具有淬火二分態(tài)的被驅(qū)動(dòng)系統(tǒng)的解析可解模型 紊亂

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摘要翻譯：
我們對(duì)放置在一維分段線性隨機(jī)勢(shì)中的過(guò)阻尼粒子的驅(qū)動(dòng)動(dòng)力學(xué)進(jìn)行了時(shí)間相關(guān)的研究。這種空間猝滅無(wú)序的設(shè)置然后對(duì)粒子施加一種二分變化的隨機(jī)力。我們導(dǎo)出了粒子位置的概率密度函數(shù)的路徑積分表示，并將這個(gè)感興趣的量轉(zhuǎn)化為傅立葉積分的形式。這樣，概率密度的演化可以在有限時(shí)間內(nèi)進(jìn)行解析研究。證明了概率密度既包含一個(gè)δ-奇異貢獻(xiàn)，又包含一個(gè)正則部分。前者在短時(shí)間內(nèi)起主導(dǎo)作用，而后者在大的演化時(shí)間內(nèi)支配著行為。詳細(xì)說(shuō)明了隨著時(shí)間趨于無(wú)窮大，概率密度緩慢地接近極限高斯形式。
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英文標(biāo)題：
《Analytically solvable model of a driven system with quenched dichotomous
  disorder》
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作者：
S. I. Denisov (1 and 2), M. Kostur (1), E. S. Denisova (2), and P.
  H\"anggi (1 and 3) ((1) Universit\"at Augsburg, Germany, (2) Sumy State
  University, Ukraine, (3) National University of Singapore, Republic of
  Singapore)
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最新提交年份：
2007
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分類信息：

一級(jí)分類：Physics        物理學(xué)
二級(jí)分類：Statistical Mechanics        統(tǒng)計(jì)力學(xué)
分類描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相變，熱力學(xué)，場(chǎng)論，非平衡現(xiàn)象，重整化群和標(biāo)度，可積模型，湍流
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一級(jí)分類：Physics        物理學(xué)
二級(jí)分類：Disordered Systems and Neural Networks        無(wú)序系統(tǒng)與神經(jīng)網(wǎng)絡(luò)
分類描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼鏡和旋轉(zhuǎn)眼鏡；隨機(jī)、非周期和準(zhǔn)周期系統(tǒng)的性質(zhì)；無(wú)序介質(zhì)中的傳輸；本地化；由缺陷和無(wú)序介導(dǎo)的現(xiàn)象；神經(jīng)網(wǎng)絡(luò)
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英文摘要：
  We perform a time-dependent study of the driven dynamics of overdamped particles which are placed in a one-dimensional, piecewise linear random potential. This set-up of spatially quenched disorder then exerts a dichotomous varying random force on the particles. We derive the path integral representation of the resulting probability density function for the position of the particles and transform this quantity of interest into the form of a Fourier integral. In doing so, the evolution of the probability density can be investigated analytically for finite times. It is demonstrated that the probability density contains both a $\delta$-singular contribution and a regular part. While the former part plays a dominant role at short times, the latter rules the behavior at large evolution times. The slow approach of the probability density to a limiting Gaussian form as time tends to infinity is elucidated in detail.
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PDF鏈接：
https://arxiv.org/pdf/704.3692

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