Quantum volume

2015 ◽  
Vol 29 (23) ◽  
pp. 1550166 ◽  
Author(s):  
V. A. Ryabov
Keyword(s):  
Degrees Of Freedom ◽  
Free Particle ◽  
External Pressure ◽  
Dynamical Variable ◽  
Model Systems ◽  
Quantum Oscillator ◽  
Optomechanical System ◽  
Breathing Mode ◽  
Quantum Deformations ◽  
Quantum Volume

Quantum systems in a mechanical embedding, the breathing mode of a small particles, optomechanical system, etc. are far not the full list of examples in which the volume exhibits quantum behavior. Traditional consideration suggests strain in small systems as a result of a collective movement of particles, rather than the dynamics of the volume as an independent variable. The aim of this work is to show that some problem here might be essentially simplified by introducing periodic boundary conditions. At this case, the volume is considered as the independent dynamical variable driven by the internal pressure. For this purpose, the concept of quantum volume based on Schrödinger’s equation in [Formula: see text] manifold is proposed. It is used to explore several 1D model systems: An ensemble of free particles under external pressure, quantum manometer and a quantum breathing mode. In particular, the influence of the pressure of free particle on quantum oscillator is determined. It is shown also that correction to the spectrum of the breathing mode due to internal degrees of freedom is determined by the off-diagonal matrix elements of the quantum stress. The new treatment not using the “force” theorem is proposed for the quantum stress tensor. In the general case of flexible quantum 3D dynamics, quantum deformations of different type might be introduced similarly to monopole mode.

Excitonic Coupled-cluster Theory: Part I, General Formalism

2017 ◽  
Author(s):  
Yuhong Liu ◽  
Anthony Dutoi
Keyword(s):  
Electron Correlation ◽  
Degrees Of Freedom ◽  
Model Systems ◽  
Coupled Cluster ◽  
Effective Hamiltonian ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Companion Article ◽  
High Level ◽  
Fragment Interaction

<div> <div>A shortcoming of presently available fragment-based methods is that electron correlation (if included) is described at the level of individual electrons, resulting in many redundant evaluations of the electronic relaxations associated with any given fluctuation. A generalized variant of coupled-cluster (CC) theory is described, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction is pre-computed and permanently folded into the effective Hamiltonian. This article provides a high-level description of the CC variant, establishing some useful notation, and it demonstrates the advantage of the proposed paradigm numerically on model systems. A companion article shows that the electronic Hamiltonian of real systems may always be cast in the form demanded. This framework opens a promising path to build finely tunable systematically improvable methods to capture precise properties of systems interacting with a large number of other systems. </div> </div>

Excitonic Coupled-cluster Theory: Part I, General Formalism

2017 ◽  
Author(s):  
Yuhong Liu ◽  
Anthony Dutoi
Keyword(s):  
Electron Correlation ◽  
Degrees Of Freedom ◽  
Model Systems ◽  
Coupled Cluster ◽  
Effective Hamiltonian ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Companion Article ◽  
High Level ◽  
Fragment Interaction

<div> <div>A shortcoming of presently available fragment-based methods is that electron correlation (if included) is described at the level of individual electrons, resulting in many redundant evaluations of the electronic relaxations associated with any given fluctuation. A generalized variant of coupled-cluster (CC) theory is described, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction is pre-computed and permanently folded into the effective Hamiltonian. This article provides a high-level description of the CC variant, establishing some useful notation, and it demonstrates the advantage of the proposed paradigm numerically on model systems. A companion article shows that the electronic Hamiltonian of real systems may always be cast in the form demanded. This framework opens a promising path to build finely tunable systematically improvable methods to capture precise properties of systems interacting with a large number of other systems. </div> </div>

Modular Distributed Models of Engineering Structures

2003 ◽  
Author(s):  
Clark J. Radcliffe ◽  
Jon Sticklen
Keyword(s):  
Engineering Design ◽  
Degrees Of Freedom ◽  
Structural Model ◽  
Integrated Design ◽  
Model Systems ◽  
Structural Stiffness ◽  
Engineering Structures ◽  
Distributed Modeling ◽  
Communications Network ◽  
Component Models

