Two-level quantum mechanical system with decay: density matrix description and shifted frequency approximation

1985 ◽  
Vol 63 (12) ◽  
pp. 1525-1531
Author(s):  
D. C. Morgan ◽  
J. Grindlay
Keyword(s):  
Dipole Moment ◽  
Density Matrix ◽  
Equations Of Motion ◽  
Quantum Mechanical ◽  
Level System ◽  
Quantum Mechanical System ◽  
Third Order ◽  
Decay Times ◽  
Frequency Approximation

The shifted frequency approximation is used to solve the equations of motion for the density matrix describing a quantum mechanical two-level system, with decay, in an applied monochromatic electric field. Expressions are obtained for the transient and the long-term linear electric dipole moment and occupation probability, and the long-term third-order dipole moment. The results are valid across the frequency spectrum, including resonance, provided the phenomenological decay times for the system are not too large or too close in value.

The quantum-mechanical two-level system with dissipation and feedback: application to nonlinear dielectric response

1986 ◽  
Vol 64 (6) ◽  
pp. 692-699 ◽  
Author(s):  
J. Grindlay
Keyword(s):  
Dipole Moment ◽  
Equations Of Motion ◽  
Power Series Expansion ◽  
Internal Field ◽  
Quantum Mechanical ◽  
Level System ◽  
Third Order ◽  
Long Time ◽  
Two Level Systems ◽  
Upper Level

A power-series expansion for long-time solutions is obtained for the density-matrix equations of motion describing a quantum-mechanical two-level system with dissipation and feedback. The resonances in the first- and third-order dipole contributions and the second-order upper level occupation probability are shown to be significantly affected by the feedback.The results are applied to the case of a uniformly polarized, finite, crystalline dielectric made up of two-level systems. Polarizabilities relating the dipole moment to each of the applied field, the internal field, and the macroscopic field are introduced and relations between them derived. The dipole-moment – macroscopic-field polarizabilities are shown in particular to be shape independent. Susceptibilities are defined and related to the single-system polarizabilities through generalized Clausius–Mossotti relations.

The quantum-mechanical two-level system with dissipation and feedback: multimode applied electric-field case

1987 ◽  
Vol 65 (4) ◽  
pp. 417-420
Author(s):  
J. Grindlay
Keyword(s):  
Dipole Moment ◽  
Electric Field ◽  
Applied Electric Field ◽  
Quantum Mechanical ◽  
Third Order ◽  
First Order ◽  
Common Value ◽  
Induced Dipole ◽  
Upper Level

A two-level dissipative quantum-mechanical system subjected to a small applied multimode electric field plus a feedback term proportional to the induced dipole moment is discussed. The long-term behaviour of the induced dipole moment and of the upper level occupation probability is represented by a series expansion in terms of the applied electric-field amplitudes. First-order and third-order internal, external, and intrinsic polarizabilites are introduced and calculated for the model. Certain ratios of third-order to first-order polarizabilities are shown to have a common value for the internal, external, and intrinsic cases. Clausius–Mossotti relations for the linear and third-order susceptibilities are derived.

Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

2021 ◽  
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Density Matrix ◽  
Time Evolution ◽  
Reduced Density Matrix ◽  
Level System ◽  
Two Level Systems ◽  
Reduced Density ◽  
Harmonic Bath

We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates.

scholarly journals Quantum resources for energy storage

2020 ◽  
Vol 230 ◽  
pp. 00003 ◽  
Author(s):  
Dario Ferraro ◽  
Michele Campisi ◽  
Gian Marcello Andolina ◽  
Vittorio Pellegrini ◽  
Marco Polini
Keyword(s):  
Energy Storage ◽  
Cavity Mode ◽  
Quantum Mechanical ◽  
Double Quantum ◽  
Level System ◽  
Close Proximity ◽  
Two Level Systems ◽  
Quantum Mechanical Effects ◽  
The One ◽  
Superradiant Phase

