scholarly journals Dynamical Invariant Applied on General Time-Dependent Three Coupled Nano-Optomechanical Oscillators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sara Hassoul ◽  
Salah Menouar ◽  
Hamid Benseridi ◽  
Jeong Ryeol Choi
Keyword(s):  
Invariant Operator ◽  
Time Dependent ◽  
Unitary Matrix ◽  
Optomechanical System ◽  
Von Neumann ◽  
Classical Counterpart ◽  
Quadratic Invariant ◽  
Fock State ◽  
The Matrix ◽  
General Time

A quadratic invariant operator for general time-dependent three coupled nano-optomechanical oscillators is investigated. We show that the invariant operator that we have established satisfies the Liouville-von Neumann equation and coincides with its classical counterpart. To diagonalize the invariant, we carry out a unitary transformation of it at first. From such a transformation, the quantal invariant operator reduces to an equal, but a simple one which corresponds to three coupled oscillators with time-dependent frequencies and unit masses. Finally, we diagonalize the matrix representation of the transformed invariant by using a unitary matrix. The diagonalized invariant is just the same as the Hamiltonian of three simple oscillators. Thanks to such a diagonalization, we can analyze various dynamical properties of the nano-optomechanical system. Quantum characteristics of the system are investigated as an example, by utilizing the diagonalized invariant. We derive not only the eigenfunctions of the invariant operator, but also the wave functions in the Fock state.

Quantum dynamics of a general time-dependent coupled oscillator

2021 ◽  
pp. 2150230
Author(s):  
Sara Hassoul ◽  
Salah Menouar ◽  
Jeong Ryeol Choi ◽  
Ramazan Sever
Keyword(s):  
Quantum Dynamics ◽  
Oscillatory System ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
Coupled Oscillator ◽  
Quantum Invariant ◽  
Classical Counterpart ◽  
Quantum Dynamical ◽  
General Time

Quantum dynamical properties of a general time-dependent coupled oscillator are investigated based on the theory of two-dimensional (2D) dynamical invariants. The quantum dynamical invariant of the system satisfies the Liouville–von Neumann equation and it coincides with its classical counterpart. The mathematical formula of this invariant involves a cross term which couples the two oscillators mutually. However, we show that, by introducing two pairs of annihilation and creation operators, it is possible to uncouple the original invariant operator so that it becomes the one that describes two independent subsystems. The eigenvalue problem of this decoupled quantum invariant can be solved by using a unitary transformation approach. Through this procedure, we eventually obtain the eigenfunctions of the invariant operator and the wave functions of the system in the Fock state. The wave functions that we have developed are necessary in studying the basic quantum characteristics of the system. In order to show the validity of our theory, we apply our consequences to the derivation of the fluctuations of canonical variables and the uncertainty products for a particular 2D oscillatory system whose masses are exponentially increasing.

GENERALIZED HANNAY ANGLE FOR THE MOST GENERAL TIME-DEPENDENT HARMONIC OSCILLATOR

1993 ◽  
Vol 07 (28) ◽  
pp. 4827-4840 ◽  
Author(s):  
DONALD H. KOBE ◽  
JIONGMING ZHU
Keyword(s):  
Harmonic Oscillator ◽  
Berry Phase ◽  
Time Dependent ◽  
Canonical Momentum ◽  
Gauge Invariant ◽  
Classical Counterpart ◽  
Mass Spring ◽  
Adiabatic Case ◽  
General Time ◽  
Total Angle

The most general time-dependent Hamiltonian for a harmonic oscillator is both linear and quadratic in the coordinate and the canonical momentum. It describes in general a harmonic oscillator with mass, spring “constant,” and friction (or antifriction) “constant,” all of which are time dependent, that is acted on by a time-dependent force. A generalized Hannay angle, which is gauge invariant, is defined by making a distinction between the Hamiltonian and the energy. The generalized Hannay angle is the classical counterpart of the generalized Berry phase in quantum theory. When friction is present the generalized Hannay angle is nonzero. If the Hamiltonian is (incorrectly) chosen to be the energy, the generalized Hannay angle is different. Nevertheless, in the adiabatic case the same total angle is obtained.

scholarly journals Expression of VEGF-A Signaling Pathway in Cartilage of ACLT-induced Osteoarthritis Mouse Model

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Jia-jia Qian ◽  
Qi Xu ◽  
Wei-min Xu ◽  
Ren Cai ◽  
Gui-cheng Huang
Keyword(s):  
Signaling Pathway ◽  
Cruciate Ligament ◽  
Time Dependent ◽  
Pathological Changes ◽  
The Matrix ◽  
Vegfr2 Signaling ◽  
Cox 2 ◽  
Anterior Cruciate ◽  
A Disintegrin And Metalloproteinase ◽  
Safranin O

