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...
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The phase-space formulation of quantum mechanics places the position and momentum variables on equal footing in phase space. In contrast, the Schrödinger...
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Phase space is a concept in physics, frequently applied in thermodynamics, statistical mechanics, dynamical systems, symplectic manifolds and chaos theory...
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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...
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classical statistical and Hamiltonian mechanics. It asserts that the phase-space distribution function is constant along the trajectories of the system—that...
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In applied mathematics, the phase space method is a technique for constructing and analyzing solutions of dynamical systems, that is, solving time-dependent...
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"Phase Space" is the sixth episode in the second season of the HBO science fiction western thriller television series Westworld. The episode aired on...
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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...
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can exist Phase (matter), a region of space throughout which all physical properties are essentially uniform Phase space, a mathematical space in which...
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Phase-space representation of quantum state vectors is a formulation of quantum mechanics elaborating the phase-space formulation with a Hilbert space...
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Quantum tunnelling (section Tunnelling in phase space)
system, where bounded classical trajectories are confined onto tori in phase space, tunnelling can be understood as the quantum transport between semi-classical...
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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...
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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...
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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...
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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...
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Moyal product (section Inside phase-space integrals)
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...
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written as a probability distribution in phase space; the microstates are the result of partitioning phase space into equal-sized units, although the size...
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Wigner–Weyl transform (redirect from Phase-space quantization)
the quantum phase space formulation and Hilbert space operators in the Schrödinger picture. Often the mapping from functions on phase space to operators...
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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...
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conditions. More specifically, given two starting trajectories in the phase space that are infinitesimally close, with initial separation δ Z 0 {\displaystyle...
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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...
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Quantum decoherence (section Phase-space picture)
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...
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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)...
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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...
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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...
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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...
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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...
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Hamiltonian optics (section Phase space)
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...
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that appears in Schrödinger's equation to a probability distribution in phase space. It is a generating function for all spatial autocorrelation functions...
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({\boldsymbol {p}},{\boldsymbol {q}})} is called phase space coordinates. (Also canonical coordinates). In phase space coordinates ( p , q ) {\displaystyle ({\boldsymbol...
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