Nonlinear semiclassical dynamics of open systems

2011 ◽  
Vol 369 (1935) ◽  
pp. 260-277 ◽  
Author(s):  
A. M. Ozorio de Almeida ◽  
O. Brodier
Keyword(s):  
Phase Space ◽  
Wigner Function ◽  
Open Systems ◽  
Semiclassical Approximation ◽  
Quadratic Function ◽  
Linear Functions ◽  
Equilibrium Solutions ◽  
Double Phase ◽  
The Fourier Transform ◽  
Chord Function

A semiclassical approximation for an evolving density operator, driven by a ‘closed’ Hamiltonian and ‘open’ Markovian Lindblad operators, is reviewed. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian is a quadratic function and the Lindblad operators are linear functions of positions and momenta. The semiclassical formulae are interpreted within a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra ‘open’ term in the double Hamiltonian is generated by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by the definition of a propagator, here developed in both representations. Generalized asymptotic equilibrium solutions are thus presented for the first time.

Qualitative Analysis of Three-Dimensional Single Food-Chain Model with Variable Consumption Rate in Chemostat

2014 ◽  
Vol 955-959 ◽  
pp. 463-470
Author(s):  
Jing Liu ◽  
Hong Wei Jiang ◽  
Chao Liu
Keyword(s):  
Food Chain ◽  
Consumption Rate ◽  
Three Dimensional ◽  
Quadratic Function ◽  
Positive Equilibrium ◽  
Chain Model ◽  
Equilibrium Solutions ◽  
Existence And Stability ◽  
Variable Consumption ◽  
Food Chain Model

The paper studies three-dimensional food-chain model with variable consumption rate in Chemostat. Assume the prey population's consumption rate of the nutrients is quadratic function, and the predator's consumption rate of the prey population is linear function. Use qualitative theory of ordinary differential equation to analyze the equilibrium solution of the model, especially the existence and stability of positive equilibrium solutions and Hopf bifurcation solutions. Finally,several numerical simulations illustrating the theoretical analysis are also given.

scholarly journals Extended Wigner function for the harmonic oscillator in the phase space

2020 ◽  
Vol 19 ◽  
pp. 103546
Author(s):  
E.E. Perepelkin ◽  
B.I. Sadovnikov ◽  
N.G. Inozemtseva ◽  
E.V. Burlakov
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Wigner Function

The mechanism of flow of gases through coniferous wood

1971 ◽  
Vol 177 (1047) ◽  
pp. 197-223 ◽  
Keyword(s):  
Gas Flow ◽  
Strong Support ◽  
Quadratic Function ◽  
Linear Functions ◽  
Modern Theory ◽  
Specific Flow ◽  
Permeability Constant ◽  
Bordered Pits ◽  
Flow Through ◽  
Coniferous Wood

The mechanism of flow of gases through coniferous wood has been examined and found to follow the viscous/slip régime. According to the general theory the specific flow K of a gas in this régime is a linear function of its mean pressure p̅. For coniferous wood, however, we have found that K is a quadratic function of p̅ approximating to a linear one at high enough values of p̅ . It is shown that this is because K is the sum of two linear functions of p̅ , k 1 and k 2 such that 1/ K = 1/ k 1 + 1/ k 2 where k 1 is believed to be the flow through the tracheids alone and k 2 the flow through the bordered pits. It is shown that the permeability constant for viscous flow K v calculated from gas flow is applicable to liquids so that liquid flow can be predicted from gas flow data. With some species the observed flow rate of a liquid differs greatly from the predicted value. Evidence has been obtained that this is because the torus and margo fibrils of the bordered pit are readily displaced by the surface tension and momentum forces developed on them by a liquid causing radical and erratic changes in permeability. Approximate values for the ‘diameter̕ of the smaller flow path have been calculated from the ratio of the viscous to the slip component of flow of k 2 . These were found to be about 1.4 to 1.7 μ m. This is the same order of size as the distances between the torus and the interior of the border of the pit and indicates that it is the geometry of this part of the structure, rather than that of the margo, that controls flow. These results provide strong support for the modern theory of pit structure based on electron microscope photographs.

Prediction of vernalisation in three Australian Vrn responsive wheats

2003 ◽  
Vol 54 (3) ◽  
pp. 283 ◽  
Author(s):  
L. D. J. Penrose ◽  
H. M. Rawson ◽  
M. Zajac
Keyword(s):  
Quadratic Function ◽  
Linear Interpolation ◽  
Development Stage ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Published Data ◽  
Floral Initiation ◽  
Maximum Temperatures ◽  
Double Ridge ◽  
Interpolation Functions

