375 research outputs found
Dynamics of finite Fermi-Hubbard and Bose-Hubbard systems
This paper analyzes dynamical properties of small Fermi-Hubbard and
Bose-Hubbard systems, focusing on the structure of the underlying Hilbert
space. We evaluate time-dependent quantities such as the return probability to
the initial state and the spin imbalance of spin-1/2 fermions. The results are
compared with recent experimental observations in ultracold gases. For the
symmetric two-site Fermi-Hubbard model we find that the spin imbalance and the
return probability are controlled by two and three frequencies, respectively.
The spin imbalance and the return probability are identical for the asymmetric
Falicov-Kimball limit and controlled by only one frequency. In general, the
transition probabilities between the initial state and energy eigenstates
depend strongly on the particle-particle interaction. This is discussed for
"self trapping" of spinless bosons in a double-well potential. We observe that
the available Hilbert space is reduced significantly by strong interaction.Comment: 12 pages, 5 figure
Stability and Complexity of Minimising Probabilistic Automata
We consider the state-minimisation problem for weighted and probabilistic
automata. We provide a numerically stable polynomial-time minimisation
algorithm for weighted automata, with guaranteed bounds on the numerical error
when run with floating-point arithmetic. Our algorithm can also be used for
"lossy" minimisation with bounded error. We show an application in image
compression. In the second part of the paper we study the complexity of the
minimisation problem for probabilistic automata. We prove that the problem is
NP-hard and in PSPACE, improving a recent EXPTIME-result.Comment: This is the full version of an ICALP'14 pape
Maximum Likelihood, Minimum Effort
We provide an efficient method for computing the maximum likelihood mixed
quantum state (with density matrix rho) given a set of measurement outcome in a
complete orthonormal operator basis subject to Gaussian noise. Our method works
by first changing basis yielding a candidate density matrix mu which may have
nonphysical (negative) eigenvalues, and then finding the nearest physical state
under the 2-norm. Our algorithm takes at worst O(d^4) for the basis change plus
O(d^3) for finding rho where d is the dimension of the quantum state. In the
special case where the measurement basis is strings of Pauli operators, the
basis change takes only O(d^3) as well. The workhorse of the algorithm is a new
linear-time method for finding the closest probability distribution (in
Euclidean distance) to a set of real numbers summing to one.Comment: 4 pages, 5 pdf figures. Replaced with corrections and expanded
figure
On the Strength of Spin-Isospin Transitions in A=28 Nuclei
The relations between the strengths of spin-isospin transition operators
extracted from direct nuclear reactions, magnetic scattering of electrons and
processes of semi-leptonic weak interactions are discussed.Comment: LaTeX, 8 pages, 1Postscript with figur
Population trapping in three-state quantum loops revealed by Householder reflections
Population trapping occurs when a particular quantum-state superposition is
immune to action by a specific interaction, such as the well-known dark state
in a three-state lambda system. We here show that in a three-state loop
linkage, a Hilbert-space Householder reflection breaks the loop and presents
the linkage as a single chain. With certain conditions on the interaction
parameters, this chain can break into a simple two-state system and an
additional spectator state. Alternatively, a two-photon resonance condition in
this Householder-basis chain can be enforced, which heralds the existence of
another spectator state. These spectator states generalize the usual dark state
to include contributions from all three bare basis states and disclose hidden
population trapping effects, and hence hidden constants of motion. Insofar as a
spectator state simplifies the overall dynamics, its existence facilitates the
derivation of analytic solutions and the design of recipes for quantum state
engineering in the loop system. Moreover, it is shown that a suitable sequence
of Householder transformations can cast an arbitrary N-dimensional hermitian
Hamiltonian into a tridiagonal form. The implication is that a general N-state
system, with arbitrary linkage patterns where each state connects to any other
state, can be reduced to an equivalent chainwise-connected system, with
nearest-neighbor interactions only, with ensuing possibilities for discovering
hidden multidimensional spectator states and constants of motion
Geometry of Polynomials and Root-Finding via Path-Lifting
Using the interplay between topological, combinatorial, and geometric
properties of polynomials and analytic results (primarily the covering
structure and distortion estimates), we analyze a path-lifting method for
finding approximate zeros, similar to those studied by Smale, Shub, Kim, and
others. Given any polynomial, this simple algorithm always converges to a root,
except on a finite set of initial points lying on a circle of a given radius.
Specifically, the algorithm we analyze consists of iterating where the form a decreasing sequence of
real numbers and is chosen on a circle containing all the roots. We show
that the number of iterates required to locate an approximate zero of a
polynomial depends only on (where is
the radius of convergence of the branch of taking to a root
) and the logarithm of the angle between and certain critical
values. Previous complexity results for related algorithms depend linearly on
the reciprocals of these angles. Note that the complexity of the algorithm does
not depend directly on the degree of , but only on the geometry of the
critical values.
