In dynamical systems theory and control theory, a phase space or state space is a space in which all possible "states" of a dynamical system or a control...

The phase-space formulation of quantum mechanics places the position and momentum variables on equal footing in phase space. In contrast, the Schrödinger...

Phase space is a concept in physics, frequently applied in thermodynamics, statistical mechanics, dynamical systems, symplectic manifolds and chaos theory...

an optical phase space is a phase space in which all quantum states of an optical system are described. Each point in the optical phase space corresponds...

classical statistical and Hamiltonian mechanics. It asserts that the phase-space distribution function is constant along the trajectories of the system—that...

In applied mathematics, the phase space method is a technique for constructing and analyzing solutions of dynamical systems, that is, solving time-dependent...

"Phase Space" is the sixth episode in the second season of the HBO science fiction western thriller television series Westworld. The episode aired on...

in the phase space. But for a system with a huge number of degrees of freedom its exact microstate usually is not important. So the phase space can be...

can exist Phase (matter), a region of space throughout which all physical properties are essentially uniform Phase space, a mathematical space in which...

Phase-space representation of quantum state vectors is a formulation of quantum mechanics elaborating the phase-space formulation with a Hilbert space...

system, where bounded classical trajectories are confined onto tori in phase space, tunnelling can be understood as the quantum transport between semi-classical...

curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space. This reveals...

theorem: Assume the phase space has a finite Liouville volume and let F be a phase space volume-preserving map and A a subset of the phase space. Then almost...

properties. In space, amorphous ice is the most common form as confirmed by observation. Thus, it is theorized to be the most common phase in the universe...

volume of k-space, such that every possible k is "equivalent" to exactly one point in this region. Phase space Reciprocal space Configuration space Fractional...

product, after Hermann Weyl and Hilbrand J. Groenewold) is an example of a phase-space star product. It is an associative, non-commutative product, ★, on the...

written as a probability distribution in phase space; the microstates are the result of partitioning phase space into equal-sized units, although the size...

the quantum phase space formulation and Hilbert space operators in the Schrödinger picture. Often the mapping from functions on phase space to operators...

complete the phase. If you land on a twist phase you can decide to play a twist phase or one of the phases on either side of the twist phase space. If you...

conditions. More specifically, given two starting trajectories in the phase space that are infinitesimally close, with initial separation δ Z 0 {\displaystyle...

Phase space crystal is the state of a physical system that displays discrete symmetry in phase space instead of real space. For a single-particle system...

each xi is a point in 3-dimensional space. This has analogies with the classical phase space. A classical phase space contains a real-valued function in...

Q} . This larger manifold is called the phase space of the system. In quantum mechanics, configuration space can be used (see for example the Mott problem)...

be a Hamiltonian; thus the cotangent bundle can be understood to be a phase space on which Hamiltonian mechanics plays out. The cotangent bundle carries...

recurrence theorem, which claims that almost all points in any subset of the phase space eventually revisit the set. Systems for which the Poincaré recurrence...

also depend on the input variable values. The state space or phase space is the geometric space in which the axes are the state variables. The system...

transients and settle the system into its typical behavior. The subset of the phase space of the dynamical system corresponding to the typical behavior is the...

points rA and rB in phase space. In general, all rays crossing axis x1 between xL and xR are represented by a volume R in phase space. The rays at the boundary...

that appears in Schrödinger's equation to a probability distribution in phase space. It is a generating function for all spatial autocorrelation functions...

({\boldsymbol {p}},{\boldsymbol {q}})} is called phase space coordinates. (Also canonical coordinates). In phase space coordinates ⁠ ( p , q ) {\displaystyle ({\boldsymbol...