Building on this picture, we formulate a topological fluctuation theorem that depends only by the winding number around each vortex core and is insensitive to other aspects of the force. The probability is robust to local deformations of the particle trajectory, reminiscent of topologically protected ...
In this work, we show the connections between different formulations of the fluctuation theorem. One formulation concerns the generating function of the currents while another one concerns the corresponding large deviation function, which we have calculated exactly for this model. A third formulation ...
Control strategies that are solely based on the network’s topological properties4 disregard the system’s dynamics, which is usually highly nonlinear. Addressing this issue, we here proposed a straightforward topology-dynamics-based control approach for multi-dimensional complex networked dynamical systems...
In this work we study the partial topological twist of 3d N = 2 theories on a spacetime with boundary HS2 × S1, where HS2 is the 2d hemisphere. Our first result is to formulate supersymmetric boundary conditions on ∂(HS2 ×S1) = T 2 for this spacetime and compute the Witten ...
Another interesting topological feature is one where instead of self-intersecting, the two sides of the curve just touch to form a “bubble”, as the limiting case between zero and two intersections, see Fig. 8. The lowest order singularity to realize that is the A4 singularity, whose unfoldi...
According to the Langevin treatment of thermally driven oscillators, the right-hand side of the equation is the time-dependent thermal force experienced by the oscillator, which depends on the dissipation factor Γi through the fluctuation-dissipation theorem. ηi(t) is a normalized white noise ter...
In equilibrium, G(ω) is closely connected to the thermal fluctuations by the fluctuation–dissipation theorem (FDT) [68]. An early instance of this powerful tool from statistical mechanics is given by the Einstein relation D = kBT/ζ [69], which amounts to a low frequency limit of the ...
Overall, there is no magnetic order in accord with the classic Mermin-Wagner theorem. The method of proof employs a rigorous version of "order by disorder," whereby a high degeneracy among the ground states is lifted according to the differences in their associated spin-wave spectra....
Aprime ribbon graphis a set of topological discs and topological rectangles satisfying the following properties: no two rectangles or two discs intersect; each rectangle has exactly one pair of opposite sides that are contained in disc’s circumferences, and this is the only intersection between rec...
Theorem 4. The generalized metric g i j ( u 1 , u 2 , t ) satisfying (49)–(51) is defined by the antisymmetric metric element g 12 ( u 1 , u 2 , t ) = − g 21 ( u 1 , u 2 , t ) , which satisfies a fourth-degree algebraic equation generating a topological manifold...