scholarly journals Husimi–Wigner representation of chaotic eigenstates

2008 ◽  
Vol 464 (2094) ◽  
pp. 1503-1524 ◽  
Author(s):  
Fabricio Toscano ◽  
Anatole Kenfack ◽  
Andre R.R Carvalho ◽  
Jan M Rost ◽  
Alfredo M Ozorio de Almeida
Keyword(s):  
Hilbert Space ◽  
Coherent State ◽  
Pure State ◽  
Degrees Of Freedom ◽  
Factor Space ◽  
Wigner Functions ◽  
Higher Dimensional ◽  
Wigner Representation ◽  
Quantum Point ◽  
The Individual

Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. Physically, this factorization corresponds to the description of interacting components of a quantum system with many degrees of freedom and the sections could be generated by conceivable partial measurements. The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi–Wigner representation. It occupies an intermediate ground between the drastic suppression of non-classical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of a chaotic Hamiltonian. Though less regular, the individual two-dimensional Wigner functions resemble those of semiclassically quantized states.

Simplifying Schmidt number witnesses via higher-dimensional embeddings

2004 ◽  
Vol 4 (3) ◽  
pp. 207-221
Author(s):  
F. Hulpke ◽  
D. Bruss ◽  
M. Levenstein ◽  
A. Sanpera
Keyword(s):  
Hilbert Space ◽  
Schmidt Number ◽  
Convex Sets ◽  
Entanglement Witness ◽  
Simple Method ◽  
Dimensional Hilbert Space ◽  
Higher Dimensional ◽  
Arbitrary Convex

We apply the generalised concept of witness operators to arbitrary convex sets, and review the criteria for the optimisation of these general witnesses. We then define an embedding of state vectors and operators into a higher-dimensional Hilbert space. This embedding leads to a connection between any Schmidt number witness in the original Hilbert space and a witness for Schmidt number two (i.e. the most general entanglement witness) in the appropriate enlarged Hilbert space. Using this relation we arrive at a conceptually simple method for the construction of Schmidt number witnesses in bipartite systems.

A Local Approach for Computing Smooth B-spline Surfaces for Arbitrary Quadrilateral Base Meshes

2021 ◽  
pp. 1-28
Author(s):  
Dennis Mosbach ◽  
Katja Schladitz ◽  
Bernd Hamann ◽  
Hans Hagen
Keyword(s):  
Degrees Of Freedom ◽  
Tangent Plane ◽  
Local Approach ◽  
Approximation Process ◽  
Surface Approximation ◽  
B Spline ◽  
Spline Surfaces ◽  
Continuous Surface ◽  
Normal Vectors ◽  
The Individual

Abstract We present a method for approximating surface data of arbitrary topology by a model of smoothly connected B-spline surfaces. Most of the existing solutions for this problem use constructions with limited degrees of freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.

Modular Origami Robot Inspired by a Scorpion Tail

2018 ◽  
Author(s):  
Jovana Jovanova ◽  
Maja Anachkova ◽  
Viktor Gavriloski ◽  
Dimitar Petrevski ◽  
Franka Grazhdani ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Basic Structure ◽  
Body Parts ◽  
Main Concept ◽  
Multiple Degrees Of Freedom ◽  
Transparent Layer ◽  
Plastic Foil ◽  
Greater Curvature ◽  
The Individual ◽  
Outer Coating

Arthropod animals like scorpions with modular body parts can be an inspiration for a robot’s structure. The design presented here relays on inter-connected origami towers, but could also be easily disassembled. Each origami tower is fully autonomous and at the same time is part of the robot as a whole. The towers are positioned between two platforms that enable modularity. The scorpion’s tale shape is achieved by the varying platform diameter resulting in cone-like form. Each tower is actuated independently to enable multiple degrees of freedom. Maneuvering with separated units, assists in easier reparation as well as replacement. Detaching the towers into separate parts makes this structure develop more precise movements, since every unit will move autonomously. Therefore, having a higher number of separated movements combined leads to a smooth bionic movement. So, the overall hierarchy will be modular contributing to a greater curvature bending of the whole structure. Actuating and maneuvering the robot in the main concept is done by separated electro motors, built in the platform. The basic structure will be built from thick paper with plastic coatings. The thick paper itself is lightweight, but at the same time flexible. To protect the paper towers, double plastic foil is placed as an outer coating which acts as an origami cover. This transparent layer is elastic hence it can follow and support the individual units’ movements. This work is focused on understanding origami towers kinematics and different combinations of inter-connected towers to achieve multiple degrees of freedom. A conceptual model is developed, supported by CAD and mathematical models. At the end a prototype is presented.

