Search results for " Statistical"
showing 10 items of 1649 documents
Stable topological textures in a classical 2D Heisenberg model
2009
We show that stable localized topological soliton textures (skyrmions) with $\pi_2$ topological charge $\nu \geq 1$ exist in a classical 2D Heisenberg model of a ferromagnet with uniaxial anisotropy. For this model the soliton exist only if the number of bound magnons exceeds some threshold value $N_{\rm cr}$ depending on $\nu $ and the effective anisotropy constant $K_{\rm eff}$. We define soliton phase diagram as the dependence of threshold energies and bound magnons number on anisotropy constant. The phase boundary lines are monotonous for both $\nu=1$ and $\nu >2$, while the solitons with $\nu=2$ reveal peculiar nonmonotonous behavior, determining the transition regime from low to high …
Unraveling modular microswimmers: From self-assembly to ion-exchange-driven motors
2018
Active systems contain self-propelled particles and can spontaneously self-organize into patterns making them attractive candidates for the self-assembly of smart soft materials. One key limitation of our present understanding of these materials hinges on the complexity of the microscopic mechanisms driving its components forward. Here, by combining experiments, analytical theory, and simulations we explore such a mechanism for a class of active system, modular microswimmers, which self-assemble from colloids and ion-exchange resins on charged substrates. Our results unveil the self-assembly processes and the working mechanism of the ion-exchange driven motors underlying modular microswimme…
Exact canonical occupation numbers in a Fermi gas with finite level spacing and a q-analog of Fermi-Dirac distribution
2011
We consider equilibrium level occupation numbers in a Fermi gas with a fixed number of particles, n, and finite level spacing. Using the method of generating functions and the cumulant expansion we derive a recurrence relation for canonical partition function and an explicit formula for occupation numbers in terms of single-particle partition function at n different temperatures. We apply this result to a model with equidistant non-degenerate spectrum and obtain close-form expressions in terms of q-polynomials and Rogers-Ramanujan partial theta function. Deviations from the standard Fermi-Dirac distribution can be interpreted in terms of a gap in the chemical potential between the particle …
Long term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development
2004
The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.
Temperature dependence of spin depolarization of drifting electrons in n-type GaAs bulks
2010
The influence of temperature and transport conditions on the electron spin relaxation in lightly doped n-type GaAs semiconductors is investigated. A Monte Carlo approach is used to simulate electron transport, including the evolution of spin polarization and relaxation, by taking into account intravalley and intervalley scattering phenomena of the hot electrons in the medium. Spin relaxation lengths and times are computed through the D'yakonov-Perel process, which is the more relevant spin relaxation mechanism in the regime of interest (10 < T < 300 K). The decay of the initial spin polarization of the conduction electrons is calculated as a function of the distance in the presence of…
Critical dynamics of long range models on Dynamical L\'evy Lattices
2023
We investigate critical equilibrium and out of equilibrium properties of a ferromagnetic Ising model in one and two dimension in the presence of long range interactions, $J_{ij}\propto r^{-(d+\sigma)}$. We implement a novel local dynamics on a dynamical L\'evy lattice, that correctly reproduces the static critical exponents known in the literature, as a function of the interaction parameter $\sigma$. Due to its locality the algorithm can be applied to investigate dynamical properties, of both discrete and continuous long range models. We consider the relaxation time at the critical temperature and we measure the dynamical exponent $z$ as a function of the decay parameter $\sigma$, highlight…
Transport and Scaling in Quenched 2D and 3D L\'evy Quasicrystals
2011
We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties. We introduce a geometric parameter $\alpha$, playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a {\it single-long jump} approximation, we analytically determine the long-time asymptotic behavior of the moments of the probability distribution, as a function of $\alpha$ and of the dynamic exponent $z$ associated to the scaling length of the process. We show that our scaling analysis also applies to e…
The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach
2019
We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the re-inter…
Scaling of the R\'enyi entropies in gapped quantum spin systems: Entanglement-driven order beyond symmetry breaking
2012
We investigate the scaling of the R\'enyi $\alpha$-entropies in one-dimensional gapped quantum spin models. We show that the block entropies with $\alpha > 2$ violate the area law monotonicity and exhibit damped oscillations. Depending on the existence of a factorized ground state, the oscillatory behavior occurs either below factorization or it extends indefinitely. The anomalous scaling corresponds to an entanglement-driven order that is independent of ground-state degeneracy and is revealed by a nonlocal order parameter defined as the sum of the single-copy entanglement over all blocks.
On the Sign Problem of the Fermionic Shadow Wave Function
2014
We present a whole series of novel methods to alleviate the sign problem of the Fermionic Shadow Wave Function in the context of Variational Monte Carlo. The effectiveness of our new techniques is demonstrated on the example of liquid 3He. We found that although the variance is substantially reduced, the gain in efficiency is restricted by the increased computational cost. Yet, this development not only extends the scope of the Fermionic Shadow Wave Function, but also facilitates highly accurate Quantum Monte Carlo simulations previously thought not feasible.