scholarly journals Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator

2016 ◽  
Vol 373 ◽  
pp. 424-455 ◽  
Author(s):  
Lin Zhang ◽  
Weiping Zhang
Keyword(s):  
Quantum State ◽  
Transformation Method ◽  
Parametric Oscillator ◽  
Time Dependent ◽  
State Evolution ◽  
Lie Transformation ◽  
General Time

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 Superconductor qubits hamiltonian approximations effect on quantum state evolution and control

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Javad Sharifi
Keyword(s):  
Quantum State ◽  
Charge Qubit ◽  
Gate Operation ◽  
Goal State ◽  
Expected Time ◽  
State Evolution ◽  
Angle Of Deviation ◽  
Hadamard Gate ◽  
Phase Qubit ◽  
And Control

AbstractMicrowave IQ-mixer controllers are designed for the three approximated Hamiltonians of charge, phase and flux qubits and the controllers are exerted both on approximate and precise quantum system models. The controlled qubits are for the implementation of the two quantum-gates with these three fundamental types of qubits, Quantum NOT-gate and Hadamard-gate. In the charge-qubit, for implementation of both gates, in the approximated and precise model, we observed different controlled trajectories. But fortunately, applying the controller designed for the approximated system over the precise system leads to the passing of the quantum state from the desired state sooner that the expected time. Phase-qubit and flux qubit have similar behaviour under the control system action. In both of them, the implementation of NOT-gate operation led to same trajectories which arrive at final goal state at different times. But in both of those two qubits for implementation of Hadamard-gate, desired trajectory and precise trajectory have some angle of deviation, then by exerting the approximated design controller to precise system, it caused the quantum state to approach the goal state for Hadamard gate implementation, and since the quantum state does not completely reach the goal state, we can not obtain very high gate fidelity.

Scavenging of Soluble Gaseous Pollutants by Rain Droplets in the Atmosphere With Nocturnal Temperature Profile

2010 ◽  
Author(s):  
Andrew Fominykh ◽  
Tov Elperin ◽  
Boris Krasovitov
Keyword(s):  
Trace Gases ◽  
Vertical Direction ◽  
Temperature Inversion ◽  
Transformation Method ◽  
Time Dependent ◽  
Trace Gas ◽  
Shear Stresses ◽  
Linear Convolution ◽  
Temperature Boundary ◽  
Transfer Equations

We analyze non-isothermal absorption of trace gases by the rain droplets with internal circulation which is caused by interfacial shear stresses. It is assumed that the temperature and concentration of soluble trace gases in the atmosphere varies in a vertical direction. The rate of scavenging of soluble trace gases by falling rain droplets is determined by solving heat and mass transfer equations. In the analysis we accounted for the accumulation of the absorbate in the bulk of the falling rain droplet. The problem is solved in the approximation of a thin concentration and temperature boundary layers in the droplet and in the surrounding air. We assumed that the bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and concentration of the absorbate and temperature are homogeneous and time-dependent in the bulk. By combining the generalized similarity transformation method with Duhamel’s theorem, the system of transient conjugate equations of convective diffusion and energy conservation for absorbate transport in liquid and gaseous phases with time-dependent boundary conditions is reduced to a system of linear convolution Volterra integral equations of the second kind which is solved numerically. Calculations are performed using available experimental data on nocturnal temperature profiles in the atmosphere. It is shown than if concentration of a trace gas in the atmosphere is homogeneous and temperature in the atmosphere increases with altitude, droplet absorbs gas during all the period of its fall. Neglecting temperature inhomogenity in the atmosphere described by nocturnal temperature inversion leads to essential underestimation of the trace gas concentration in a droplet on the ground.

Coupled Consolidation of Layered Unsaturated Soil under General Time-Dependent Loading

2018 ◽  
Vol 18 (8) ◽  
pp. 04018088 ◽  
Author(s):  
Abdoreza Fazeli ◽  
Amin Keshavarz ◽  
Mohammadhossein Moradi
Keyword(s):  
Unsaturated Soil ◽  
Time Dependent ◽  
General Time

scholarly journals Eddy growth and mixing in mesoscale oceanographic flows

1997 ◽  
Vol 4 (4) ◽  
pp. 223-235 ◽  
Author(s):  
G. Haller ◽  
A. C. Poje
Keyword(s):  
Direct Relationship ◽  
Kinematic Model ◽  
Fluid Flows ◽  
Time Dependent ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Fluid Particles ◽  
Lagrangian Tracers ◽  
Particle Paths ◽  
General Time

Abstract. We study the relation between changes in the Eulerian topology of a two dimensional flow and the mixing of fluid particles between qualitatively different regions of the flow. In general time dependent flows, streamlines and particle paths are unrelated. However, for many mesoscale oceanographic features such as detaching rings and meandering jets, the rate at which the Euierian structures evolve is considerably slower than typical advection speeds of Lagrangian tracers. In this note we show that for two-dimensional, adiabatic fluid flows there is a direct relationship between observable changes in the topology of the Eulerian field and the rate of transport of fluid particles. We show that a certain class of flows is amenable to adiabatic or near adiabatic analysis, and, as an example, we use our results to study the chaotic mixing in the Dutkiewicz and Paldor (1994) kinematic model of the interaction of a meandering barotropic jet with a strong eddy.

Improved linear representation of surface waves. Part 2. Slowly varying bottoms and currents

1994 ◽  
Vol 261 ◽  
pp. 65-74 ◽  
Author(s):  
Jon Wright ◽  
Dennis B. Creamer
Keyword(s):  
Free Surface ◽  
Nonlinear Effects ◽  
Linear Representation ◽  
Finite Depth ◽  
Transformation Method ◽  
Leading Order ◽  
Short Waves ◽  
Hamiltonian Theory ◽  
Lie Transformation ◽  
Correct Implementation

We extend the results of a previous paper to fluids of finite depth. We consider the Hamiltonian theory of waves on the free surface of an incompressible fluid, and derive the canonical transformation that eliminates the leading order of nonlinearity for finite depth. As in the previous paper we propose using the Lie transformation method since it seems to include a nearly correct implementation of short waves interacting with long waves. We show how to use the Eikonal method for slowly varying currents and/or depths in combination with the nonlinear transformation. We note that nonlinear effects are more important in water of finite depth. We note that a nonlinear action conservation law can be derived.

scholarly journals Exact time-dependent decoherence factor and its adiabatic classical limit

2003 ◽  
Vol 81 (10) ◽  
pp. 1185-1191
Author(s):  
J -Q Shen ◽  
P Chen ◽  
H Mao
Keyword(s):  
Invariant Theory ◽  
Geometric Phase ◽  
Classical Limit ◽  
Unitary Transformation ◽  
Time Dependent ◽  
Quantum Decoherence ◽  
Dynamical Models ◽  
Complete Set ◽  
General Time ◽  
03.65 Ge

The present paper finds the complete set of exact solutions of the general time-dependent dynamical models for quantum decoherence, by making use of the Lewis–Riesenfeld invariant theory and the invariant-related unitary transformation formulation. Based on this, the general explicit expression for the decoherence factor is then obtained and the adiabatic classical limit of an illustrative example is discussed. The result (i.e., the adiabatic classical limit) obtained in this paper is consistent with what is obtained by other authors, and furthermore we obtain more general results concerning time-dependent nonadiabatic quantum decoherence. It is shown that the invariant theory is appropriate for treating both the time-dependent quantum decoherence and the geometric phase factor. PACS Nos.: 03.65.Ge, 03.65.Bz

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