On the Stability of Permanent Rotations of a Chain of Two Lagrange Gyrostats in a Central Gravitational Field

2016 ◽  
Author(s):  
Dmitriy Chebanov ◽  
Jose A. Salas
Keyword(s):  
Gravitational Field ◽  
Sufficient Conditions ◽  
Vertical Axis ◽  
Many Body ◽  
A Chain ◽  
The Stability ◽  
The Many ◽  
The One ◽  
Permanent Rotations ◽  
Central Gravitational Field

In this paper we study the problem of the motion of a two-gyrostat chain about a fixed point in a central gravitational field. We assume that the mass distribution of each gyrostat is analogous to the one of a Lagrange top, the gyrostatic moment of each gyrostat is constant relative to its carrier, and the center of a spherical joint connecting the gyrostats belongs to their dynamic symmetry axes. We establish and analyze sufficient conditions for stability of the chain’s permanent rotations about a vertical axis. Our findings extend corresponding results in the dynamics of a single gyrostat to a case of the two-gyrostat chain as well as generalize some of the known properties of permanent rotations in the many-body dynamics.

On Permanent Rotations of a System of Two Coupled Gyrostats in a Central Newtonian Force Field

2015 ◽  
Author(s):  
Dmitriy Chebanov ◽  
Jose A. Salas
Keyword(s):  
Force Field ◽  
Vertical Axis ◽  
Many Body ◽  
Newtonian Force ◽  
Body Dynamics ◽  
A Chain ◽  
The Many ◽  
The One ◽  
Permanent Rotations ◽  
Newtonian Force Field

This paper studies the problem of the motion of a chain of two gyrostats coupled by an ideal spherical joint. The chain moves about a fixed point in a central Newtonian force field. Under the assumption that the gyrostatic moment of each gyrostat is constant relative to its carrier, the paper establishes and analyzes the conditions for existence of the chain’s permanent rotations about a vertical axis. For a case when each gyrostat has the mass distribution analogous to the one of a Lagrange gyroscope, the paper derives and analyzes the necessary conditions for stability of the permanent rotations. The findings of the paper extend corresponding results in the dynamics of a single gyrostat to a case of the multibody chain as well as generalize some of the known properties of permanent rotations in the many-body dynamics.

scholarly journals Entangling Lattice-Trapped Bosons with a Free Impurity: Impact on Stationary and Dynamical Properties

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 290
Author(s):  
Maxim Pyzh ◽  
Kevin Keiler ◽  
Simeon I. Mistakidis ◽  
Peter Schmelcher
Keyword(s):  
Structural Changes ◽  
Many Body ◽  
Wide Range ◽  
Entropy Measures ◽  
Particle Level ◽  
The Many ◽  
The One ◽  
Tunneling Dynamics ◽  
The Individual ◽  
Trapped Bosons

We address the interplay of few lattice trapped bosons interacting with an impurity atom in a box potential. For the ground state, a classification is performed based on the fidelity allowing to quantify the susceptibility of the composite system to structural changes due to the intercomponent coupling. We analyze the overall response at the many-body level and contrast it to the single-particle level. By inspecting different entropy measures we capture the degree of entanglement and intraspecies correlations for a wide range of intra- and intercomponent interactions and lattice depths. We also spatially resolve the imprint of the entanglement on the one- and two-body density distributions showcasing that it accelerates the phase separation process or acts against spatial localization for repulsive and attractive intercomponent interactions, respectively. The many-body effects on the tunneling dynamics of the individual components, resulting from their counterflow, are also discussed. The tunneling period of the impurity is very sensitive to the value of the impurity-medium coupling due to its effective dressing by the few-body medium. Our work provides implications for engineering localized structures in correlated impurity settings using species selective optical potentials.

Many-body Green functions in nuclear physics

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740025 ◽  
Author(s):  
J. Speth ◽  
N. Lyutorovich
Keyword(s):  
Nuclear Physics ◽  
Green Functions ◽  
Many Body ◽  
General Applicability ◽  
Pair Correlations ◽  
Self Consistent ◽  
The Many ◽  
The One ◽  
General Relations ◽  
Three Body

Many-body Green functions are a very efficient formulation of the many-body problem. We review the application of this method to nuclear physics problems. The formulas which can be derived are of general applicability, e.g., in self-consistent as well as in nonself-consistent calculations. With the help of the Landau renormalization, one obtains relations without any approximations. This allows to apply conservation laws which lead to important general relations. We investigate the one-body and two-body Green functions as well as the three-body Green function and discuss their connection to nuclear observables. The generalization to systems with pair correlations are also presented. Numerical examples are compared with experimental data.

Stability and Construction of Caverns for The Disposal Of Cemented Low-And Medium-Level Wastes

1981 ◽  
Vol 11 ◽  
Author(s):  
W. Raab ◽  
C. Frohn ◽  
M.W. Schmidt
Keyword(s):  
Stability Analysis ◽  
Vertical Axis ◽  
Short Term ◽  
Advantages And Disadvantages ◽  
Medium Level ◽  
Practical Engineering ◽  
The Stability ◽  
The One ◽  
Salt Caverns

