The zero-temperature physics of interacting quantum dots attached to superconducting leads is now well understood. overall qualitative picture obtained from the static mean-field approximation. situation drastically changes at non-zero temperatures. No reliable solutions apart numerical simulations exist there. We show that any approximation fails temperatures since magnetic fluctuations induce...

We present two tools, which could be useful in determining whether or not a non-Homogenous Linear Recurrence can reach a desired rational. First, we derive the determinant that is equal to the i term in a non-Homogenous Linear Recurrence. We use this to derive the infinite determinant that is zero, if and only if, the desired rational can be reached by some term in the recurrence. Second, we de...

We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zero-temperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 3/10 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales with the longer stemming from the influence of a long...

Let G be an additively written, finite abelian group, and exp(G ) its exponent. Let S=(a1 , ..., ak) be a sequence of elements in G; we say that S is a zero-sum sequence if i=1 ai=0. Let s(G ) be the samllest integer t such that every sequence of t elements in G contains a zero-sum subsequence of length exp(G ). This constant has been studied by serveral authors during last 20 years [1 9, 11]. ...

Assuming that the population remains small, one can truncate at given values of n1 and n2 to yield a finite set of differential equations. For an initial condition, we take the population to be zero, that is, ρ1,1,1,1 = 1 with all other elements of the density matrix set to zero. Eq. A.6 can then be solved numerically (we used the Adams-Moulton-Bashforth procedure) until a steady state is reach...