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Supersymmetric Theory of Stochastics:Demystification of Self-Organized Criticality
Published in Christos H. Skiadas, Charilaos Skiadas, Handbook of Applications of Chaos Theory, 2017
In transient processes, boundary conditions for the bosonic fields are open as opposed to the PBC implied by the operation of taking trace of the evolution operator. The building blocks of transient dynamics are instantons. The latter are classical solutions that lead from less stable invariant manifolds to more stable ones. In terms of DS theory, instantons are the pieces of unstable manifolds connecting invariant manifolds of different stability. In the pathintegral representation, invariant manifolds correspond to perturbative (not global) ground states that are Poincare-duals of unstable manifolds of these invariant manifolds (see below). Instantons in their turn are the matrix elements between such perturbative ground states. We will have more to say about instantons below.
Coulomb Effects in Short Coherent Conductors
Published in Andrei D. Zaikin, Dmitry S. Golubev, Dissipative Quantum Mechanics of Nanostructures, 2019
Andrei D. Zaikin, Dmitry S. Golubev
Next we consider the general configuration of N instantons describing tunneling of the phase between topological sectors l = 0 and l. The contribution from this configuration to the partition function takes the form analogous to that in Eq. (7.167). We again have to (i) integrate out the zero modes, (ii) evaluate the ratio of the determinants, and (iii) account for interactions between different instantons. As in Chapter 7, Step (iii) is problematic because of a complicated form of the inter-instanton interactions. Fortunately, this can only affect the pre-exponential factor in our final result.
Master–slave synchronization in a 4D dissipative nonlinear fermionic system
Published in International Journal of Control, 2022
In the 1950s, great efforts were begun among theoretical physicists in searching new nonlinear conformal invariant field equations without dimensional parameters that especially would have classical solutions. In this context Gursey proposed a spinor wave equation as a possible basis for a unitary description of elementary particles (Gursey, 1956). Gursey used a non-polynomial form to be able to write a conformally invariant Lagrangian. Gursey model is the first conformally invariant four-dimensional pure fermionic model (Gursey, 1956). For the first time exact solutions of the model were obtained by Kortel with the help of the Heisenberg anstaz and these solutions were shown to be instantonic in character (Kortel, 1956). Instantons are classical topological solutions with zero energy and finite action of the field equations of any given model, which lie behind the Standard Model of particles (Rebbi & Solliani, 1984). It is well-known that the Standart Model is a well-tested physics theory and describes the fundamental interactions between elementary particles. Although the model works very well, it has certain anomalies such as the chirality in the strong interactions and the violation of baryon and lepton conservations in the electroweak interactions. Instantons have an important role in solving unanswered problems like chiral anomalies (Chandia & Zanelli, 1997). Also the physics beyond the Standart Model is very important (Lee, 2019).