phase space

Definitions

1. Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point;
   countable, uncountable
2. Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point; (less formally) the underlying set of such a topological space.
   countable, uncountable
3. the underlying set of such a topological space.
   countable, uncountable

Equivalents

Examples

“For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.”

“The phase space of a single material point⟳ is a manifold M×V*, and the Newton state-space is identifical^([sic]) with M×V.”

“2006, Matthew Charles Cargo, Phase Space Approaches to Higher Order⟳ WKB Approximations, University of California, Berkeley, page 8, Their energies are those of the level sets p²/2+V(x)=E that enclose an area of 2π hbar (n+1/2) in the classical phase space. Despite embracing a configuration space point⟳ of view⟳, these methods have⟳ produced a phase space result⟳.”

“The distribution of particles in phase space is given either by the injector characteristics and injection process⟳ or in the case of electron beams by the equilibrium of quantum excitation due to synchrotron radiation and damping.”

CEFR level