Sentence examples for be the evolution operator from inspiring English sources

Let be the evolution operator associated to the linear homogeneous equation (2.1).

In the rest of the section, we let T ˆ λ ( t, s ) be the evolution operator associated to system (3.1) for each λ ∈ Y.

Let T ( t, s ) be the evolution operator satisfying T ( t, s ) x ( s ) = x ( t ) for t, s ∈ T and any solution x ( t ) of system (2.1).

For a densely defined self-adjoint operator H in Hilbert space F the operator exp(−itH) is the evolution operator for the Schrödinger equation iψt′="Hψ, i.e. if ψ 0,x)="ψ0 x) then ψ t,x)="(exp⁡(−itH ψ0)(x) for x∈Q.

Our closed-form expression allows us, for cell j, to write its state at time (t_{i+1}) as a function of its state at time (t_{i}): X_{j}(t_{i+1}) = varphi_{Delta t} bigl(t_{i},X_{j}(t_{i}) bigr), where (varphi_{h}) is the evolution operator acting over a time h.

In this paper a general scheme of the MPE is given, the evolution operator is derived for problems with smooth coefficients and the numerical algorithm is discussed.

Every solution ψ can be written ψ (x, t ) = U ˆ t ψ 0 (x ) and U ˆ t is called the evolution operator (or "propagator") for the Schrödinger equation (37).

Here R u (t, s) can be extracted from the evolution operator of the generator - A t, u).

We mention here that the resolvent operator (R t,s)) can be reduced from the evolution operator of the generator (A t)) under some suitable conditions (see [26] for the details).

Suppose that f(x) is the macrostate of the system for some chosen initial time, and let Tt be the time evolution operator associated with the Hamiltonian for the system, which governs its time evolution from the initial time to some other time t.

A new P system and related interaction rules are designed, and particle swarm optimization (PSO) algorithm with different inertia weights is adopted as the evolution operator of new P system.