Search results for "curse of dimensionality"
showing 10 items of 100 documents
Analyzing and organizing the sonic space of vocal imitations
2015
The sonic space that can be spanned with the voice is vast and complex and, therefore, it is difficult to organize and explore. In order to devise tools that facilitate sound design by vocal sketching we attempt at organizing a database of short excerpts of vocal imitations. By clustering the sound samples on a space whose dimensionality has been reduced to the two principal components, it is experimentally checked how meaningful the resulting clusters are for humans. Eventually, a representative of each cluster, chosen to be close to its centroid, may serve as a landmark in the exploration of the sound space, and vocal imitations may serve as proxies for synthetic sounds.
Quantum magnetism of spin-ladder compounds with trapped-ion crystals
2012
Abstract The quest for experimental platforms that allow for the exploration, and even control, of the interplay of low dimensionality and frustration is a fundamental challenge in several fields of quantum many-body physics, such as quantum magnetism. Here, we propose the use of cold crystals of trapped ions to study a variety of frustrated quantum spin ladders. By optimizing the trap geometry, we show how to tailor the low dimensionality of the models by changing the number of legs of the ladders. Combined with a method for selectively hiding ions provided by laser addressing, it becomes possible to synthesize stripes of both triangular and Kagome lattices. Besides, the degree of frustrat…
Bounds on mixed state entanglement
2020
In the general framework of d 1 ×
Brownian dynamics simulations of colloidal hard spheres. Effects of sample dimensionality on self-diffusion
1994
The self-diffusion coefficients of colloidal hard spheres were determined by Brownian dynamics (BD) computer simulations using a new efficient algorithm for treatment of the hard-sphere interactions. Calculations were done on an Apple PC type MacIIcx and on a Micro VAX 3000, considering samples in two and three dimensions at varying particle concentrations. Our results in three dimensions are compared with experimental results from our own group which were obtained by forced Rayleigh scattering (FRS), and with numerical results from a dynamical Monte Carlo simulation by Cichocki and Hinsen. Good agreement with the latter was found for particle volume fractions up to 0.40. Differences in the…
Role of dimensionality in spontaneous magnon decay: easy-plane ferromagnet
2014
We calculate magnon lifetime in an easy-plane ferromagnet on a tetragonal lattice in transverse magnetic field. At zero temperature magnons are unstable with respect to spontaneous decay into two other magnons. Varying ratio of intrachain to interchain exchanges in this model we consider the effect of dimensionality on spontaneous magnon decay. The strongest magnon damping is found in the quasi-one-dimensional case for momenta near the Brillouin zone boundary. The sign of a weak interchain coupling has a little effect on the magnon decay rate. The obtained theoretical results suggest possibility of experimental observation of spontaneous magnon decay in a quasi-one-dimensional ferromagnet C…
Robust non-Markovianity in ultracold gases
2012
We study the effect of thermal fluctuations on a probe qubit interacting with a Bose-Einstein condensed (BEC) reservoir. The zero-temperature case was studied in [Haikka P et al 2011 Phys. Rev. A 84 031602], where we proposed a method to probe the effects of dimensionality and scattering length of a BEC based on its behavior as an environment. Here we show that the sensitivity of the probe qubit is remarkably robust against thermal noise. We give an intuitive explanation for the thermal resilience, showing that it is due to the unique choice of the probe qubit architecture of our model.
Quantitative modeling of spin relaxation in quantum dots
2011
Physics Department, Harvard University, 02138 Cambridge MA, USA(Dated: December 16, 2011)We use numerically exact diagonalization to calculate the spin-orbit and phonon-induced triplet-singlet relaxation rate in a two-electron quantum dot exposed to a tilted magnetic field. Our schemeincludes a three-dimensional description of the quantum dot, the Rashba and the linear and cubicDresselhaus spin-orbit coupling, the ellipticity of the quantum dot, and the full angular descriptionof the magnetic field. We are able to find reasonable agreement with the experimental results ofMeunier et al. [Phys. Rev. Lett. 98, 126601 (2007)] in terms of the singlet-triplet energy splittingand the spin relaxation …
The effect of reducing dimensionality on the excitonic recombination in InAs/InP heterostructures
1997
In this work we study the exciton recombination of InAs/InP self-organized quantum dots by means of photolumincscence (PL) as a function of temperature and excitation density. Well defined islands, spatially separated in most cases, and with different size distribution, make localized exciton recombination the dominant contribution to the PL spectrum. From our experimental results, we propose the co-existence of two types of islands, one with small height whose contribution to the PL spectra is important in samples with low InAs coverage (below two monolayers), and the properly 3D islands, whose dimensions and sheet concentration increase with the InAs coverage. Good quality structures are …
Dynamic heterogeneities in the out-of-equilibrium dynamics of simple spherical spin models.
2003
The response of spherical two-spin interaction models, the spherical ferromagnet (s-FM) and the spherical Sherrington-Kirkpatrick (s-SK) model, is calculated for the protocol of the so-called nonresonant hole burning experiment (NHB) for temperatures below the respective critical temperatures. It is shown that it is possible to select dynamic features in the out-of-equilibrium dynamics of both models, one of the hallmarks of dynamic heterogeneities. The behavior of the s-SK model and the s-FM in three dimensions is very similar, showing dynamic heterogeneities in the long time behavior, i.e. in the aging regime. The appearence of dynamic heterogeneities in the s-SK model explicitly demonstr…
Application of the Density Matrix Renormalization Group in momentum space
2001
We investigate the application of the Density Matrix Renormalization Group (DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$ hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increa…