Time evolution, relaxation function, and random force for a single-spin model via the method of Mori

1983 ◽  
Vol 61 (3) ◽  
pp. 428-433 ◽  
Author(s):  
M. Howard Lee
Keyword(s):  
Time Evolution ◽  
Relaxation Function ◽  
Memory Function ◽  
Random Force ◽  
Spin Model ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Single Spin ◽  
Dependent Behavior ◽  
Insight Into

We introduce a single-spin model defined by the Hamiltonian H = aSz + bSx, where a and b are constants and Sx and Sz are the x- and z-components of the spin [Formula: see text] operator. We obtain for this model the time-dependent behavior exactly and completely via the method of Mori. To gain an insight into the quantum mechanical mechanisms of time evolution, we make a comparison with Brownian motion by deducing a number of Brownian analogs. Brownian analogs include the spin memory function as well as the random force and its power spectrum.

Time evolution of a single-spin model coupled to a harmonic oscillator via the method of Mori

1983 ◽  
Vol 61 (11) ◽  
pp. 1475-1478 ◽  
Author(s):  
A. S. T. Pires ◽  
M. E. de Gouvea
Keyword(s):  
Harmonic Oscillator ◽  
Formal Analysis ◽  
Memory Function ◽  
Transverse Field ◽  
Spin Model ◽  
Single Spin ◽  
Complex Models ◽  
Physical Insight ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

We use Mori's memory function method for coupled operators to calculate the time-dependent behaviour of a single-spin model coupled to a harmonic oscillator. This model enables us to carry out the formal analysis of Mori exactly and gives us the physical insight required to treat more complex models, such as the Ising model in a transverse field coupled to phonons.

scholarly journals On relevance of time-dependent Poisson’s ratio for determination of relaxation function parameters

2019 ◽  
Vol 41 (11) ◽  
Author(s):  
Cyprian Suchocki ◽  
Rafał Molak
Keyword(s):  
Poisson’S Ratio ◽  
Relaxation Function ◽  
Memory Function ◽  
Viscoelastic Model ◽  
Three Dimensional ◽  
Acrylonitrile Butadiene Styrene ◽  
Time Dependent ◽  
Poisson's Ratio ◽  
Viscoelastic Constants

Abstract The current study concerns the determination of material constants of a three-dimensional linear viscoelastic model. It is assumed that the constitutive equation utilizes a Prony series as a memory function. A method for the evaluation of relaxation function parameters is presented which can be used for arbitrary loading histories. The proposed methodology is applied to the identification of the viscoelastic constants of acrylonitrile butadiene styrene (ABS). For that purpose, a number of rheological tests in tension have been performed on ABS standard dogbone specimens. The significance of the time-dependent Poisson’s ratio for the determination of material parameters is investigated. It is found that taking into account the measurements of specimen’s lateral contraction over time has a particularly strong influence on the identified values of parameters responsible for the bulk behavior. Several boundary value problems have been analyzed in order to assess the influence of the material parameter values on the obtained solutions. It is demonstrated that some oversimplifications assumed during the determination of viscoelastic constants can lead to a loss of precision or even wrong results.

Quantum Mechanical Interpretation of the Ultra-Low Energy Methyl-Rotation Dynamics in Porous Metal-Organic Frameworks Probed by Low-Frequency Vibrational Spectroscopy and ab initio Simulations

2018 ◽  
Author(s):  
Qi Li ◽  
Adam J. Zaczek ◽  
Timothy M. Korter ◽  
J. Axel Zeitler ◽  
Michael T. Ruggiero
Keyword(s):  
Ab Initio ◽  
Metal Organic Frameworks ◽  
Low Frequency ◽  
Rotor Dynamics ◽  
Quantum Mechanical ◽  
Valuable Insight ◽  
Void Space ◽  
Ab Initio Simulations ◽  
Metal Organic ◽  
Insight Into

