We study the diffusive behavior of colloidal particles which are confined to one-dimensional channels generated by scanning optical tweezers. At long times t, the mean-square displacement is found to scale as t 1=2 , which is expected for systems where single-file diffusion occurs. In addition, we experimentally obtain the long-time, self-diffusive behavior from the short-time collective density fluctuations of the system as suggested by a recent analytical approach [M. Kollmann, Phys. Rev. Lett. 90, 180602 (2003)]. DOI: 10.1103/PhysRevLett.93.026001 PACS numbers: 83.50.Ha, 82.70.Dd, 83.80.Hj Single-file diffusion (SFD), prevalent in many physical, chemical, and biological processes, refers to the onedimensional (1D) motion of interacting particles in pores which are so narrow that the mutual passage of particles is excluded. Since the sequence of particles in such a situation remains unaffected over time t, this leads to strong deviations from normal diffusion. One of the most striking features of SFD is that the mean-square displacement (MSD) Wt of a tracer particle for t much larger than the direct interaction time (i.e., the time a particle needs to move a significant fraction of the mean particle distance) is given by [1][2][3][4][5] where F is the SFD mobility. While most of the results for SFD are limited to hard-rod systems [6 -8], only recently has it been demonstrated by one of us that Eq. (1) remains valid for colloidal and atomic systems with arbitrary interaction potentials, provided the correlation length between the particles is of finite range and collisions are associated with some energy dissipation [9]. In addition, it was shown that the SFD mobility F can be determined by the compressibility and the short-time collective diffusion coefficient of the system. This is an interesting result, because it relates in a unique way a long-time feature, i.e., the SFD mobility to the short-time collective diffusional properties of the system. Although the asymptotic t 1=2 behavior of SFD systems was predicted almost 40 years ago, experimental studies of such non-Fickian diffusion processes were lacking for a long time. However, due to recent progress in the synthesis of zeolitic materials which consist of long quasicylindrical pores with diameters of several angstroms [10], experimentally accessible SFD systems are now available. By means of pulsed force gradient nuclear magnetic resonance (PFG-NMR) experiments, it was demonstrated that the transport of methane and ethane in such molecular sieves can indeed be described by SFD [2,3]. Experimental evidence for the occurrence of SFD as provided by different authors, however, remains contradictory [11]. In addition, some of the results obtained with PFG-NMR are not in agreement with recent quasielastic neutron scattering studies, which show that both methane and ethane exhibit normal diffusion in AlPO 4 molecular sieves [12]. Several possible reasons have been suggested to account for this discrepancy: First, due to almost inevitable deviations of the ...

The Einstein relation connecting the diffusion constant and the mobility is violated beyond the linear response regime. For a colloidal particle driven along a periodic potential imposed by laser traps, we test the recent theoretical generalization of the Einstein relation to the nonequilibrium regime which involves an integral over measurable velocity correlation functions. DOI: 10.1103/PhysRevLett.98.210601 PACS numbers: 05.40.ÿa, 82.70.Dd A comprehensive theory of systems driven out of equilibrium is still lacking quite in contrast to the universal description of equilibrium systems by the GibbsBoltzmann distribution. Linear response theory provides exact relations valid, however, only for small deviations from equilibrium [1]. The arguably most famous linear response relation is the Einstein relationinvolving the diffusion constant D, the mobility , and the thermal energy k B T [2]. In his original derivation for a suspension in a force field, Einstein balances the diffusive current with a linear drift. The Einstein relation embodies a deep connection between fluctuations causing diffusion and dissipation responsible for friction expressed by a finite mobility.In the present Letter, we report on the extension of the classical Einstein relation beyond the linear response regime using a driven colloidal particle as a paradigmatic system. Our previous theoretical work [3] and its present experimental test thus introduce a third type of exact relation valid for and relevant to small driven systems coupled to a heat bath of constant temperature T. The previously discovered exact relations comprise, first, the fluctuation theorem [4,5] which quantifies the steady state probability of observing trajectories of negative entropy production. Second, the Jarzynski relation [6] expresses the free energy difference between different equilibrium states by a nonlinear average of the work spent in driving such a transition [7]. Both the fluctuation theorem and the Jarzynski relation as well as their theoretical extensions [8][9][10] have been tested in various experimental systems such as micromechanically manipulated biomolecules [11,12], colloids in time-dependent laser traps [13][14][15], Rayleigh-Benard convection [16], mechanical oscillators [17], and optically driven single two-level systems [18]. Such exact relations (and the study of their limitations) are fundamentally important since they provide the first elements of a future more comprehensive theory of nonequilibrium systems.For a nonequilibrium extension of the Einstein relation (1), consider the overdamped motion xt of a particle moving along a periodic one-dimensional potential Vx governed by the Langevin equationwith F ÿ@V=@x f and f a nonconservative force. The friction coefficient determines the correlations htt 0 i 2k B T=t ÿ t 0 of the white noise . Therefore, Eq. (2) describes a colloidal bead driven to nonequilibrium under the assumption that the fluctuating forces arising from the heat bath are not affected by the driving.For the crucial quantiti...

Single-file diffusion (SFD), prevalent in many chemical and biological processes, refers to the one-dimensional motion of interacting particles in pores which are so narrow that the mutual passage of particles is excluded. Since the sequence of particles in such a situation remains unaffected over time t, this leads to strong deviations from normal diffusion, e.g. an increase of the particle mean-square-displacement as the square root of t. We present experimental results of the diffusive behaviour of colloidal particles in one-dimensional channels with varying particle density. The channels are realized by means of a scanning optical tweezers. Based on a new analytical approach (Kollmann 2003 Phys. Rev. Lett. 90 180602) for SFD, we can predict quantitatively the long-time, diffusive behaviour from the short time density fluctuations in our systems.