values of shares in a portfolio onto Ising spins. The method is applied to historical data from the London Financial Times Stock Exchange 100 index (FTSE 100) over an arbitrarily chosen period. By following the time dependence of the spins, we find evidence for a power law decay of the proportion of shares that remain either above or below their ‘starting’ values. As a result, we estimate a persistence exponent for the underlying financial market to be ≈0.5. Preliminary results from computer simulations on persistence in the economic dynamics of a toy model appear to reproduce the behaviour observed in real markets.     

Statistical regularities in the return intervals of volatility

We discuss recent results concerning statistical regularities in the return intervals of volatility in financial markets. In particular, we show how the analysis of volatility return intervals, defined as the time between two volatilities larger than a given threshold, can help to get a better understanding of the behavior of financial time series. We find scaling in the distribution of return intervals for thresholds ranging over a factor of 25, from 0.6 to 15 standard deviations, and also for various time windows from one minute up to 390 min (an entire trading day). Moreover, these results are universal for different stocks, commodities, interest rates as well as currencies. We also analyze the memory in the return intervals which relates to the memory in the volatility and find two scaling regimes, ℓ<ℓ^* with α₁=0.64±0.02 and ℓ> ℓ^* with α₂=0.92±0.04; these exponent values are similar to results of Liu et al. for the volatility. As an application, we use the scaling and memory properties of the return intervals to suggest a possibly useful method for estimating risk.     

Spectroscopy of the neutron-deficient nuclide 171Pt

The decay out of the πh _11/2νh _11/2 band to the known low-energy levels in ¹³²La was studied using the reaction ¹⁰⁰Mo + ³⁶S at 160 MeV beam energy. The low-energy level scheme has been further developed and unambiguous spin and parity values have been assigned to the levels connecting the band to the 6^- isomeric state. According to the new level scheme the spins in the πh _11/2νh _11/2 band are shifted up by one unit compared to the earlier tentative experimental values. The obtained new spins prove the existence of signature inversion in ¹³²La and give further support to the spin assignments made for the πh _11/2νh _11/2 bands in the neighbouring odd-odd La isotopes from level energy systematics. Received: 7 May 2002 / Accepted: 31 October 2002 / Published online: 17 January 2003 RID="a" ID="a"e-mail: timar@atomki.hu RID="b" ID="b"Present address: Dipartimento di Matematica e Fisica, Università di Camerino, via Madonna delle Carceri, I-62032 Camerino, Italy. Communicated by J. ?yst?     

Magnetic susceptibility in quasi one-dimensional Ba<Subscript>a2</Subscript>V<Subscript>3</Subscript>O<Subscript>9</Subscript>: chain segmentation versus the staggered field effect

A pronounced Curie-like upturn of the magnetic susceptibility χ( T ) of the quasi one-dimensional spin chain compound Ba₂V₃O₉ has been found recently [#!kaul:02!#]. Frequently this is taken as a signature for a staggered field mechanism due to the presence of g-factor anisotropy and Dzyaloshinskii-Moriya interaction. We calculate this contribution within a realistic structure of vanadium 3 d- and oxygen 2 p-orbitals and conclude that this mechanism is far too small to explain experimental results. We propose that the Curie term is rather due to a segmentation of spin chains caused by broken magnetic bonds which leads to uncompensated S = ? spins of segments with odd numbers of spins. Using the finite-temperature Lanczos method we calculate their effective moment and show that ∼ 1% of broken magnetic bonds is sufficient to reproduce the anomalous low-T behavior of χ( T ) in Ba₂V₃O₉. Received 19 December 2002 / Received in final form 29 January 2003 Published online 14 March 2003     

Quantum fluctuations in a scale-free network-connected Ising system

We study the effect of quantum fluctuations in an Ising spin system on a scale-free network of degree exponent γ>5 using a quantum Monte Carlo simulation technique. In our model, one can adjust the magnitude of the magnetic field perpendicular to the Ising spin direction and can therefore control the strength of quantum fluctuations for each spin. Our numerical analysis shows that quantum fluctuations reduce the transition temperature T_c of the ferromagnetic-paramagnetic phase transition. However, the phase transition belongs to the same mean-field type universality class both with and without the quantum fluctuations. We also study the role of hubs by turning on the quantum fluctuations exclusively at the nodes with the most links. When only a small number of hub spins fluctuate quantum mechanically, T_c decreases with increasing magnetic field until it saturates at high fields. This effect becomes stronger as the number of hub spins increases. In contrast, quantum fluctuations at the same number of “non-hub” spins do not affect T_c. This implies that the hubs play an important role in maintaining order in the whole network.     

