Thermalization in a Quantum Harmonic Oscillator with Random Disorder

We propose a possible scheme to study the thermalization in a quantum harmonic oscillator with random disorder. Our numerical simulation shows that through the effect of random disorder, the system can undergo a transition from an initial nonequilibrium state to a equilibrium state. Unlike the classical damped harmonic oscillator where total energy is dissipated, total energy of the disordered quantum harmonic oscillator is conserved. In particular, at equilibrium the initial mechanical energy is transformed to the thermodynamic energy in which kinetic and potential energies are evenly distributed. Shannon entropy in different bases are shown to yield consistent results during the thermalization.

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QUANTUM AND THERMAL STATE FOR EXPONENTIALLY DAMPED HARMONIC OSCILLATOR WITH AND WITHOUT INVERSE QUADRATIC POTENTIAL

International Journal of Modern Physics B ◽

10.1142/s021797920201018x ◽

2002 ◽

Vol 16 (09) ◽

pp. 1341-1351 ◽

Cited By ~ 12

Author(s):

J. R. CHOI

Keyword(s):

Harmonic Oscillator ◽

Density Operator ◽

Thermal State ◽

Mechanical Energy ◽

Invariant Operator ◽

Diagonal Element ◽

Quadratic Potential ◽

Damped Harmonic Oscillator ◽

Energy Expectation ◽

Quantum Mechanical Energy

By taking advantage of dynamical invariant operator, we derived Schrödinger solution for exponentially damped harmonic oscillator with and without inverse quadratic potential. We investigated quantum mechanical energy expectation value, uncertainty relation, partition function and density operator of the system. The various expectation values in thermal state are calculated using the diagonal element of density operator.

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QUANTUM MECHANICAL SOLUTION OF A DAMPED HARMONIC OSCILLATOR WITH TIME-DEPENDENT PARAMETERS

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30554-x ◽

1985 ◽

Vol 5 (3) ◽

pp. 319-325

Author(s):

Honghua Xu

Keyword(s):

Harmonic Oscillator ◽

Time Dependent ◽

Quantum Mechanical ◽

Damped Harmonic Oscillator ◽

Quantum Mechanical Solution

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Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v4i1.6966 ◽

2014 ◽

Vol 4 (1) ◽

pp. 404-426

Author(s):

Vincze Gy. Szasz A.

Keyword(s):

Harmonic Oscillator ◽

Classical Mechanics ◽

Universal Time ◽

Variation Theory ◽

Quantum Oscillator ◽

Variation Principle ◽

Poisson Brackets ◽

Mathematical Meaning ◽

Damped Harmonic Oscillator ◽

Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

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Hydrodynamic constraints on the energy efficiency of droplet electricity generators

Microsystems & Nanoengineering ◽

10.1038/s41378-021-00269-8 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Antoine Riaud ◽

Cui Wang ◽

Jia Zhou ◽

Wanghuai Xu ◽

Zuankai Wang

Keyword(s):

Energy Efficiency ◽

Kinetic Energy ◽

Total Energy ◽

Viscous Dissipation ◽

Shear Force ◽

Mechanical Energy ◽

Electric Energy ◽

The Past ◽

Viscous Shear ◽

Impingement Velocity

AbstractElectric energy generation from falling droplets has seen a hundred-fold rise in efficiency over the past few years. However, even these newest devices can only extract a small portion of the droplet energy. In this paper, we theoretically investigate the contributions of hydrodynamic and electric losses in limiting the efficiency of droplet electricity generators (DEG). We restrict our analysis to cases where the droplet contacts the electrode at maximum spread, which was observed to maximize the DEG efficiency. Herein, the electro-mechanical energy conversion occurs during the recoil that immediately follows droplet impact. We then identify three limits on existing droplet electric generators: (i) the impingement velocity is limited in order to maintain the droplet integrity; (ii) much of droplet mechanical energy is squandered in overcoming viscous shear force with the substrate; (iii) insufficient electrical charge of the substrate. Of all these effects, we found that up to 83% of the total energy available was lost by viscous dissipation during spreading. Minimizing this loss by using cascaded DEG devices to reduce the droplet kinetic energy may increase future devices efficiency beyond 10%.

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