  We investigate directed thermal heat flux across 1D homogenous nonlinear
lattices when no net thermal bias is present on average. A nonlinear lattice of
Fermi-Pasta-Ulam-type or Lennard-Jones-type system is connected at both ends to
thermal baths which are held at the same temperature on temporal average. We
study two different modulations of the heat bath temperatures, namely: (i) a
symmetric, harmonic ac-driving of temperature of one heat bath only and (ii) a
harmonic mixing drive of temperature acting on both heat baths. While for case
(i) an adiabatic result for the net heat transport can be derived in terms of
the temperature dependent heat conductivity of the nonlinear lattice a similar
such transport approach fails for the harmonic mixing case (ii). Then, for case
(ii), not even the sign of the resulting Brownian motion induced heat flux can
be predicted a priori. A non-vanishing heat flux (including a non-adiabatic
reversal of flux) is detected which is the result of an induced dynamical
symmetry breaking mechanism in conjunction with the nonlinearity of the lattice
dynamics. Computer simulations demonstrate that the heat flux is robust against
an increase of lattice sizes. The observed ratchet effect for such directed
heat currents is quite sizable for our studied class of homogenous nonlinear
lattice structures, thereby making this setup accessible for experimental
implementation and verification.