Flow equations for the one-dimensional Kondo lattice model: static and dynamic ground state properties

The one-dimensional Kondo lattice model is investigated by means of Wegner's flow equation method. The renormalization procedure leads to an effective Hamiltonian which describes a free one-dimensional electron gas and a Heisenberg chain. The localised spins of the effective model are coupled by the well-known RKKY interaction. They are treated within a Schwinger boson mean field theory which permits the calculation of static and dynamic correlation functions. In the regime of small interaction strength static expectation values agree well with the expected Luttinger liquid behaviour. The parameter K_ρ of the Luttinger liquid theory is estimated and compared to recent results from density matrix renormalization group studies.     

Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: a computational discussion

We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs Γ-space. Using paradigmatic first-neighbor models, namely, the inertial XY ferromagnet and the Fermi-Pasta-Ulam β-model, we show that at intermediate energies the Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law (F=ma). At higher energies we discuss partial agreement between time and ensemble averages.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Electronic properties of arrayed K clusters in zeolite LTA with Si/Al = 1.5

Arrayed cationic K clusters including one 4s-electron in each cluster, i.e., K_m+1 ^m+, were incorporated into α-cages of zeolite LTA with Si/Al=1.5. Although no magnetic phase transition was observed regarding the temperature (T) dependence of magnetic susceptibilities originating from the 4s-electron spins (χ_spin) between 2 and 300 K, the χ_spin-T curve could be fitted by the sum of magnetic susceptibilities based on the Curie-Weiss law and Pauli paramagnetism. A possible explanation of this behavior is the existence of a narrow energy band formed out of 1s-cluster orbitals of arrayed K clusters, and the existence of a finite density of state at the Fermi energy.     

Quantum topological excitations: from the sawtooth lattice to the Heisenberg chain

From the recently determined structure of the delafossite YCuO_2.5, we argue that the Cu-O network has nearly independent Δ chains but with different interactions between the s = 1/2 spins. Motivated by this observation, we study the Δ chain for different ratios of the base-base and base-vertex interactions, J _bb/J _bv. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum is the same for total spins S _tot = 0 and 1, but not for S _tot = 2, and has a gap only in the interval 0.4874(1) ⩽ J _bb/J _bv ⩽ 1.53(1). The gap, known to be dispersionless for J _bb = J _bv, is found to acquire increasing k-dependence as J _bb/J _bv moves away from unity. Received 29 October 2002 / Received in final form 14 January 2003 Published online 6 March 2003 RID="a" ID="a"e-mail: sblundell@cea.fr RID="b" ID="b"e-mail: nunezreg@lps.u-psud.fr     

The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis

We have investigated the proof of the H theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002); G. Kaniadakis, Phys. Rev. E 72, 036108 (2005)]. As it happens in the nonrelativistic limit, the molecular chaos hypothesis is slightly extended within the Kaniadakis formalism. It is shown that the collisional equilibrium states (null entropy source term) are described by a κ power law generalization of the exponential Juttner distribution, e.g., , with θ=α(x)+β_μp^μ, where α(x) is a scalar, β_μ is a four-vector, and p^μ is the four-momentum. As a simple example, we calculate the relativistic κ power law for a dilute charged gas under the action of an electromagnetic field F^μν. All standard results are readly recovered in the particular limit κ→0.     

