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We demonstrate experimentally a gating ratchet with cold rubidium atoms in a driven near-resonant optical lattice. A single-harmonic periodic modulation of the optical potential depth is applied, together with a single-harmonic rocking force. Directed motion is observed as a result of the breaking of the symmetries of the system. DOI: 10.1103/PhysRevLett.100.040603 PACS numbers: 05.60.Cd, 05.40.ÿa, 05.45.ÿa, 05.70.Ln The rectification of Brownian motion in the absence of net applied bias forces is an intriguing phenomenon, termed the ratchet effect, which has recently attracted much attention in different fields [1][2][3][4][5][6][7][8]. In fact, ratchets have been implemented in a variety of physical systems [9][10][11][12][13][14][15] ranging from solid state devices and optical trap setups to granular gases and nanopores in polymer films. All the different implementations of the ratchet effect can be traced back to two main elements. First, the system has to be driven out of equilibrium, so to overcome the restrictions imposed by the second principle of thermodynamics. Second, the relevant symmetries of the system, which would otherwise inhibit directed motion, have to be broken.In the rocking ratchet [2], particles in a periodic potential experience also an applied ac force. The applied force is zero average and time symmetric. However, there is an eventual net flux due to the symmetry-breaking anisotropy of the potential. The same effect can be obtained for a spatially symmetric potential and a biharmonic drive, with the time symmetry of the system controlled by the symmetry of the drive [4 -7,11].In the gating ratchet [16], particles experience an oscillating potential which is spatially symmetric. A zeroaverage and time-symmetric ac force is also applied. A current can be generated following a gating effect, with the lowering of the potential barriers synchronized with the motion produced by the additive force. This mechanism has to be contrasted with the previously demonstrated acdriven ratchets with additive biharmonic driving [11], in which the underlying mechanism is harmonic mixing [17].In this work we present the experimental demonstration of a gating ratchet with cold rubidium atoms in a dissipative optical lattice. We demonstrate that the gating mechanism can indeed lead to the generation of a current and show that such a current generation is controlled by the symmetries of the system.Before presenting the experimental results, it is important to carry out the symmetry analysis for the gating ratchet. This will serve as a guide for the experimental work. We consider a weakly damped particle in an amplitude modulated symmetric potential Vx1 mt. A rocking force Ft is also applied. The Langevin equation for the particle of mass M isHere x is the position of the particle at the time t, and and are the damping coefficient and a stationary Gaussian noise, respectively. Both the amplitude modulation mt and the rocking force Ft are single-harmonic fields:For the symmetry analysis, the noise term t ca...

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A (w, r ) cover-free family is a family of subsets of a finite set such that no intersection of w members of the family is covered by a union of r others. A binary (w, r ) superimposed code is the incidence matrix of such a family. Such a family also arises in cryptography as a concept of key distribution patterns. In this paper, we develop a method of constructing superimposed codes and prove that some superimposed codes constructed in this way are optimal.

Directed transport in ratchets is determined by symmetry breaking in a system out of equilibrium. A hallmark of rocking ratchets is current reversals: an increase in the rocking force changes the direction of the current. In this work for a biharmonically driven spatially symmetric rocking ratchet we show that a class of current reversal is precisely determined by symmetry breaking, thus creating a link between dynamical and symmetry-breaking mechanisms. Many processes in physics, chemistry, and biology involve directed transport through periodic structures. For the equilibrium situation of Brownian motion, diffusion can be turned into directed diffusion by the application of a dc bias. In out-of-equilibrium systems, new mechanisms for directed transport may arise. Counterintuitively, far from equilibrium it is possible to obtain directed transport through a macroscopically flat potential in the absence of an applied dc bias. This is the so-called ratchet effect ͓1-7͔.The archetypal of a ratchet device is the rocking ratchet. In this setup, Brownian particles experience an asymmetric sawtooth potential and a sinusoidal rocking force. The rocking force drives the system out of equilibrium, and directed transport is generated following the breaking of the symmetries of the system. An analogous effect can also be produced in a spatially symmetric potential and a biharmonic force, with the latter playing the double role of driving the system out of equilibrium and breaking the relevant time symmetries ͓8-16͔.A hallmark of rocking ratchets is current reversals. By progressively increasing the rocking force from zero, the generation of a current is observed, whose magnitude is first an increasing function of the strength of the driving. However, at larger values of the rocking force the current reaches a maximum, then decreases to zero, and changes sign. This feature can appear several times in a given system for different values of the force, thus producing multiple current reversals. Single and multiple current reversals have been observed in a variety of systems, both for an asymmetric potential and a symmetric drive and for a symmetric potential and a time-asymmetric drive ͓17-19͔.Current reversals are usually considered a dynamical effect, not related to the symmetry breaking required to allow directed motion. In this work, for the specific system with a spatially symmetric potential and a time-asymmetric drive, we show that a class of current reversal is actually determined by dissipation-induced symmetry breaking. As a consequence, these reversals are not present in the Hamiltonian limit or in the overdamped limit.Our work consists of a theoretical analysis of the relationship between current reversals and dissipation-induced symmetry breaking. This is carried out comparing differing regimes: weakly damped, Hamiltonian, and overdamped. In the case of weak damping, where current reversals associated with dissipative effects are present, the theoretical analysis is also supported by experimental results obtained ...

Based on archival Hubble Space Telescope images, we have performed stellar photometry for the galaxy M 101 and other neighboring galaxies located at a small angular distance from M 101 and having radial velocities similar to that of M 101: M 51, M 63, NGC 5474, NGC 5477, UGC 9405, Ho IV, KUG1413+573, and others. Based on the TRGB method, we have determined the distances to these galaxies. We have found that the M 101 group lies at a distance of 6.8 Mpc and is a small compact galaxy group consisting of four galaxies: NGC 5474, NGC 5477, UGC 9405, and Ho IV. The bright massive galaxies M 51 and M 63 are considerably farther (D = 9.0 and 9.3 Mpc, respectively) than the M 101 group and do not belong to it. Applying the virial theorem to 27 objects (H II regions and galaxies), M 101 satellites located at different distances from the galaxy, has revealed an increase in the dynamical mass of M 101 with increasing sizes of the system of satellites used in calculating the mass. The maximum calculated mass of M 101 is 7.5 × 10 11 M . The dynamical mass of M 101 calculated on the basis of the four galaxies constituting the group is 6.2 × 10 11 M . The mass-to-light ratio for this mass is M/L = 18 (at the adopted luminosity of M 101, M B = −20.8).

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