Furthermore, for any polynomial with distinct roots, the average number
of steps required over all starting points taken on a circle containing all the
roots is bounded by a constant times the average of . The
average of over all polynomials with roots in the
unit disk is . This algorithm readily generalizes to
finding all roots of a polynomial (without deflation); doing so increases the
complexity by a factor of at most .Comment: 44 pages, 12 figure
A mathematical framework for contact detection between quadric and superquadric surfaces
The calculation of the minimum distance between surfaces plays an important role in computational mechanics, namely, in the study of constrained multibody systems where contact forces take part. In this paper, a general rigid contact detection methodology for non-conformal bodies, described by ellipsoidal and superellipsoidal surfaces, is presented. The mathematical framework relies on simple algebraic and differential geometry, vector calculus, and on the C2 continuous implicit representations of the surfaces. The proposed methodology establishes a set of collinear and orthogonal constraints between vectors defining the contacting surfaces that, allied with loci constraints, which are specific to the type of surface being used, formulate the contact problem. This set of non-linear equations is solved numerically with the Newton-Raphson method with Jacobian matrices calculated analytically. The method outputs the coordinates of the pair of points with common normal vector directions and, consequently, the minimum distance between both surfaces. Contrary to other contact detection methodologies, the proposed mathematical framework does not rely on polygonal-based geometries neither on complex non-linear optimization formulations. Furthermore, the methodology is extendable to other surfaces that are (strictly) convex, interact in a non-conformal fashion, present an implicit representation, and that are at least C2 continuous. Two distinct methods for calculating the tangent and binormal vectors to the implicit surfaces are introduced: (i) a method based on the Householder reflection matrix; and (ii) a method based on a square plate rotation mechanism. The first provides a base of three orthogonal vectors, in which one of them is collinear to the surface normal. For the latter, it is shown that, by means of an analogy to the referred mechanism, at least two non-collinear vectors to the normal vector can be determined. Complementarily, several mathematical and computational aspects, regarding the rigid contact detection methodology, are described. The proposed methodology is applied to several case tests involving the contact between different (super)ellipsoidal contact pairs. Numerical results show that the implemented methodology is highly efficient and accurate for ellipsoids and superellipsoids.Fundação para a Ciência e a Tecnologia (FCT
Investigating the Atmospheric Mass Loss of the Kepler-105 Planets Straddling the Radius Gap
An intriguing pattern among exoplanets is the lack of detected planets
between approximately R and R. One proposed
explanation for this "radius gap" is the photoevaporation of planetary
atmospheres, a theory that can be tested by studying individual planetary
systems. Kepler-105 is an ideal system for such testing due to the ordering and
sizes of its planets. Kepler-105 is a sun-like star that hosts two planets
straddling the radius gap in a rare architecture with the larger planet closer
to the host star ( R, days, R, days). If photoevaporation sculpted the
atmospheres of these planets, then Kepler-105b would need to be much more
massive than Kepler-105c to retain its atmosphere, given its closer proximity
to the host star. To test this hypothesis, we simultaneously analyzed radial
velocities (RVs) and transit timing variations (TTVs) of the Kepler-105 system,
measuring disparate masses of M ( g cm) and M ( g cm). Based on these masses, the difference in gas
envelope content of the Kepler-105 planets could be entirely due to
photoevaporation (in 76\% of scenarios), although other mechanisms like
core-powered mass loss could have played a role for some planet albedos.Comment: 14 pages, 3 figures, 2 table
Statistical indicators useful in real spectrum location
In this paper some new results are described, useful for locating the spectrum of a matrix A through mean, standard deviation and third centered moment of the spectrum distribution which can be expressed in terms of traces
The Behavioral Roots of Information Systems Security:Exploring Key Factors Related to Unethical IT Use
Unethical information technology (IT) use, related to activities such as hacking, software piracy, phishing, and spoofing, has become a major security concern for individuals, organizations, and society in terms of the threat to information systems (IS) security. While there is a growing body of work on this phenomenon, we notice several gaps, limitations, and inconsistencies in the literature. In order to further understand this complex phenomenon and reconcile past findings, we conduct an exploratory study to uncover the nomological network of key constructs salient to this phenomenon, and the nature of their interrelationships. Using a scenario-based study of young adult participants, and both linear and nonlinear analyses, we uncover key nuances of this phenomenon of unethical IT use. We find that unethical IT use is a complex phenomenon, often characterized by nonlinear and idiosyncratic relationships between the constructs that capture it. Overall, ethical beliefs held by the individuals, along with economic, social, and technological considerations are found to be relevant to this phenomenon. In terms of practical implications, these results suggest that multiple interventions at various levels may be required to combat this growing threat to IS security
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