ABSTRACTThe geomechanical and mining-technological aspects of the construction of salt caverns as disposal chambers have been investigated during project phase 2, completed by mid 1981. With a view towards the stability analysis of such a cavern, FEM-estimates have been carried out and evaluated. From these it can be derived that- a rotational ellipsoid would be the most suitable shape- its dimensions should be 82 m (vertical axis) and 42 m (horizontal axis)- the distance (safety pillar) between the neighbouring caverns should be 170 m (vertical) and 180 m (horizontal).For practical engineering purposes the rotational ellipsoid can be modified into a cylinder with conic bottom and top. The numerical model simulated the short term as well as the long term characteristics of the surrounding salt rocks. The short term characteristics were assessed by an elastic approach, the long term characteristics by a rheological model. The input parameters have been determined by means of laboratory tests on ASSE rock salt.In a second step the characteristics of partially and completely filled caverns were simulated. It was shown clearly that deformation of the salt rock comes to a halt when counteracted by the filling.Based upon the results of the stability analysis, investigations were made to find out a suitable mining technique for the construction of the cavern. Solution mining and conventional development by means of drilling and blasting have been studied alternatively. Since both methods have their advantages and disadvantages a decision in favour of the one or the other cannot be made until the actual site has been defined.

STRUCTURAL PROPERTIES OF BIMETALLIC CLUSTERS FROM DENSITY FUNCTIONAL CALCULATIONS

2005 ◽  
Vol 19 (15n17) ◽  
pp. 2339-2344 ◽  
Author(s):  
EVA M. FERNÁNDEZ ◽  
LUIS C. BALBÁS ◽  
LUIS A. PÉREZ ◽  
KARO MICHAELIAN ◽  
IGNACIO L. GARZÓN
Keyword(s):  
Structural Properties ◽  
Density Functional ◽  
Geometry Optimization ◽  
Model Potential ◽  
Bimetallic Clusters ◽  
Many Body ◽  
Generalized Gradient ◽  
The Many ◽  
The One ◽  
Gupta Potential

The structural properties and energy ordering of the lowest lying isomers of bimetallic ( CuAu )n and ( PtPd )n, n=5-22 clusters have been investigated by means of density functional theory (DFT) in the generalized gradient approximation (GGA). The initial cluster geometry optimization is performed by using a genetic algorithm with the many body Gupta potential. This technique provide a distribution of the lowest energy cluster structures, that are further reoptimized using the DFT-GGA methodology. The energy ordering of isomers obtained with the Gupta potential does not agree, in general, with the one obtained using DFT-GGA for the two bimetallic clusters investigated. However, the lowest energy strucutures of the ( CuAu )n nanoalloy show icosahedral patterns in agreement with the results obtained with the model potential. For the ( PtPd )n clusters segregation effects are found, where the Pt atoms are forming the cluster core and the Pd atoms are on the cluster surface, in agreement with previous calculations using the many body Gupta potential.

scholarly journals Many-Electron QED with Redefined Vacuum Approach

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1014
Author(s):  
Romain N. Soguel ◽  
Andrey V. Volotka ◽  
Dmitry A. Glazov ◽  
Stephan Fritzsche
Keyword(s):  
Perturbation Theory ◽  
Electronic Configuration ◽  
Bound State ◽  
Many Body ◽  
Photon Exchange ◽  
Self Energy ◽  
Many Body Perturbation Theory ◽  
Formula Derivation ◽  
The Many ◽  
The One

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.

scholarly journals Frozen-Density Embedding Based Many-Body Expansions

2020 ◽  
Author(s):  
Daniel Schmitt-Monreal ◽  
Christoph R. Jacob
Keyword(s):  
Density Functional ◽  
Molecular Clusters ◽  
Test Case ◽  
Chemical Calculation ◽  
Many Body ◽  
Functional Theory ◽  
Truncation Errors ◽  
Potential Benefits ◽  
The Many ◽  
The One

<div>Fragmentation methods allow for the accuratequantum-chemical treatment of large molecular clusters and materials. Here, we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account of the environmentin the subsystem calculation performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the systems' total energy. This provides a correctionto the energies calculated with a conventional, energy-based MBE that only depends on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate quantum-chemical calculation of molecular clusters and materials.</div>

scholarly journals Detecting a many-body mobility edge with quantum quenches

2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Piero Naldesi ◽  
Elisa Ercolessi ◽  
Tommaso Roscilde
Keyword(s):  
Periodic Potential ◽  
Cold Atom ◽  
Many Body ◽  
Mobility Edge ◽  
Scaling Properties ◽  
Quasi Stationary State ◽  
Quantum Quenches ◽  
A Chain ◽  
The Many ◽  
Practical Scheme

The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from “extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to “localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder – if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using “quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.

Few-electron quantum-dot spintronics

2017 ◽  
Author(s):  
D.V. Melnikov ◽  
J. Kim ◽  
L.-X. Zhang ◽  
J.-P. Leburton
Keyword(s):  
Electron System ◽  
Stability Diagram ◽  
Theoretical Description ◽  
Exact Diagonalization ◽  
Many Body ◽  
Approximate Methods ◽  
Diagonalization Method ◽  
The Stability ◽  
The Many ◽  
Exact Diagonalization Method

This article examines the spin and charge properties of double and triple quantum dots (QDs) populated containing just a few electrons, with particular emphasis on laterally coupled QDs. It first describes the theoretical approach, known as exact diagonalization method, utilized on the example of the two-electron system in coupled QDs that are modelled as two parabolas. The many-body problem is solved via the exact diagonalization method as well as variational Heitler–London and Monte Carlo methods. The article proceeds by considering the general characteristics of the two-electron double-QD structure and limitations of the approximate methods commonly used for its theoretical description. It also discusses the stability diagram for two circular dots and investigates how its features are affected by the QD elliptical deformations. Finally, it assesses the behavior of the two-electron system in the realistic double-dot confinement potentials.

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