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Dynamical Symmetry Breaking

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Phase Space

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An abstract space where all possible states of a system are represented, each state corresponds to one unique point in the phase space.

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Dynamical System

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A mathematical framework used to model the time-dependent evolution of a point in a geometrical space, often characterized by a set of differential equations.

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Hamiltonian Systems

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A class of dynamical systems governed by the Hamiltonian function, which is the total energy of the system, often found in physics to describe conservative systems.

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Symmetry in Dynamical Systems

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A property that is preserved under some transformations, such as rotations or translations, leading to invariant behavior in the dynamics.

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Spontaneous Symmetry Breaking

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A process where a symmetrical system results in an asymmetrical outcome during state change, often seen in physics.

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Fixed Point

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In dynamical systems, a point in the phase space where the system remains constant or 'fixed' over time.

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Attractor

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A set of numerical values toward which a system tends to evolve, regardless of the initial conditions of the system.

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Bifurcation

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A qualitative change in the behavior of a dynamical system, where a small change in a parameter value leads to a sudden topological change in its orbit structure.

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