Microscopic quantities in discharge in air obtained from an electro-mechanical experiment

The results of an experiment of impulsive electrodynamics [Eur. Phys. J. D 15, 87 (2001)] are shown to be due to electrons and ions in run-aways. By fitting the theoretical values with the experimental data, the values of microscopic quantities, at present unknown, can be derived, thus opening a new field of research. The obtained quantities are three, namely: (i) the contribution to air ionization due to the current (mainly of run-aways) and characterized by a parameter ρ; (ii) the product ζ=n_ein_ie (where n_ei is the number of ions extracted by one electron in run-away and n_ie the number of electrons extracted by one run-away ion colliding on the electrodes in electrical discharges with temperatures (for non run-aways) of ≃4×10⁴ K); (iii) the reconstruction time constant of the high-energy tail of the distribution function, from which we can derive the concentration per unit time of electrons and ions which become run-aways. The value is useful for the theoretical explanation of the electronic noise with power spectral density inversely proportional to the frequency.     

High spin states and evidence for octupole correlations in 117Xe

High-spin states of ¹¹⁷Xe were investigated by means of in-beam γ-ray spectroscopic techniques via the reaction of ²⁸Si bombarding a ⁹²Mo target at beam energies of 100-120 MeV. A positive-parity rotational band decaying into the yrast negative-parity band by a series of enhanced E1 transitions was observed for the first time, implying the existence of octupole correlations in ¹¹⁷Xe. The B(E1) values increase with spin. The νd_5/2 band was firmly established up to 27/2⁺ and the B(M1)/B(E2) ratios were extracted from the relative intensities of γ-rays in this band. The previously known νh_11/2 and νg_7/2 [413]5/2⁺α=−1/2 bands were confirmed and extended up to high spins and two bandcrossings are observed in the latter at ħω=0.33 and 0.44 MeV, respectively. The bandcrossings and configurations of these bands are discussed by TRS and CSM calculations. In a γ–γ–t measurement, the 11/2⁻ and 7/2⁻ levels were identified as two isomers with half-lives of 59.4±20 ns and 16.5±8.0 ns, respectively. Received: 17 June 1997 / Revised version: 29 September 1997     

Monte Carlo test of the Goldstone mode singularity in 3D XY model

Monte Carlo simulations of magnetization and susceptibility in the 3D XY model are performed for system sizes up to L=384 (significantly exceeding the largest size L=160 considered in work published previously), and fields h ≥ 0.0003125 at two different coupling constants β=0.5, and β=0.55 in the ordered phase. We examine the prediction of the standard theory that the longitudinal susceptibility χ_∥ has a Goldstone mode singularity such that χ_∥ ∝h^-1/2 holds when h↦0. Most of our results, however, support another theoretical prediction that the singularity is of a more general form χ_∥ ∝h^ρ-1, where 1/2<ρ<1 is a universal exponent related to the ∼h^ρ variation of the magnetization.     

Pinning-depinning of the contact line on nanorough surfaces

We study the pinning-depinning phenomenon of a contact line on a solid surface decorated by a random array of nanometric structures. For this purpose, we have investigated the contact angle hysteresis behaviour of six different wetting and non-wetting fluids with surface tensions varying from 25 to 72mN m^-1. For low values of the areal density of defects φ_d, the hysteresis H increases linearly with φ_d indicating that “individual” defects pin the contact line. Then, from a given value of φ_d, the hysteresis H becomes to decrease with increasing φ_d, indicating a new kind of collective depinning. These two regimes were observed for all fluids used. In both cases, our experimental results are compared with the theoretical predictions for contact angle hysteresis induced by single or multiple topographical defects. We ascribe the decrease of H to the formation of cavities along the wetting front.     

