scholarly journals Coordinated self-interference of wave packets: a new route towards classicality for structurally stable systems

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
M. Ćosić ◽  
S. Petrović ◽  
S. Bellucci
Keyword(s):  
Proton Beam ◽  
Structural Stability ◽  
Phase Function ◽  
Quantum Dynamics ◽  
Wave Packets ◽  
The Self ◽  
Levels Of Reality ◽  
Classical Behavior ◽  
Diffraction Patterns ◽  
Structurally Stable

Abstract This is a study of proton transmission through planar channels of tungsten, where a proton beam is treated as an ensemble of noninteracting wave packets. For this system, the structural stability manifests in an appearance of caustic lines, and as an equivalence of self-interference produced waveforms with canonical diffraction patterns. We will show that coordination between particle self-interference is an additional manifestation of the structural stability existing only in ensembles. The main focus of the analysis was on the ability of the coordination to produce classical structures. We have found that the structures produced by the self-interference are organized in a very different manner. The coordination can enhance or suppress the quantum aspects of the dynamics. This behavior is explained by distributions of inflection, undulation, and singular points of the ensemble phase function, and their bifurcations. We have shown that the coordination has a topological origin which allows classical and quantum levels of reality to exist simultaneously. The classical behavior of the ensemble emerges out of the quantum dynamics without a need for reduction of the quantum to the classical laws of motion.

scholarly journals Opacity from Loops in AdS

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Alexandria Costantino ◽  
Sylvain Fichet
Keyword(s):  
Imaginary Part ◽  
Quantum Dynamics ◽  
Model Building ◽  
Asymptotic Properties ◽  
The Self ◽  
Effective Theory ◽  
Self Energy ◽  
Higher Dimensional ◽  
Timelike Region ◽  
Spectral Representations

Abstract We investigate how quantum dynamics affects the propagation of a scalar field in Lorentzian AdS. We work in momentum space, in which the propagator admits two spectral representations (denoted “conformal” and “momentum”) in addition to a closed-form one, and all have a simple split structure. Focusing on scalar bubbles, we compute the imaginary part of the self-energy ImΠ in the three representations, which involves the evaluation of seemingly very different objects. We explicitly prove their equivalence in any dimension, and derive some elementary and asymptotic properties of ImΠ.Using a WKB-like approach in the timelike region, we evaluate the propagator dressed with the imaginary part of the self-energy. We find that the dressing from loops exponentially dampens the propagator when one of the endpoints is in the IR region, rendering this region opaque to propagation. This suppression may have implications for field-theoretical model-building in AdS. We argue that in the effective theory (EFT) paradigm, opacity of the IR region induced by higher dimensional operators censors the region of EFT breakdown. This confirms earlier expectations from the literature. Specializing to AdS5, we determine a universal contribution to opacity from gravity.

Relation of Phase Stability Boundary to the Fill-Up Bonding States In Ni3V,Co3V and Fe3V

1990 ◽  
Vol 213 ◽  
Author(s):  
W. Lin ◽  
Jian-Hua Xu ◽  
A.J. Freeman
Keyword(s):  
Structural Stability ◽  
Electronic Structures ◽  
Local Density ◽  
Stability Boundary ◽  
The Self ◽  
Orbital Method ◽  
Density Approximation ◽  
Cohesive Properties ◽  
Self Consistent ◽  
Electronic Concentration

ABSTRACTThe electronic structures and cohesive properties of the intermetallics Ni3V, Co3V, and Fe3V in the L12 structure have been studied using the self-consistent total energy linear muffin-tin orbital method based on the local density approximation. The simple rigid-band concept appears to be adequate to explain the structural stability of these compounds. Further,the structural stability of the pseudobinary compounds (Ni,Co,Fe)3V has been investigated based on the rigid-band scheme. The correlation between the electronic concentration and the crystal structure is shown to be related to the fill-up of the bonding states.

