Supersymmetric theory of stochastic dynamics: Difference between revisions

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==== Instantons ====

There are other classes of topological objects in TFTs including instantons, i.e., the matrix elements between states thatof representthe [[Morse–Smale system|Witten-Morse-Smale-Bott complex]]. In fact, cohomological TFTs are often called intersection theory on instantons. From the STS viewpoint, instantons refers to quanta of transient dynamics, such as neuronal avalanches or solar flares, and complex or composite instantons represent nonlinear dynamical processes that occur in response to quenches -- external changes in parameters -- such as paper crumpling, protein folding etc. The TFT aspect of STS in instantons remains largely<ref>{{cite unexplored.book

| last1 = Hori

| first1 = Kentaro

| last2 = Katz

| first2 = Sheldon

| last3 = Klemm

| first3 = Albrecht

| last4 = Pandharipande

| first4 = Rahul

| last5 = Thomas

| first5 = Richard

| last6 = Vafa

| first6 = Cumrun

| last7 = Vakil

| first7 = Ravi

| last8 = Zaslow

| first8 = Eric

| title = Mirror Symmetry

| series = Clay Mathematics Monographs

| volume = 1

| publisher = American Mathematical Society

| year = 2003

| isbn = 978-0-8218-2955-4

| url = https://bookstore.ams.org/cmim-1

| access-date = 2025-06-05

}}</ref>

which is the algebraic representation of the [[Morse–Smale system|Morse-Smale complex]]. In fact, cohomological TFTs are often called intersection theory on instantons. From the STS viewpoint, instantons refers to quanta of transient dynamics, such as neuronal avalanches or solar flares, and complex or composite instantons represent nonlinear dynamical processes that occur in response to quenches -- external changes in parameters -- such as paper crumpling, protein folding etc. The TFT aspect of STS in instantons remains largely unexplored.

=== Operator representation ===