1549380323-Statistical Mechanics Theory and Molecular Simulation

524 Classical time-dependent statistical mechanics Applying the prescription in eqn. (13.5.16) using eqns. (13.5.1) and (13.5.17 ...

Nonequilibrium molecular dynamics 525 For a general incompressible flow with constant strain-rate tensor, we seek a set of equat ...

526 Classical time-dependent statistical mechanics Fig. 13.8 Two-dimensional representation of a fluid confined between corrugat ...

Problems 527 Uwf(x,y) =ǫ {[ σ y−f(l)(x) ] 12 + [ σ Ly−y−f(u)(x) ] 12 } , (13.5.27) whereLyis the length of the box in theydirect ...

528 Classical time-dependent statistical mechanics b. Comparing the two diffusion constants, what two physical situations do the ...

Problems 529 a. Write a program to integrate the driven equations of motion under con- ditions of constant energy, and use the p ...

14 Quantum time-dependent statistical mechanics 14.1 Time-dependent systems in quantum mechanics In this chapter, we will explor ...

Time-dependent systems 531 spatial and time dependence of the vector fields. The elegance andbeauty of Maxwell’s theory lies in ...

532 Quantum time-dependent statistical mechanics into the free-field Maxwell equations, then the vector potential isseen to sati ...

Time-dependent systems 533 E B k λ Fig. 14.1Sketch of an electromagnetic wave described by eqn. (14.1.7). and massesm 1 ,...,mN, ...

534 Quantum time-dependent statistical mechanics |E >i |E >f Fig. 14.2 A transition from an initial eigenstate ofH 0 with ...

Time-dependent perturbation theory 535 between the Schr ̈odinger and Heisenberg pictures. Recall that inthe Schr ̈odinger pic- t ...

536 Quantum time-dependent statistical mechanics 14.2.2 Iterative solution for the interaction-picture state vector The solution ...

Time-dependent perturbation theory 537 =Iˆ− i ̄h ∫t t 0 dt′HˆI(t′) + ( i ̄h ) 2 ∫t t 0 dt′ ∫t′ t 0 dt′′HˆI(t′)HˆI(t′′), (14.2.14 ...

538 Quantum time-dependent statistical mechanics From eqn. (14.2.20), the structure of the full propagator is revealed. Let us u ...

Time-dependent perturbation theory 539 = + + + ... t 0 t t 0 t t 0 t t’ t 0 t t’’ t’ t 0 t t’’’ t’’ t’ Fig. 14.3 Pictorial repre ...

540 Quantum time-dependent statistical mechanics t’ t’’ t 0 t t 0 t t’ t’’ t 0 t t 0 t (a) (b) Fig. 14.4The two integration regi ...

Time-dependent perturbation theory 541 UˆI(t;t 0 ) =T [ exp ( − i ̄h ∫t t 0 dt′HˆI(t′) )] , (14.2.31) which is known as atime-or ...

542 Quantum time-dependent statistical mechanics =− i ̄h e−iEft/ ̄heiEit^0 / ̄h ∫t t 0 dt′ei(Ef−Ei)t ′/ ̄h 〈Ef|Hˆ 1 (t′)|Ei〉. (1 ...

Time-dependent perturbation theory 543 ∫T/ 2 −T/ 2 dt [ ei(ωfi+ω)t+ ei(ωfi−ω)t ] = T [ sin[(ωfi+ω)T/2] (ωfi+ω)T/ 2 + sin[(ωfi−ω) ...