<div>Understanding the nature of the interatomic interactions present within the pores of metal-organic frameworks</div><div>is critical in order to design and utilize advanced materials</div><div>with desirable applications. In ZIF-8 and its cobalt analogue</div><div>ZIF-67, the imidazolate methyl-groups, which point directly</div><div>into the void space, have been shown to freely rotate - even</div><div>down to cryogenic temperatures. Using a combination of ex-</div><div>perimental terahertz time-domain spectroscopy, low-frequency</div><div>Raman spectroscopy, and state-of-the-art ab initio simulations,</div><div>the methyl-rotor dynamics in ZIF-8 and ZIF-67 are fully charac-</div><div>terized within the context of a quantum-mechanical hindered-</div><div>rotor model. The results lend insight into the fundamental</div><div>origins of the experimentally observed methyl-rotor dynamics,</div><div>and provide valuable insight into the nature of the weak inter-</div><div>actions present within this important class of materials.</div>

scholarly journals Continuous and Cyclic Progesterone Differentially Interact with Estradiol in the Regulation of Alzheimer-Like Pathology in Female 3×Transgenic-Alzheimer’s Disease Mice

Endocrinology ◽  
2010 ◽  
Vol 151 (6) ◽  
pp. 2713-2722 ◽  
Author(s):  
Jenna C. Carroll ◽  
Emily R. Rosario ◽  
Angela Villamagna ◽  
Christian J. Pike
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Postmenopausal Women ◽  
Transgenic Mouse Model ◽  
Dependent Behavior ◽  
Potential Efficacy ◽  
Increased Risk ◽  
Neural Interactions ◽  
Β Amyloid ◽  
Insight Into

Depletion of estrogens and progesterone at menopause has been linked to an increased risk for the development of Alzheimer’s disease (AD) in women. A currently controversial literature indicates that although treatment of postmenopausal women with hormone therapy (HT) may reduce the risk of AD, several parameters of HT may limit its potential efficacy and perhaps, even exacerbate AD risk. One such parameter is continuous vs. cyclic delivery of the progestogen component of HT. Recent experimental evidence suggests that continuous progesterone can attenuate neural actions of estradiol (E2). In the present study, we compared the effects of continuous and cyclic progesterone treatment in the presence and absence of E2 in ovariectomized 3×Tg-AD mice, a transgenic mouse model of AD. We found that ovariectomy-induced hormone depletion increases AD-like pathology in female 3×Tg-AD mice, including accumulation of β-amyloid, tau hyperphosphorylation, and impaired hippocampal-dependent behavior. E2 treatment alone prevents the increases in pathology. Continuous progesterone did not affect β-amyloid levels when delivered alone but blocked the Aβ-lowering action of E2. In contrast, cyclic progesterone significantly reduced β-amyloid levels by itself and enhanced rather than inhibited the E2 effects. These results provide new insight into the neural interactions between E2 and progesterone that may prove valuable in optimizing HT regimens in postmenopausal women.

scholarly journals The time-dependent angular analysis of Bd → KSℓℓ, a new benchmark for new physics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Sébastien Descotes-Genon ◽  
Martín Novoa-Brunet ◽  
K. Keri Vos
Keyword(s):  
Time Evolution ◽  
Form Factors ◽  
New Physics ◽  
Time Dependent ◽  
Angular Analysis ◽  
Time Dependent Analysis ◽  
Tensor Operators

Abstract We consider the time-dependent analysis of Bd→ KSℓℓ taking into account the time-evolution of the Bd meson and its mixing into $$ {\overline{B}}_d $$ B ¯ d . We discuss the angular conventions required to define the angular observables in a transparent way with respect to CP conjugation. The inclusion of time evolution allows us to identify six new observables, out of which three could be accessed from a time-dependent tagged analysis. We also show that these observables could be obtained by time-integrated measurements in a hadronic environment if flavour tagging is available. We provide simple and precise predictions for these observables in the SM and in NP models with real contributions to SM and chirally flipped operators, which are independent of form factors and charm-loop contributions. As such, these observables provide robust and powerful cross-checks of the New Physics scenarios currently favoured by global fits to b → sℓℓ data. In addition, we discuss the sensitivity of these observables with respect to NP scenarios involving scalar and tensor operators, or CP-violating phases. We illustrate how these new observables can provide a benchmark to discriminate among the various NP scenarios in b → sμμ. We discuss the extension of these results for Bs decays into f0, η or η′.

Time-dependent behavior of nitric oxide excited states under the effect of electron impact

2021 ◽  
Vol 28 (2) ◽  
pp. 024503
Author(s):  
Mohammed amin Ferdi ◽  
Abdelaaziz Bouziane ◽  
Mourad Djebli
Keyword(s):  
Nitric Oxide ◽  
Electron Impact ◽  
Excited States ◽  
Time Dependent ◽  
Dependent Behavior
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