Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called stateful systems). In...

evolves with time. The evolution for a closed quantum system is brought about by a unitary operator, the time evolution operator. For time evolution from a...

Evolution is the change in the heritable characteristics of biological populations over successive generations. It occurs when evolutionary processes...

{e} ^{\pm \mathrm {i} H_{0,{\text{S}}}t/\hbar }} by the corresponding time-evolution operator in the definitions below. Let | ψ S ( t ) ⟩ = e − i H S t /...

path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical...

U(t)=e^{-iHt/\hbar }} is known as the time-evolution operator, and has the crucial property that it is unitary. This time evolution is deterministic in the sense...

In telecommunications, long-term evolution (LTE) is a standard for wireless broadband communication for mobile devices and data terminals, based on the...

Evolutionism is a term used (often derogatorily) to denote the theory of evolution. Its exact meaning has changed over time as the study of evolution...

used to describe the time evolution of a system that can be modeled as being in a probabilistic combination of states at any given time, and the switching...

=H(t)|\psi (t)\rangle } Equivalently, the time evolution postulate can be stated as: Postulate III The time evolution of a closed system is described by a...

physics, unitarity is (or a unitary process has) the condition that the time evolution of a quantum state according to the Schrödinger equation is mathematically...

}^{\alpha }} can be appropriately called the shape gradient of area. An evolution governed by C ≡ B α α {\displaystyle C\equiv B_{\alpha }^{\alpha }} is...

Koopman and John von Neumann: the time evolution of the Wigner function approaches, in the limit ħ → 0, the time evolution of the Koopman–von Neumann wavefunction...

is to consider the time-evolution of the expected position and expected momentum, which can then be compared to the time-evolution of the ordinary position...

the evolution of the state variables. In physics, a dynamical system is described as a "particle or ensemble of particles whose state varies over time and...

covers the evolution of time-sharing systems, providing links to major early time-sharing operating systems, showing their subsequent evolution. The meaning...

paradox) is a feature of quantum-mechanical systems allowing a particle's time evolution to be slowed down by measuring it frequently enough with respect to...

neglect the time evolution of the system, so the above definition is re-written with τ = 0 {\displaystyle \tau =0} . This defines the equal-time correlation...

series, formulated by Freeman Dyson, is a perturbative expansion of the time evolution operator in the interaction picture. Each term can be represented by...

a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes...

Human evolution is the evolutionary process within the history of primates that led to the emergence of Homo sapiens as a distinct species of the hominid...

of the problem of time is the Frozen Formalism Problem. The non-relativistic equation of quantum mechanics includes time evolution: i ℏ ∂ ∂ t ψ ( t )...

square the time-evolution operator in the S representation: e i ε S , {\displaystyle e^{i\varepsilon S},} and this gives the time-evolution operator between...

total energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of...

"world tube" (the time evolution of a closed surface) that cannot be continuously deformed (shrunk) to a world line (the time evolution of a point or observer)...

describes the forward-time evolution of the system, and one that describes the backwards-time evolution. As of 2006, this type of time-symmetry breaking has...

arbitrary quantum system, and by subdividing the time into many segments, it allows the time evolution to be expressed as a path integral. The spreading...

realistic situation. The diffusion equation yields an approximation of the time evolution of the probability density function associated with the position of...

\mathbf {U} (t)} is called the time evolution matrix (which comprises the matrix elements of the corresponding time evolution operator U ( t ) {\displaystyle...

evolves in time (see also the Belavkin equation for the evolution under continuous measurement). This uses the Schrödinger picture, where evolution of the...