Approaches to engineering design and manufacturing such as integrated design and manufacture and just in time fabrication depend on interaction with and among component supply companies that most often use very diverse technologies. The Internet Engineering Design Agents (i-EDA) software system uses a distributed, component-based, agent methodology that is realized following a strong black box approach to modeling. An individual Design Agent (DA) is a virtual product capable of encapsulating both descriptive and model based information about the product it represents. Hierarchically recursive agents for sub-systems and/or components are linked via a communications network to form larger integrated model systems. A two dimensional bridge system structural model is used as an example to illustrate the distributed assembly of structural models from components registered as DA’s on a communications network. Modular Distributed Modeling (MDM) of engineering structures performs static deflection analysis using traditional, fixed causality, structural stiffness models. This paper presents the methodology required to assemble traditional structural stiffness models provided by internet agents representing structural components. The methodology discussed assembles these component models into the structural stiffness model of an assembly distributed by an agents represent that physical assembly of components. Using this modular distributed modeling method; models of complex assemblies can be built and distributed while hiding the topology and characteristics of their structural subassemblies. The automated, modular, assembly of structural stiffness models will be derived for discrete physical connections. Discrete connections are important to the assembly of components such as truss and shaft structures where the relationship between component displacements involve discrete, matching, degrees of freedom on components to be assembled. Specific examples of discrete assembly of truss bridge component models will be presented.

scholarly journals PERIODIC ORBIT THEORY INCLUDING SPIN DEGREES OF FREEDOM

2004 ◽  
Vol 13 (01) ◽  
pp. 19-28 ◽  
Author(s):  
MATTHIAS BRACK ◽  
CHRISTIAN AMANN ◽  
MIKHAIL PLETYUKHOV ◽  
OLEG ZAITSEV
Keyword(s):  
Degrees Of Freedom ◽  
Model Systems ◽  
Periodic Orbit Theory ◽  
New Approach ◽  
Shell Effects ◽  
Fermion Systems ◽  
Recent Developments ◽  
Orbit Theory ◽  
Classical Phase Space ◽  
Spin Orbit Interactions

We summarize recent developments of the semiclassical description of shell effects in finite fermion systems with explicit inclusion of spin degrees of freedom, in particluar in the presence of spin-orbit interactions. We present a new approach that makes use of spin coherent states and a correspondingly enlarged classical phase space. Taking suitable limits, we can recover some of the earlier approaches. Applications to some model systems are presented.

scholarly journals ON UNITARITY OF A LINEARIZED YANG–MILLS FORMULATION FOR MASSLESS AND MASSIVE GRAVITY WITH PROPAGATING TORSION

2010 ◽  
Vol 25 (26) ◽  
pp. 4911-4932
Author(s):  
ROLANDO GAITAN DEVERAS
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Massive Gravity ◽  
Dynamical Variable ◽  
General Covariance ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Perturbative Regime ◽  
Massive Theory ◽  
Extended Theories

A perturbative regime based on contortion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang–Mills formulation for gravity in a (2+1)-dimensional space–time. In the massless case, we show that the theory contains three degrees of freedom and only one is a nonunitary mode. Next, we introduce quadratical terms dependent on torsion, which preserve parity and general covariance. The linearized version reproduces an analogue Hilbert–Einstein–Fierz–Pauli unitary massive theory plus three massless modes, two of them represents nonunitary ones. Finally, we confirm the existence of a family of unitary Yang–Mills-extended theories which are classically consistent with Einstein's solutions coming from nonmassive and topologically massive gravity. The unitarity of these Yang–Mills-extended theories is shown in a perturbative regime. A possible way to perform a nonperturbative study is remarked.

scholarly journals A hybrid approach to simulation of electron transfer in complex molecular systems

2013 ◽  
Vol 10 (87) ◽  
pp. 20130415 ◽  
Author(s):  
Tomáš Kubař ◽  
Marcus Elstner
Keyword(s):  
Electron Transfer ◽  
Density Functional ◽  
Degrees Of Freedom ◽  
Hybrid Approach ◽  
Theoretical Description ◽  
Model Systems ◽  
Hole Transfer ◽  
Model Calculations ◽  
Hand Model ◽  
Quantum Mechanical Treatment

Electron transfer (ET) reactions in biomolecular systems represent an important class of processes at the interface of physics, chemistry and biology. The theoretical description of these reactions constitutes a huge challenge because extensive systems require a quantum-mechanical treatment and a broad range of time scales are involved. Thus, only small model systems may be investigated with the modern density functional theory techniques combined with non-adiabatic dynamics algorithms. On the other hand, model calculations based on Marcus's seminal theory describe the ET involving several assumptions that may not always be met. We review a multi-scale method that combines a non-adiabatic propagation scheme and a linear scaling quantum-chemical method with a molecular mechanics force field in such a way that an unbiased description of the dynamics of excess electron is achieved and the number of degrees of freedom is reduced effectively at the same time. ET reactions taking nanoseconds in systems with hundreds of quantum atoms can be simulated, bridging the gap between non-adiabatic ab initio simulations and model approaches such as the Marcus theory. A major recent application is hole transfer in DNA, which represents an archetypal ET reaction in a polarizable medium. Ongoing work focuses on hole transfer in proteins, peptides and organic semi-conductors.