Abstract Background Anterior cruciate ligament transection surgery (ACLT)-induced OA model was often used to investigate the molecular mechanism of knee osteoarthritis (KOA). Researches have shown that vascular endothelial growth factor (VEGF) played an important role in OA. The present study aimed to investigate the pathological changes after ACLT surgery and reveal the expression characteristics of the VEGF-A/VEGFR2 signaling pathway in this model. Methods Moderate KOA model was established by ACLT, and 1, 2, 4, 8, and 12 weeks after surgery, hematoxylin-eosin (HE) and Safranin-O(S-O) staining were used to detect the pathological changes in mouse knee cartilage, and the matrix biomarkers A Disintegrin and Metalloproteinase with Thrombospondin Motifs 5(ADAMTS5), Collagen II (COL-II) were detected using immunohistochemistry (IHC), CD31 was detected by immunofluorescence (IF) to show the vascular invasion in cartilage, and proteins expression of VEGF-A pathway were detected by Western blot (WB). Meanwhile, the inflammatory biomarkers cyclooxygenase-2 (COX-2) and inducible nitric oxide synthase (iNOS) in cartilage were detected by WB. Results ACLT surgery can lead to degeneration of cartilage in mice, and the characteristics of the lesion were time-dependent. The ADAMTS5-positive cells increased while COL-II decreased in OA cartilage with time, and new blood vessels labeled by CD31 can be seen from 1 week in OA cartilage, and increased in 8 and 12 weeks. The expression of VEGF-A, VEGFR2, COX-2, and iNOS were higher than control groups, which were basically consistent with the degree of osteoarthritis. Conclusions The degenerative degree of articular cartilage was time-dependent; angiogenesis and inflammation were important pathological changes of cartilage in KOA. The expression of the VEGF-A/VEGFR2 signaling pathway was basically correlated with the degree of KOA.

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

scholarly journals A New Iterative Algorithm for Solving a Class of Matrix Nearness Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Xuefeng Duan ◽  
Chunmei Li
Keyword(s):  
Iterative Algorithm ◽  
Projection Algorithm ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Von Neumann ◽  
Numerical Examples ◽  
Matrix Nearness Problem ◽  
Least Frobenius Norm Solution ◽  
Alternating Projection ◽  
The Matrix

Based on the alternating projection algorithm, which was proposed by Von Neumann to treat the problem of finding the projection of a given point onto the intersection of two closed subspaces, we propose a new iterative algorithm to solve the matrix nearness problem associated with the matrix equations AXB=E, CXD=F, which arises frequently in experimental design. If we choose the initial iterative matrix X0=0, the least Frobenius norm solution of these matrix equations is obtained. Numerical examples show that the new algorithm is feasible and effective.

The pseudo Hermitian invariant operator and time-dependent non-Hermitian Hamiltonian exhibiting a SU(1,1) and SU(2) dynamical symmetry

2018 ◽  
Vol 59 (7) ◽  
pp. 072103 ◽  
Author(s):  
Walid Koussa ◽  
Naima Mana ◽  
Oum Kaltoum Djeghiour ◽  
Mustapha Maamache
Keyword(s):  
Dynamical Symmetry ◽  
Invariant Operator ◽  
Time Dependent

GEOMETRIC PHASES, SQUEEZED QUANTUM STATES AND GAUSSIAN WAVE PACKET STATES OF RELIC GRAVITONS

2012 ◽  
Vol 18 ◽  
pp. 13-17
Author(s):  
K. BAKKE ◽  
I. A. PEDROSA ◽  
C. FURTADO
Keyword(s):  
Wave Packet ◽  
Linear Time ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Geometric Phases ◽  
Uncertainty Product ◽  
Quantized Field ◽  
Generalized Time

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.

A UNIFIED FORMALISM OF THERMAL QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (14) ◽  
pp. 2363-2409 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum Polarization ◽  
Time Dependent ◽  
Quantum Field ◽  
Bogoliubov Transformation ◽  
Transformation Matrices ◽  
Thermo Field Dynamics ◽  
The Matrix ◽  
Recent Developments

We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.

scholarly journals Mortality Risk and The Progression of The Electronic Frailty Index and Hospital Frailty Risk Score Over Time

2020 ◽  
Vol 5 (5) ◽  
Author(s):  
Joe Hollinghurst ◽  
Alan Watkins
Keyword(s):  
Risk Score ◽  
Frailty Index ◽  
Time Frame ◽  
Time Dependent ◽  
Cox Models ◽  
Hazard Ratios ◽  
Increased Risk ◽  
The Matrix ◽  
Time Dependent Covariates ◽  
Over Time

IntroductionThe electronic Frailty Index (eFI) and the Hospital Frailty Risk Score (HFRS) have been developed in primary and secondary care respectively. Objectives and ApproachOur objective was to investigate how frailty progresses over time, and to include the progression of frailty in a survival analysis.To do this, we performed a retrospective cohort study using linked data from the Secure Anonymised Information Linkage Databank, comprising 445,771 people aged 65-95 living in Wales (United Kingdom) on 1st January 2010. We calculated frailty, using both the eFI and HFRS, for individuals at quarterly intervals for 8 years with a total of 11,702,242 observations. ResultsWe created a transition matrix for frailty states determined by the eFI (states: fit, mild, moderate, severe) and HFRS (states: no score, low, intermediate, high), with death as an absorbing state. The matrix revealed that frailty progressed over time, but that on a quarterly basis it was most likely that an individual remained in the same state. We calculated Hazard Ratios (HRs) using time dependent Cox models for mortality, with adjustments for age, gender and deprivation. Independent eFI and HFRS models showed increased risk of mortality as frailty severity increased. A combined eFI and HFRS revealed the highest risk was primarily determined by the HFRS and revealed further subgroups of individuals at increased risk of an adverse outcome. For example, the HRs (95% Confidence Interval) for individuals with an eFI as fit, mild, moderate and severe with a high HFRS were 18.11 [17.25,19.02], 20.58 [19.93,21.24], 21.45 [20.85,22.07] and 23.04 [22.34,23.76] respectively with eFI fit and no HFRS score as the reference category. ConclusionFrailty was found to vary over time, with progression likely in the 8-year time-frame analysed. We refined HR estimates of the eFI and HFRS for mortality by including time dependent covariates.

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