This study sought to better estimate vernalisation in winter wheats, so that their early development and time of anthesis can be better predicted. For this, an accurate relationship between temperature and the effectiveness of vernalisation is required. Using previously published data, our study found that the relationship between temperature and effectiveness of vernalisation can be suitably described by a quadratic function. In contrast, most previous studies used linear interpolation functions to describe vernalising effectiveness. These consist of a series of linear functions of temperature over adjoining temperature ranges. An advantage of quadratic functions is that they allow effectiveness of vernalisation to be described in terms of underlying physiological processes, and require the estimation of fewer parameters to predict wheat development. Our study found the cardinal temperatures for vernalisation to be –3�C, 6.5�C, and 15.9�C, that is for the lower, optimum, and maximum temperatures respectively. To allow for different upper temperature limits for vernalisation, 2 quadratic temperature-vernalising effectiveness functions were used to predict accumulated daily vernalisation at 3 field sites. These predictions of daily vernalisation were compared with corresponding estimates produced with 3 previously proposed linear interpolation functions. Varying degrees of agreement were found between estimates produced by the 2 types of vernalising effectiveness functions. Equations that have been developed to predict floral initiation in winter wheats have not been previously evaluated in Australian field environments. These equations utilise the same underlying relationship between accumulated daily vernalisation and a measure of floral initiation, often the appearance of double ridges. Two of these equations were used to predict the appearance of double ridges for a field-grown Australian winter wheat, JF87%014. Neither equation could satisfactorily predict the timing of the double ridge development stage for this wheat, whatever vernalising effectiveness function was used to predict vernalisation in the field. Both equations had greatest difficulty in predicting the double ridge stage, in environments where vernalisation most delayed development. This finding suggests that equations currently predicting floral initiation in winter wheats do not utilise an accurate relationship between accumulated vernalisation and floral initiation. An alternative method of predicting anthesis in winter wheats is to predict final leaf number, but this approach has not been reliably applied in environments where vernalising temperatures vary.

Signal characters and non-classical properties of quadratically amplified squeezed vacuum

2020 ◽  
pp. 2150028
Author(s):  
Qiang Ke ◽  
Yi-Fan Wang ◽  
Yan-Bei Cheng ◽  
Xue-Xiang Xu
Keyword(s):  
Wigner Function ◽  
Photon Number ◽  
Quadratic Function ◽  
Interaction Parameters ◽  
Intensity Noise ◽  
Number Operator ◽  
Squeezing Effect ◽  
Squeezed Vacuum ◽  
Antibunching Effect ◽  
Noise Squeezing

Based on the squeezed vacuum (SV) and the quadratic function of the photon number operator, we introduce the quadratically amplified squeezed vacuum (QASV) in this paper. We study the intensity, noise, squeezing effect, antibunching effect, and Wigner function of the QASVs. Compared with the SV, the QASVs have distinctive signal characters and possess peculiar non-classical properties in the proper range of interaction parameters.

scholarly journals Eggplant growth as affected by bovine manure and magnesium thermophosphate rates

2008 ◽  
Vol 65 (1) ◽  
pp. 77-86 ◽  
Author(s):  
Marinice Oliveira Cardoso ◽  
Walter Esfrain Pereira ◽  
Ademar Pereira de Oliveira ◽  
Adailson Pereira de Souza
Keyword(s):  
Leaf Area ◽  
Dry Matter ◽  
Quadratic Function ◽  
Potassium Sulfate ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Positive Interaction ◽  
Relative Growth ◽  
High K ◽  
Cow Urine

Plant growth is influenced by nutrient availability. The objective of this research was to study, under greenhouse conditions, eggplant growth as affected by rates of bovine manure and magnesium thermophosphate (g kg-1 and mg kg-1, respectively), according to a "Box central composite" matrix: 4.15-259; 4.15-1509; 24.15-259; 24.15-1509; 0.0-884; 28.3-884; 14.15-0,0; 14.15-1768; 14.15-884. Potassium sulfate (170 mg kg-1) and 200 mL per pot of cow urine solution were applied four times, but the concentration of the last two applications (200 mL/H2O L) was twice of that of the first two. Additional treatments: magnesium thermophosphate without cow urine and triple superphosphate with urea, both with nutrient levels equivalent to the bovine manure, P2O5 and potassium sulfate to the combination 14.15-884. The experimental design consisted of randomized blocks with four replicates. Leaf area (LA) and LA ratio increased as quadratic functions with manure rates, with negative interaction for thermophosphate. Leaf dry matter mass (DMM) had an increasing quadratic function with rates for both fertilizers. The higher combined rates of both fertilizers resulted in the smallest specific leaf area, but also the highest values of shoot and root DMM, total DMM and, with positive interaction in relation to root shoot dry matter ratio. The relative growth rate in stem height, and also in diameter, increased with manure, according to quadratic and linear functions, respectively. The cow urine effect was, in general, lower than that of urea. The plant's overall growth was more influenced by manure. Root DMM and shoot DMM were greater with high K and P.

Phase-Space Approach to Berry Phases

2006 ◽  
Vol 13 (01) ◽  
pp. 67-74 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Wigner Function ◽  
Berry Phase ◽  
Space Formulation ◽  
Berry Phases ◽  
Classical Phase Space ◽  
New Formula ◽  
Space Approach

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light onto the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay angle with averaging over the classical torus and Berry phase with averaging over the entire classical phase space with respect to the corresponding Wigner function.

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