Brownian motion under a time-dependent periodic potential proportional to the square of the position of a particle and classical fluctuation squeezing

Tashiro, Tohru; Morita, Akio

doi:10.1016/j.physa.2006.11.055

Cited by 6 publications

(21 citation statements)

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“…Therefore, we can reach a conclusion that the asymmetry suppresses the fluctuation of position for the case w = 0 as well as the case w > 0 reported in Ref. [1].…”

Section: Periodic Function With C0 >supporting

confidence: 80%

“…(1). For this case with w = 0, however, MSD in the long-time limit cannot be represented by a series of q in [1],…”

Section: Introductionmentioning

confidence: 95%

“…We shall deal with the Brownian motion described by the following Langevin equation which is the same one in the previous work [1]:ẍ (t) + βẋ(t) + [w + qφ(t)] x(t) = f (t) (1) where x(t) is a position of the Brownian particle at time t, β is a damping constant per unit mass and f (t) is a centered Gaussian-white noise with correlation function…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point

Tashiro¹

2009

J. Phys. A: Math. Theor.

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A parametric oscillator with damping driven by white noise is studied. The mean square displacement (MSD) in the long-time limit is derived analytically for the case that the static force vanishes, which was not treated in the past work [1]. The formula is asymptotic but is applicable to a general periodic function. On the basis of this formula, some periodic functions reducing MSD remarkably are proposed. PERIODICITY OF VARIANCES IN THE LONG-TIME LIMITHere, we shall examine the periodicity of variances in the long-time limit which is a very important property when investigating the asymptotic behavior of MSD. Of course, the periodicity is clear in the previous paper [1], but the proof is valid as long as w > 0 holds. The proof on this section remains true even if w ≤ 0.

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“…Therefore, we can reach a conclusion that the asymmetry suppresses the fluctuation of position for the case w = 0 as well as the case w > 0 reported in Ref. [1].…”

Section: Periodic Function With C0 >supporting

confidence: 80%

“…(1). For this case with w = 0, however, MSD in the long-time limit cannot be represented by a series of q in [1],…”

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point

Tashiro¹

2009

J. Phys. A: Math. Theor.

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“…The rms fluctuation dependence on the driving parameters when a ¼ 0 is theoretically studied in several works (22,(25)(26)(27). The magnitude of the minimal fluctuation (which determines the size of a virtual nanopore) can be expressed as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 8k B T∕MΩ 2 p , which is dependent only on the environment temperature T, the particle mass M, and the tunable working frequency Ω.…”

Section: Methodsmentioning

confidence: 99%

Paul trapping of charged particles in aqueous solution

Guan

Joseph

Park

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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We experimentally demonstrate the feasibility of an aqueous Paul trap using a proof-of-principle planar device. Radio frequency voltages are used to generate an alternating focusing/defocusing potential well in two orthogonal directions. Individual charged particles are dynamically confined into nanometer scale in space. Compared with conventional Paul traps working in frictionless vacuum, the aqueous environment associated with damping forces and thermally induced fluctuations (Brownian noise) exerts a fundamental influence on the underlying physics. We investigate the impact of these two effects on the confining dynamics, with the aim to reduce the rms value of the positional fluctuations. We find that the rms fluctuations can be modulated by adjusting the voltages and frequencies. This technique provides an alternative for the localization and control of charged particles in an aqueous environment.ac electrophoretic effect | aqueous trapping | virtual nanopore

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“…Outro casoé o confinamento em um poço harmônico pulsante, ou seja a Eq. (4) com ω 0 descrito por uma função periódica no tempo [15]. Ainda outro casoé um poço duplo cuja força de confinamentoé do tipo ax + bx 3 [16].…”

Section: A Ilustrar a Eq (1)unclassified

O papel das flutuações na biologia

Oliveira

2007

Rev. Bras. Ensino Fís.

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As flutuações do meio ambiente, bem como flutuações aleatórias no interior de um organismo biológico participam ativamente da sua vida ou evolução. O citado "organismo" pode ser uma célula, um orgão multicelular, um indivíduo, uma população ou um grupo de populações, etc. Pode-se compreender muitos aspectos gerais da influência destas flutuações na vida ou na evolução destes organismos através de modelos simplificados, em particular equações dinâmicas do tipo Langevin. Palavras-chave: flutuações e dissipação, evolução biológica.Environment fluctuations as well as random fluctuations within a biological organism take part of its life or evolution. The quoted "organism" maybe a cell, a multicellular organ, an individual, a population or a set of populations, etc. It is possible to understand many general aspects of these fluctuations' influence on the life or evolution of these organisms through simplified models, in particular dynamic equations like that of Langevin. Keywords: fluctuations and dissipation, biological evolution. IntroduçãoEu estava a ler o excelente livro de Kunihiko Kaneko [1], que trata de biologia, quando me deparei com a equação(1) E a conhecida equação de Langevin. No livro, Kaneko adotou a letra x mas aqui preferi a letra v representando a "variável dinâmica".É uma grandeza genérica que varia com o tempo t, cuja interpretação depende do sistema em estudo. Em particular, na interpretação usual, v representa a velocidade de uma partícula que se desloca ao longo do eixo X (por isto resolvi mudar a letra), submetida a duas forças. A primeira, dada pelo termo −γv,é um atrito viscoso que o meio externo fluido exerce sobre a partícula. A segunda força, representada pela função η(t),é o chamado ruído branco que nos interessa aqui. Vamos a ele.A partícula macroscópica está submetida a pancadas microscópicas de um lado e do outro, em uma escala de tempo muito menor do que o ritmo lento de seu movimento. Nesta escala mais lenta pode-se modelar η(t) por um valor aleatório tomado de uma distribuição de probabilidades simétrica em torno de η = 0. Ignoramse, assim, as correlações entre valores sucessivos da verdadeira função η(t). Em outras palavras, considera-se que η(t+τ ) não guarde nenhuma memória de quanto valia anteriormente η(t), passado um intervalo de tempo τ grande na escala de suas rápidas flutuações. Este mesmo intervalo τ , no entanto,é pequeno na escala de tempo do movimento da partícula macroscópica.

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Brownian motion under a time-dependent periodic potential proportional to the square of the position of a particle and classical fluctuation squeezing

Cited by 6 publications

References 6 publications

Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point

Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point

Paul trapping of charged particles in aqueous solution

O papel das flutuações na biologia

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