Transport between multiple users in complex networks

We study the transport properties of model networks such as scale-free and Erd?s-Rényi networks as well as a real network. We consider few possibilities for the trnasport problem. We start by studying the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G, with a power-law tail distribution $\Phi_{\rm SF}(G)\sim G^{-g_G}$ , where g_G=2λ-1, and λ is the decay exponent for the scale-free network degree distribution. The power-law tail in Φ_SF(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erd?s-Rényi networks where the tail of the conductivity distribution decays exponentially. We develop a simple physical picture of the transport to account for the results. The other model for transport is the max-flow model, where conductance is defined as the number of link-independent paths between the two nodes, and find that a similar picture holds. The effects of distance on the value of conductance are considered for both models, and some differences emerge. We then extend our study to the case of multiple sources ans sinks, where the transport is defined between two groups of nodes. We find a fundamental difference between the two forms of flow when considering the quality of the transport with respect to the number of sources, and find an optimal number of sources, or users, for the max-flow case. A qualitative (and partially quantitative) explanation is also given.     

Muon spin relaxation in diluted triangular‐lattice antiferromagnet

Zero and longitudinal field μSR measurements on diluted triangular‐lattice antiferromagnet LuFeMgO₄ have revealed gradual and highly anisotropic slowing‐down of spin fluctuation. Relaxation rate \lambda in the condition with initial muon spins perpendicular to the hexagonal c‐plane shows divergent behavior while that in the parallel configuration remains finite. At certain temperature range the fluctuation of spins is suppressed by a small external magnetic field. Monte Carlo calculation suggests that the correlation time for z(c)‐component of spins diverges first on cooling. This revised version was published online in July 2006 with corrections to the Cover Date.     

0-π oscillations in nanostructured Nb/Fe/Nb Josephson junctions

The physics of the π phase shift in ferromagnetic Josephson junctions may enable a range of applications for spin-electronic devices and quantum computing. We investigate transitions from “0” to “π” states in Nb/Fe/Nb Josephson junctions by varying the Fe barrier thickness from 0.5 nm to 5.5 nm. From magnetic measurements we estimate for Fe a magnetic dead layer of about 1.1 nm. By fitting the characteristic voltage oscillations with existing theoretical models we extrapolate an exchange energy of 256 meV, a Fermi velocity of 1.98 ×10⁵ m/s and an electron mean free path of 6.2 nm, in agreement with other reported values. From the temperature dependence of the I_CR_N product we show that its decay rate exhibits a nonmonotonic oscillatory behavior with the Fe barrier thickness.     

Separable-entangled frontier in a bipartite harmonic system

We consider a statistical mixture based on that of two identical harmonic oscillators which is characterized by four parameters, namely, the concentrations (x and y) of diagonal and nondiagonal bipartite states, and their associated thermal-like noises (T/α and T, respectively). The fully random mixture of two spins 1/2 as well as the Einstein-Podolsky-Rosen (EPR) state are recovered as particular instances. By using the conditional nonextensive entropy as introduced by Abe and Rajagopal, we calculate a bound for the separable-entangled frontier. Although this procedure is known to provide a necessary but in general not sufficient condition for separability, it does recover, in the particular case x = T = 0 ( ∀α), the 1/3 exact result known as Peres' criterion. The x = 0 frontier remarkably resembles to the critical line associated with standard diluted ferromagnetism where the entangled region corresponds to the ordered one and the separable region to the paramagnetic one. The entangled region generically shrinks for increasing T or increasing α. Received 18 April 2002 / Received in final form 11 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: celia@cbpf.br     

A study of 223Ra populated by α-decay

The low spin states of ²²³Ra have been populated via α-decay from ²²⁷Th which was itself produced following β⁻ decay of an ²²⁷Ac source. α–γ and α−e _K,L,M angular correlation measurements have been analysed using the correct ground state spins of ²²⁷Th(=1/2⁺) and ²²³Ra(=3/2⁺) for the first time. The analysis has allowed unique J^π values to be assigned to almost all levels below 400 keV excitation in ²²³Ra. Values of (g _K−g _R)/Q ₀ have been deduced for several members of the K= 3/2^± bands (for the first time in an odd N nucleus in this mass region) allowing estimates of g _K and g _R to be extracted. The values of g _K and g _R are not significantly different for the positive and negative parity band members and tend to support other strong evidence that stable octupole deformation exists in ²²³Ra at low excitation energies. Received: 17 November 1997 / Revised version: 8 January 1998