scholarly journals COHERENT STATES OF QUANTUM NONLINEAR SYSTEMS

1995 ◽  
Vol 09 (28n29) ◽  
pp. 1839-1844 ◽  
Author(s):  
Z. HABA
Keyword(s):  
Nonlinear Systems ◽  
Wave Packet ◽  
Integrable Systems ◽  
Coherent States ◽  
Quantum Dynamics ◽  
Wave Packets

Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape for times of order [Formula: see text].

scholarly journals Scalar field cosmology — geometry of dynamics

2014 ◽  
Vol 11 (02) ◽  
pp. 1460012 ◽  
Author(s):  
Marek Szydłowski ◽  
Orest Hrycyna ◽  
Aleksander Stachowski
Keyword(s):  
Phase Space ◽  
Scalar Field ◽  
Dynamical Systems ◽  
Potential Function ◽  
Structural Stability ◽  
Saddle Points ◽  
Scalar Fields ◽  
Fine Tuning ◽  
Scalar Field Cosmology ◽  
Structurally Stable

We study the Scalar Field Cosmology (SFC) using the geometric language of the phase space. We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric. The metric in the ensemble is used to measure a distance between different models. We point out the advantages of visualization of dynamics in the phase space. It is investigated the genericity of some class of models in the context of fine tuning of the form of the potential function in the ensemble of SFC. We also study the symmetries of dynamical systems of SFC by searching for their exact solutions. In this context, we stressed the importance of scaling solutions. It is demonstrated that scaling solutions in the phase space are represented by unstable separatrices of the saddle points. Only critical point itself located on two-dimensional stable submanifold can be identified as scaling solution. We have also found a class of potentials of the scalar fields forced by the symmetry of differential equation describing the evolution of the Universe. A class of potentials forced by scaling (homology) symmetries was given. We point out the role of the notion of a structural stability in the context of the problem of indetermination of the potential form of the SFC. We characterize also the class of potentials which reproduces the ΛCDM model, which is known to be structurally stable. We show that the structural stability issue can be effectively used is selection of the scalar field potential function. This enables us to characterize a structurally stable and therefore a generic class of SFC models. We have found a nonempty and dense subset of structurally stable models. We show that these models possess symmetry of homology.

scholarly journals Characterisations of Ω-stability and structural stability via inverse shadowing

2006 ◽  
Vol 74 (2) ◽  
pp. 185-196 ◽  
Author(s):  
Taeyoung Choi ◽  
Keonhee Lee ◽  
Yong Zhang
Keyword(s):  
Structural Stability ◽  
Shadowing Property ◽  
Inverse Shadowing ◽  
Orbital Inverse Shadowing ◽  
Structurally Stable

We give characterisations of Ω-stable diffeomorphisms and structurally stable diffeomorphisms via the notions of weak inverse shadowing and orbital inverse shadowing, respectively. More precisely, it is proved that the C1 interior of the set of diffeomorphisms with the weak inverse shadowing property coincides with the set of Ω-stable diffeomorphisms and the C1 interior of the set of diffeomorphisms with the orbital inverse shadowing property coincides with the set of structurally stable diffeomorphisms.

Shadowing and structural stability for operators

2020 ◽  
pp. 1-20
Author(s):  
NILSON C. BERNARDES ◽  
ALI MESSAOUDI
Keyword(s):  
Banach Space ◽  
Dynamical Systems ◽  
Structural Stability ◽  
Invertible Operator ◽  
Hyperbolic Operator ◽  
Weighted Shifts ◽  
Shadowing Property ◽  
Finite Dimensional ◽  
Structurally Stable

A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained by Hartman in 1960 for operators on finite-dimensional spaces. The general case was independently obtained by Palis and Pugh around 1968. We will exhibit a class of examples of structurally stable operators that are not hyperbolic, thereby showing that the converse of the above-mentioned result is false in general. We will also prove that an invertible operator on a Banach space is hyperbolic if and only if it is expansive and has the shadowing property. Moreover, we will show that if a structurally stable operator is expansive, then it must be uniformly expansive. Finally, we will characterize the weighted shifts on the spaces $c_{0}(\mathbb{Z})$ and $\ell _{p}(\mathbb{Z})$ ( $1\leq p<\infty$ ) that satisfy the shadowing property.

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