Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model

We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. The both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson (SD) equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the SD equation corresponding to the extreme value conditions of the two potentials have the same form.Comment: 7 pages, no figur

Limits to compression with cascaded quadratic soliton compressors

We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong. This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find that it is theoretically possible to reach the single-cycle regime by compressing high-energy fs pulses for wavelengths $\lambda=1.0-1.3 \mu{\rm m}$ in a $\beta$-barium-borate crystal, and it requires that the system is in the stationary regime, where the phase mismatch is large enough to overcome the detrimental GVM effects. However, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account.Comment: 16 pages, 5 figures, submitted to Optics Expres

Crystalline free energies of micelles of diblock copolymer solutions

We report a characterization of the relative stability and structural behavior of various micellar crystals of an athermal model of AB-diblock copolymers in solution. We adopt a previously devel- oped coarse-graining representation of the chains which maps each copolymer on a soft dumbbell. Thanks to this strong reduction of degrees of freedom, we are able to investigate large aggregated systems, and for a specific length ratio of the blocks f = MA/(MA + MB) = 0.6, to locate the order-disorder transition of the system of micelles. Above the transition, mechanical and thermal properties are found to depend on the number of particles per lattice site in the simulation box, and the application of a recent methodology for multiple occupancy crystals (B.M. Mladek et al., Phys. Rev. Lett. 99, 235702 (2007)) is necessary to correctly define the equilibrium state. Within this scheme we have performed free energy calculations at two reduced density {\rho}/{\rho}\ast = 4,5 and for several cubic structures as FCC,BCC,A15. At both densities, the BCC symmetry is found to correspond to the minimum of the unconstrained free energy, that is to the stable symmetry among the few considered, while the A15 structure is almost degenerate, indicating that the present sys- tem prefers to crystallize in less packed structures. At {\rho}/{\rho}\ast = 4 close to melting, the Lindemann ratio is fairly high (~ 0.29) and the concentration of vacancies is roughly 6%. At {\rho}/{\rho}\ast = 5 the mechanical stability of the stable BCC structure increases and the concentration of vacancies ac- cordingly decreases. The ratio of the corona layer thickness to the core radius is found to be in good agreement with experimental data for poly(styrene-b-isoprene)(22-12) in isoprene selective solvent which is also reported to crystallize in the BCC structure

Bubble generation in a twisted and bent DNA-like model

The DNA molecule is modeled by a parabola embedded chain with long-range interactions between twisted base pair dipoles. A mechanism for bubble generation is presented and investigated in two different configurations. Using random normally distributed initial conditions to simulate thermal fluctuations, a relationship between bubble generation, twist and curvature is established. An analytical approach supports the numerical results.Comment: 7 pages, 8 figures. Accepted for Phys. Rev. E (in press

Collapse arrest and soliton stabilization in nonlocal nonlinear media

We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric, but can be of completely arbitrary shape. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.Comment: 4 pages with 3 figure