scholarly journals Classical Chaos Described by a Density Matrix

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 739-746
Author(s):  
Andres Mauricio Kowalski ◽  
Angelo Plastino ◽  
Gaspar Gonzalez
Keyword(s):  
Density Matrix ◽  
Pure State ◽  
Classical Limit ◽  
Degrees Of Freedom ◽  
Temporal Evolution ◽  
Entropy Density ◽  
State Density ◽  
Unexpected Result ◽  
Semiclassical Model ◽  
Classical Chaos

In this paper, a reference to the semiclassical model, in which quantum degrees of freedom interact with classical ones, is considered. The classical limit of a maximum-entropy density matrix that describes the temporal evolution of such a system is analyzed. Here, it is analytically shown that, in the classical limit, it is possible to reproduce classical results. An example is classical chaos. This is done by means a pure-state density matrix, a rather unexpected result. It is shown that this is possible only if the quantum part of the system is in a special class of states.

scholarly journals The association gene’s TNFα G(308) with quantity of TNFα and degree of liver’s fibrosis in patients with chronic hepatitis C

2018 ◽  
Vol 22 (4) ◽  
pp. 682-685
Author(s):  
E.N. Usychenko ◽  
Yu.I. Bazhora ◽  
E.M. Usychenko ◽  
V.A. Gudz
Keyword(s):  
Chronic Hepatitis ◽  
Hepatitis C ◽  
Liver Fibrosis ◽  
Chronic Hepatitis C ◽  
Degrees Of Freedom ◽  
Morphological Changes ◽  
Polymorphic Marker ◽  
Pathological Process ◽  
Hepatic Tissue ◽  
The Individual

The data on the polymorphism of cytokine genes associated with individual reactivity on the effects of hepatitis C virus, predict the rate of progression of liver fibrosis. The purpose of this work is study the association of the polymorphic marker G308A of the TNFα gene with its quantitative content and degree of liver fibrosis in patients with chronic hepatitis C. A total of 100 patients with CSF were examined. The polymorphism of G308A gene’s TNFα was studied by amplification of the corresponding genome zones by PCR. The assessment of the degree of fibrosis was performed using the non-invasive Fibrotest method. The study of the quantity of TNFα cytokine in serum of patients was performed by ELISA. The distribution of genotypes on the investigated polymorphic loci was verified using Pearson's χ2 criterion. The frequencies of alleles and genotypes in the groups were compared using Pearson's χ2 criterion with Yates correction for continuity with the number of degrees of freedom 1. In order to detect the correlation dependencies between the individual parameters, the Spearman correlation coefficient was applied. It was found that a smaller degree of fibrosis was observed in carriers of the GG TNFα genotype, and a greater degree of fibrosis in the carriers of the genotype AA TNFα (moderate feedback between the degree of fibrosis and the genotypes of TNFα). The higher content of TNFα is noted in the carriers of the AA genotype TNFα, the lower content of TNFα - in the carriers of the GG TNFα genotype (moderate feedback between the TNFα genotypes and the TNFα content). It has been established that a higher TNFα content is observed in patients with F1-F0 fibrosis, a lower TNFα content in patients with F2-F3 fibrosis (a strong correlation between the degree of fibrosis and the amount of TNFα cytokine). It is assumed that the production of the cytokine is determined at the genetic level, and the severity of changes in the cytokine profile in chronic hepatitis C affects the course of the pathological process. An increase in the TNFα content in chronic hepatitis C may be a marker for significant morphological changes in the hepatic tissue and high activity of the inflammatory process.

scholarly journals Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains

Science ◽  
2020 ◽  
Vol 367 (6474) ◽  
pp. 186-189 ◽  
Author(s):  
Jayadev Vijayan ◽  
Pimonpan Sompet ◽  
Guillaume Salomon ◽  
Joannis Koepsell ◽  
Sarah Hirthe ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Spatial Separation ◽  
Real Space ◽  
Quantum Gas ◽  
Interacting Particles ◽  
Time Resolved ◽  
One Dimensional ◽  
Quantum Numbers ◽  
Charge Correlations ◽  
The Individual

Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.

scholarly journals Hypothesized, Directly-Coded Curve Shapes in Growth Curve Analysis: An Example

2013 ◽  
Vol 3 (2) ◽  
pp. 13 ◽  
Author(s):  
Patricia M. Herman ◽  
Lee Sechrest
Keyword(s):  
Hierarchical Linear Modeling ◽  
Growth Curve ◽  
Degrees Of Freedom ◽  
Growth Curves ◽  
Curve Analysis ◽  
Small Samples ◽  
Growth Curve Analysis ◽  
Linear Modeling ◽  
Individual Level ◽  
The Individual