Recently the possibility to exploit quantum-mechanical effects to increase the performance of energy storage has raised a great interest. It consists of N two-level systems coupled to a single photonic mode in a cavity. We demonstrate the emergence of a quantum advantage in the charging power on this collective model (Dicke Quantum Battery) with respect to the one in which each two-level system is coupled to its own separate cavity mode (Rabi Quantum Battery). Moreover, we discuss the model of a Quantum Supercapacitor. This consists of two chains, one containing electrons and the other one holes, hosted by arrays of double quantum dots. The two chains are in close proximity and embedded in the same photonic cavity, in the same spirit of the Dicke model. We find the phase diagram of this model showing that, when transitioning from the ferro/antiferromagnetic to the superradiant phase, the quantum capacitance of the model is greatly enhanced.

Broadband EM radiation amplification by means of a monochromatically driven two-level system

2017 ◽  
Vol 31 (04) ◽  
pp. 1750027 ◽  
Author(s):  
Andrey V. Soldatov
Keyword(s):  
Dipole Moment ◽  
Quantum System ◽  
High Frequency ◽  
Laser Field ◽  
Diagonal Matrix ◽  
Matrix Elements ◽  
Level System ◽  
Dipole Moment Operator ◽  
Moment Operator ◽  
Radiation Amplification

It is shown that a two-level quantum system possessing dipole moment operator with permanent non-equal diagonal matrix elements and driven by external semiclassical monochromatic high-frequency electromagnetic (EM) (laser) field can amplify EM radiation waves of much lower frequency.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

scholarly journals Magnetic reversal dynamics of a quantum system on a picosecond timescale

2015 ◽  
Vol 6 ◽  
pp. 1946-1956 ◽  
Author(s):  
Nikolay V Klenov ◽  
Alexey V Kuznetsov ◽  
Igor I Soloviev ◽  
Sergey V Bakurskiy ◽  
Olga V Tikhonova
Keyword(s):  
Magnetic Moment ◽  
Magnetization Reversal ◽  
Quantum Mechanical ◽  
Magnetic Reversal ◽  
Level System ◽  
Macroscopic Theory ◽  
Atomic Systems ◽  
Quantum Mechanical Description ◽  
Classical Behavior ◽  
Flux Qubit

We present our approach for a consistent, fully quantum mechanical description of the magnetization reversal process in natural and artificial atomic systems by means of short magnetic pulses. In terms of the simplest model of a two-level system with a magnetic moment, we analyze the possibility of a fast magnetization reversal on the picosecond timescale induced by oscillating or short unipolar magnetic pulses. We demonstrate the possibility of selective magnetization reversal of a superconducting flux qubit using a single flux quantum-based pulse and suggest a promising, rapid Λ-scheme for resonant implementation of this process. In addition, the magnetization reversal treatment is fulfilled within the framework of the macroscopic theory of the magnetic moment, which allows for the comparison and explanation of the quantum and classical behavior.

Chaotic Motion of a Functionally Graded Materials Square Thin Plate

2012 ◽  
Vol 531 ◽  
pp. 593-596
Author(s):  
Shuang Bao Li ◽  
Yu Xin Hao
Keyword(s):  
Thin Plate ◽  
Functionally Graded Materials ◽  
Chaotic Motion ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Materials ◽  
Steady State Heat ◽  
Steady State Heat Transfer

Chaotic motion of a simply supported functionally graded materials (FGM) square thin plate under one-to-two internal resonance is studied in this paper. The FGM plate is subjected to the transversal and in-plane excitations. Material properties are assumed to be temperature-dependent and change continuously throughout the thickness of the plate. The temperature variation is assumed to occur in the thickness direction only and satisfy the steady-state heat transfer equation. Based on the Reddy’s third-order plate theory and Hamilton’s principle, the nonlinear governing equations of motion for the FGM plate are derived by using the Galerkin’s method to describe the transverse oscillation in the first two modes Numerical simulations illustrate that there exist chaotic motion for the FGM rectangular plate.

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