Monoidal Hom-Hopf algebras

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras and Lie algebras.Comment: 25 pages; extended version: compared to the version that appeared in Comm. Algebra, the Section Preliminary Results and Remarks 5.1 and 6.1 have been adde

Single-cycle THz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3

Using the tilted-pulse-intensity-front scheme, we generate single-cycle terahertz (THz) pulses by optical rectification of femtosecond laser pulses in LiNbO3. In the THz generation setup, the condition that the image of the grating coincides with the tilted-optical-pulse front is fulfilled to obtain optimal THz beam characteristics and pump-to-THz conversion efficiency. The designed focusing geometry enables tight focus of the collimated THz beam with a spot size close to the diffraction limit, and the maximum THz electric field of 1.2 MV/cm is obtained

Effective Edwards-Wilkinson equation for single-file diffusion

In this work, we present an effective discrete Edwards-Wilkinson equation aimed to describe the single-file diffusion process. The key physical properties of the system are captured defining an effective elasticity, which is proportional to the single particle diffusion coefficient and to the inverse squared mean separation between particles. The effective equation gives a description of single-file diffusion using the global roughness of the system of particles, which presents three characteristic regimes, namely normal diffusion, subdiffusion and saturation, separated by two crossover times. We show how these regimes scale with the parameters of the original system. Additional repulsive interaction terms are also considered and we analyze how the crossover times depend on the intensity of the additional terms. Finally, we show that the roughness distribution can be well characterized by the Edwards-Wilkinson universal form for the different single-file diffusion processes studied here.Comment: 9 pages, 9 figure

Dumbbell diffusion in a spatially periodic potential

We present a numerical investigation of the Brownian motion and diffusion of a dumbbell in a two-dimensional periodic potential. Its dynamics is described by a Langevin model including the hydrodynamic interaction. With increasing values of the amplitude of the potential we find along the modulated spatial directions a reduction of the diffusion constant and of the impact of the hydrodynamic interaction. For modulation amplitudes of the potential in the range of the thermal energy the dumbbell diffusion exhibits a pronounced local maximum at a wavelength of about 3/2 of the dumbbell extension. This is especially emphasized for stiff springs connecting the two beads.Comment: 4 pages, 7 figures, published in Phys. Rev. E (2008

Entanglement reduction induced by geometrical confinement in polymer thin films

We report simulation results on melts of entangled linear polymers confined in a free-standing thin film. We study how the geometric constraints imposed by the confinement alter the entanglement state of the system compared to the equivalent bulk system using various observables. We find that the confinement compresses the chain conformation uniaxially, decreasing the volume pervaded by the chain, which in turn reduces the number of the accessible inter-chain contact that could lead to entanglements. This local and non-uniform effect depends on the position of the chain within the film. We also test a recently presented theory that predicts how the number of entanglements decreases with geometrical confinement.Comment: 28 pages, 10 figure

The quark-gluon Mixed Condensate calculated via Field Correlators

The quark-gluon mixed condensate $g$ is calculated in the Gaussian approximation of the Field Correlator Method. In the large N_c limit and for zero mass quarks one obtains a simple result, $m^2_0 \equiv \frac{g}{} = \frac{16\sigma}{\pi}$, where $\sigma$ is the string tension. For a standard value $\sigma=0.18 GeV^2$ one obtains $m^2_0=1 GeV^2$ in good agreement with the QCD sum rules estimate $m^2_0 = (0.8\pm 0.2) GeV^2$ and the latest lattice result $m^2_0 \cong 1 GeV^2$.Comment: 10 pages, no figures; discussion of accuracy of the result added and misprints correcte