Jump transition due to a time‐dependent bifurcation parameter: An experimental, numerical, and analytical study of the bistable iodate–arsenous acid reaction

1991 ◽  
Vol 94 (1) ◽  
pp. 371-378 ◽  
Author(s):  
J. P. Laplante ◽  
T. Erneux ◽  
M. Georgiou
Keyword(s):  
Analytical Study ◽  
Time Dependent ◽  
Bifurcation Parameter ◽  
Jump Transition ◽  
Acid Reaction

A Time-Dependent Bifurcation Model with Control and Pulsing Oscillations

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4260-4266
Author(s):  
Qishao Lu ◽  
Cuncai Hua
Keyword(s):  
Control Problem ◽  
Memory Effects ◽  
Time Dependent ◽  
Bifurcation Parameter ◽  
Bifurcation Transition ◽  
Delayed Bifurcation ◽  
With Memory

A time-dependent bifurcation model and its control problem are studied. Firstly, the delayed bifurcating transition with memory effects due to time-dependent parameters are analysed. Secondly, a control problem with time-dependent parametric feedback in this bifurcation model is investigated. Finally, an important mechanism for pulsing oscillation is found as the result of the delayed bifurcation transition occurring when the bifurcation parameter varies periodically across the steady bifurcation value.

scholarly journals Specifying the Unitary Evolution of a Qudit for a General Nonstationary Hamiltonian via the Generalized Gell-Mann Representation

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 521
Author(s):  
Elena R. Loubenets ◽  
Christian Käding
Keyword(s):  
Vector Space ◽  
Wide Class ◽  
Analytical Study ◽  
Evolution Operator ◽  
Unit Vector ◽  
Time Dependent ◽  
Unitary Evolution ◽  
Analytical Expression ◽  
Optimal Realizations ◽  
Quantum Technology

Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a d-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism describing the unitary evolution of a qudit ( d ≥ 2 ) in terms of the Bloch-like vector space and specify how, in a general case, this formalism is related to finding time-dependent parameters in the exponential representation of the evolution operator under an arbitrary time-dependent Hamiltonian. Applying this new general formalism to a qubit case ( d = 2 ) , we specify the unitary evolution of a qubit via the evolution of a unit vector in R 4 , and this allows us to derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians. This new analytical expression includes the qubit solutions known in the literature only as particular cases.

TIME DEVELOPMENT OF FLUORESCENCE SPECTRA OF A THREE-LEVEL ATOM IN A SQUEEZED VACUUM

1992 ◽  
Vol 06 (14) ◽  
pp. 891-899
Author(s):  
ARUNDHATI S. JAYARAO ◽  
SURESH V. LAWANDE ◽  
RICHARD D'SOUZA
Keyword(s):  
Fluorescence Spectra ◽  
Analytical Study ◽  
Time Development ◽  
Time Dependent ◽  
Initial State ◽  
State Preparation ◽  
Squeezed Vacuum ◽  
Level Atom

We present an analytical study of the time-dependent spectra of a three-level atom in the cascade configuration driven by two intense coherent fields and damped by a broadband squeezed vacuum. We have also studied the influence of the initial state preparation of the atom on the transient spectrum.

scholarly journals Transient times in linear metabolic pathways under constant affinity constraints

1997 ◽  
Vol 327 (2) ◽  
pp. 493-498 ◽  
Author(s):  
Mónica LLORÉNS ◽  
C. Juan NUÑO ◽  
Francisco MONTERO
Keyword(s):  
Steady State ◽  
Metabolic Pathways ◽  
Analytical Study ◽  
Time Dependent ◽  
State Function ◽  
Transient Time ◽  
Input Flux ◽  
Linear Reaction ◽  
Transition Times ◽  
Reaction Schemes

In the early seventies, Easterby began the analytical study of transition times for linear reaction schemes [Easterby (1973) Biochim. Biophys. Acta 293, 552-558]. In this pioneer work and in subsequent papers, a state function (the transient time) was used to measure the period before the stationary state, for systems constrained to work under both constant and variable input flux, was reached. Despite the undoubted usefulness of this quantity to describe the time-dependent features of these kinds of systems, its application to the study of chemical reactions under other constraints is questionable. In the present work, a generalization of these magnitudes to linear metabolic pathways functioning under a constant-affinity constraint is carried out. It is proved that classical definitions of transient times do not reflect the actual properties of the transition to the steady state in systems evolving under this restriction. Alternatively, a more adequate framework for interpretation of the transient times for systems with both constant and variable input flux is suggested. Within this context, new definitions that reflect more accurately the transient characteristics of constant affinity systems are stated. Finally, the meaning of these transient times is discussed.

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