Growth curve analysis provides important informational benefits regarding intervention outcomes over time. Rarely, however, should outcome trajectories be assumed to be linear. Instead, both the shape and the slope of the growth curve can be estimated. Non-linear growth curves are usually modeled by including either higher-order time variables or orthogonal polynomial contrast codes. Each has limitations (multicollinearity with the first, a lack of coefficient interpretability with the second, and a loss of degrees of freedom with both) and neither encourages direct testing of alternative hypothesized curve shapes. Especially in studies with relatively small samples it is likely to be useful to preserve as much information as possible at the individual level. This article presents a step-by-step example of the use and testing of hypothesized curve shapes in the estimation of growth curves using hierarchical linear modeling for a small intervention study. DOI:10.2458/azu_jmmss_v3i2_herman

scholarly journals Gravitational Theory Without the Cosmological Constant Problem

1997 ◽  
Vol 12 (32) ◽  
pp. 2421-2424 ◽  
Author(s):  
E. I. Guendelman ◽  
A. B. Kaganovich
Keyword(s):  
Cosmological Constant ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
Realistic Model ◽  
Gravitational Theory ◽  
Space Time ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time

We develop a gravitational theory where the measure of integration in the action principle is not necessarily [Formula: see text] but it is determined dynamically through additional degrees of freedom. This theory is based on the demand that such measure respects the principle of "non-gravitating vacuum energy" which states that the Lagrangian density L can be changed to L + const. without affecting the dynamics. Formulating the theory in the first-order formalism we get as a consequence of the variational principle a constraint that enforces the vanishing of the cosmological constant. The most realistic model that implements these ideas is realized in a six or higher dimensional space–time. The compactification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic masses. It turns out that the remaining four-dimensional space–time must have effective zero cosmological constant.

A Precision System for Computed Tomography-Guided Needle Placement in the Thorax and Abdomen—Technical Design and Performance Analysis

2018 ◽  
Vol 12 (2) ◽  
Author(s):  
Maarten M. Arnolli ◽  
Martijn Buijze ◽  
Michel Franken ◽  
Ivo A. M. J. Broeders ◽  
Dannis M. Brouwer
Keyword(s):  
Computed Tomography ◽  
Degrees Of Freedom ◽  
Drive System ◽  
Needle Placement ◽  
Technical Design ◽  
User Requirement ◽  
Registration System ◽  
Ct Guided ◽  
And Performance ◽  
The Individual

A system was developed for computed tomography (CT)-guided needle placement in the thorax and abdomen, providing precise aiming of a needle guide (NG) to reach a user-specified target in a single manual insertion. The objective of this work is to present its technical design and analyze its performance in terms of placement error in air. The individual contributions to the placement error of a fiducial marker based system-to-CT registration system, a two degrees-of-freedom (2DOFs) drive system to aim the NG, and a structural link between NG and CT table were experimentally determined, in addition to the placement error of the overall system. An error contribution of 0.81 ± 0.34 mm was determined for the registration system, <1.2 mm and <3.3 mm for the drive system, and 0.35 mm and 0.43 mm for two load cases of the structural link. The overall unloaded system achieved 1.0 ± 0.25 mm and 2.6 ± 0.7 mm at 100 mm and 250 mm depth, respectively. The overall placement errors in air do not exceed the ≤5 mm error specified as a clinical user requirement for needle placement in tissue.

scholarly journals QUANTUM FIELD THEORY ON CURVED BACKGROUNDS — A PRIMER

2013 ◽  
Vol 28 (17) ◽  
pp. 1330023 ◽  
Author(s):  
MARCO BENINI ◽  
CLAUDIO DAPPIAGGI ◽  
THOMAS-PAUL HACK
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Degrees Of Freedom ◽  
Algebraic Approach ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
System A ◽  
Step Procedure ◽  
Free Fields

Goal of this paper is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, it is assigned to a physical system a suitable algebra of observables, which is meant to encode all algebraic relations among observables, such as commutation relations. In the second step, one must select an algebraic state in order to recover the standard Hilbert space interpretation of a quantum system. As quantum field theories possess infinitely many degrees of freedom, many unitarily inequivalent Hilbert space representations exist and the power of such approach is the ability to treat them all in a coherent manner. We will discuss in detail the algebraic approach for free fields in order to give the reader all necessary information to deal with the recent literature, which focuses on the applications to specific problems, mostly in cosmology.

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