Structure and Energy of Grain Boundaries in Metals

MRS Bulletin ◽  
1990 ◽  
Vol 15 (9) ◽  
pp. 42-50 ◽  
Author(s):  
K.L. Merkle ◽  
D. Wolf
Keyword(s):  
Grain Boundaries ◽  
Degrees Of Freedom ◽  
Bulk Material ◽  
Complex Structure ◽  
Model Systems ◽  
Structure Property ◽  
Interfacial Chemistry ◽  
Impurity Segregation ◽  
Interface Parameters ◽  
Property Correlations

The investigation of structure-property correlations is a rather complex endeavor not only because interfacial Systems are intrinsically inhomogeneous, with chemical composition and physical properties differing from the surrounding bulk material, but also since three different aspects of the geometrical structure are involved — namely the macroscopic, microscopic, and atomic structures. As outlined in the Guest Editors' introduction, in addition to the choice of the materials which form the interface, five macroscopic and three microscopic degrees of freedom (DOFs) are needed to characterize a single bicrystalline interface. The importance of the atomic structure at the interface as well as the local interfacial chemistry, extrinsic (i.e., impurity segregation) or intrinsic (for example, via interfacial reactions or space-charge phenomena), greatly add to the task's complexity.Grain boundaries (GBs) in pure metals represent ideal model Systems for investigating the strictly geometrical aspects of structure-property correlations for the following three reasons. First, the complexity due to the myriad of possible choices of materials combinations forming the interface is avoided, enabling a focus on the different roles of the three distinct geometrical aspects of the structure. Second, because GBs are bulk interfaces, dimensional interface parameters (such as the modulation wavelength in strained-layer superlattices, or the thickness of epitaxial layers) do not enter into the problem. Finally, the GB energy is thought to play a central role in various GB properties, such as impurity segregation, GB mobility and fracture, GB diffusion and cavitation, to name a few. A better understanding of the correlation between the structure and energy of GBs, therefore, promises to offer insights into more complex structure-property correlations, as well.

scholarly journals Propagating Degrees of Freedom in f(R) Gravity

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Yun Soo Myung
Keyword(s):  
Wave Equation ◽  
Gravitational Waves ◽  
Degrees Of Freedom ◽  
Ricci Scalar ◽  
Metric Tensor ◽  
Breathing Mode

We have computed the number of polarization modes of gravitational waves propagating in the Minkowski background in f(R) gravity. These are three of two from transverse-traceless tensor modes and one from a massive trace mode, which confirms the results found in the literature. There is no massless breathing mode and the massive trace mode corresponds to the Ricci scalar. A newly defined metric tensor in f(R) gravity satisfies the transverse-traceless (TT) condition as well as the TT wave equation.

Statistics in Deterministic Sciences: An Introduction

2011 ◽  
Author(s):  
Gidon Eshel
Keyword(s):  
Physical System ◽  
Degrees Of Freedom ◽  
Probability Distributions ◽  
Dynamical Variable ◽  
Natural Sciences ◽  
The State ◽  
Space And Time ◽  
Ocean Atmosphere ◽  
Relevant Variables ◽  
Physical Phenomena

This chapter focuses on the relevance of statistics in deterministic science. While most physical phenomena of concern to natural sciences are governed by fundamental, mostly known, physics, their application to such complex systems as the ocean, atmosphere, or ecosystems is monumentally difficult. For most such systems, the full problems—the values of all relevant variables at all space and time locations—are essentially intractable, even with the fastest computers. Hence, there is always more to the focus of inquiry that cannot be modeled; we must somehow fill in the gaps. This is where statistics come in. Until the state of the physical system under investigation is fully quantified (i.e., until the value of every dynamical variable is perfectly known at every point in space and time), there is a certain amount of indeterminacy in every statement made about the state of the system. The remainder of the chapter discusses probability distributions and degrees of freedom.

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