T. B. Smith
This paper develops further the semi-classical theory of an harmonic oscillator acted on by a Gaussian white noise force discussed in (arXiv:1508.02379). Here I add to that theory the effects of Brownian damping (friction). Albeit semi-classical, the theory can be used to model quantum expectations and probabilities. I consider several examples.
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We investigate the Shortcuts To Adiabaticity (STA) of a quantum harmonic oscillator under time-dependent frictional force, using invariant based inverse engineering method with a class of invariants characterized by a time-dependent frictional coefficient. We discuss the implementation of shortcut protocol in a generalized framework for any arbitrary time-dependent frictional interaction and study a class of such interaction from which the STA for the quantum harmonic oscillator can be obtained. We also discuss the application of the above protocol for the harmonic oscillator with time-varying…
This paper is a second in a series devoted to the study of a two-oscillator system in linear relative motion (the first one published as a letter in Europhys. Lett. 91, 60003 (2010)). The main idea behind considering this kind of system is to use it as a simple model for Casimir friction. In the present paper we extend our previous theory so as to obtain the change in the oscillator energy to second order in the perturbation, even though we employ first order perturbation theory only. The results agree with, and confirm, our earlier results obtained via different routes. The friction force is …
The Casimir friction problem can be dealt with in a simplified way by considering two harmonic oscillators moving with constant relative velocity. Recently we calculated the energy dissipation for such a case, [EPL {\bf 91}, 60003 (2010); Europ. Phys. J. D {\bf 61}, 335 (2011)]. A recent study of Barton [New J. Phys. {\bf 12}, 113044 (2010)] seemingly leads to a different result for the dissipation. If such a discrepancy really were true, it would imply a delicate difficulty for the basic theory of Casimir friction. In the present note we show that the expressions for the dissipation are in fa…
The Casimir friction problem for a pair of dielectric particles in relative motion is analyzed, utilizing a microscopic model in which we start from statistical mechanics for harmonically oscillating particles at finite temperature moving nonrelativistically with constant velocity. The use of statistical mechanics in this context has in our opinion some definite advantages, in comparison with the more conventional quantum electrodynamic description of media that involves the use of a refractive index. The statistical-mechanical description is physical and direct, and the oscillator model, in s…
Multibranched parametric resonance and swallowtail catastrophe in electromechanical oscillators with nonlinear friction
该研究从实验和理论上证明，带常规受控非线性摩擦的微机械振荡器中可通过燕尾突变诱导两对周期二态共存，拓宽了参数共振的理解并确立了相关研究平台。
Casimir friction is analyzed for a pair of dielectric particles in relative motion. We first adopt a microscopic model for harmonically oscillating particles at finite temperature T moving non-relativistically with constant velocity. We use a statistical-mechanical description where time-dependent correlations are involved. This description is physical and direct, and, in spite of its simplicity, is able to elucidate the essentials of the problem. This treatment elaborates upon, and extends, an earlier theory of ours back in 1992. The energy change Delta E turns out to be finite in general, co…
In this paper we study a two-dimensional [2D] rotationally symmetric harmonic oscillator with time-dependent frictional force. At the classical level, we solve the equations of motion for a particular case of the time-dependent coefficient of friction. At the quantum level, we use the Lewis-Riesenfeld procedure of invariants to construct exact solutions for the corresponding time-dependent Schrödinger equations. The eigenfunctions obtained are in terms of the generalized Laguerre polynomials. By mean of the solutions we verify a generalization version of the Heisenberg's uncertainty relation a…
Floquet driven frictional effects
针对强Floquet驱动下玻恩-奥本海默近似失效的问题，研究推导了含电子摩擦的Floquet驱动非绝热分子动力学Fokker-Planck方程，发现无自旋轨道耦合时也存在类洛伦兹力。
In the framework of Lindblad theory for open quantum systems, we calculate the entropy of a damped quantum harmonic oscillator which is initially in a quasi-free state. The maximally predictable states are identified as those states producing the minimum entropy increase after a long enough time. In general, the states with a squeezing parameter depending on the environment's diffusion coefficients and friction constant are singled out, but if the friction constant is much smaller than the oscillator's frequency, coherent states (or thermalized coherent states) are obtained as the preferred cl…
Quantum "contact" friction: the contribution of kinetic friction coefficient from thermal fluctuations
本研究建立经典受载粒子的动摩擦热模型，通过量子化表面涨落的简谐振子波振幅，结合声色散关系与力自相关函数计算摩擦系数，揭示了表面涨落量子化引发的动摩擦系数温度依赖特性及高低温下的不同行为。
A new analytical method is presented here, offering a physical view of driven cavities where the external field cannot be neglected. We introduce a new dimensionless complex parameter, intrinsically linked to the cooperativity parameter of optical bistability, and analogous to the scaled Rabbi frequency for driven systems where the field is classical. Classes of steady states are iteratively constructed and expressions for the diffusion and friction coefficients at lowest order also derived. They have in most cases the same mathematical form as their free-space analog. The method offers a semi…
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and squeezed reference frames in the system's phase space. For some specific oscillator states like coherent states and nth excited states, the tomographic-probability distributions (called the state tomograms) are found in an explicit form. The evolution equation for the tomograms is discussed for the classical and quantum driven oscillators, and the tomographic …
The paper deals with the problem of dynamics of externally driven open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two externally driven coupled quantum oscillators interacting with different baths of oscillators. It is shown that at the zeroing of external forces the density matrix becomes identical to the previously obtained one for freely developing coupled oscillators. Mean values of observables are computed by using the Hermitian part of the matrix. All elements of the covariance matrix composed by coordinates and…
The symlectic quantum tomography for the general linear quantization is introduced. Using the approach based upon the Wigner function techniques the evolution equation of quantum tomograms is derived for a parametric driven oscillator.
Temporal Coarse-Graining as the Origin of Macroscopic Friction in Quantum Spin Chains via Data-Driven Liouvillian Extraction
本文通过数据驱动方法揭示量子自旋链中宏观摩擦的起源，发现摩擦和粘性源于观测时间粗粒化，而非绝对属性。
We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability phenomenon. The quantum-classical correspondence for the oscillator dynamics is discussed in details.
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