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$R(t)$ is a function of time that represents complicated time-dependence of forces due to other molecules on the studied molecule. Since only correlation function is assumed, there is no single unique function $R(t)$ assumed; although not all, many functions would be appropriate. You can generate many of them in computer using Cholesky decomposition of ...


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The spontaneous emission rate $[cm^{-3}s^{-1}J^{-1}]$ for photons of energy $\hbar\omega$ for parabolic semiconductors is, $$r_{sp}(\hbar\omega) = A_{21}(\hbar\omega) g_{12}(\hbar\omega) (1 - f_1(E_l)) f_2(E_u) $$ where $A_{21}(\hbar\omega)$ [$s^{-1}$] is the inverse lifetime of the transition from energy state $E_u$ [$J$] in the upper band 2 to an ...


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The premise of the question is false. $\nu$ is never exactly 0. It tends toward 0 as $\mu_c$ decreases. However, it is always non-zero and positive. Hence, the value of $CV$ depends on the other variables in its definition.


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Let $I$ denote our integral: $$ I=\int{{e}^{x^2}(1+erfi(x))} dx $$ Using IBP: $$ u=(1+erfi(x))\quad dv={e}^{x^2}dx\\ du=\frac{2}{\sqrt{\pi}} {e}^{x^2}dx \quad v=erfi(x)\frac{\sqrt{\pi}}{2} $$ You get: $$ I=(1+erfi(x))erfi(x)\frac{\sqrt{\pi}}{2}-\int{erfi(x) {e}^{x^2}dx}\\ I=(1+erfi(x))erfi(x)\frac{\sqrt{\pi}}{2}-\int{erfi(x){e}^{x^2}-{e}^{x^2}dx} ...


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Physically, a negative total energy is a necessary and sufficient condition for avoiding all particles flying off to infinity separately. However, it is always possible for some particles to be given enough energy to escape a system. In fact, this tends to happen in real life. Planets get ejected from their solar systems over millions of years, and stars ...


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I would choose highly symmetric initial conditions which are easily shown to be periodic. Then I would perturb the system by small steps. For example, four identical particles (of mass $m$) moving on a circle and interacting through Newton gravitation alone is a solution of the equations of motion. $$ \vec{x}_i = R \left(\begin{array}{c}\cos\left(\omega t ...


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This is pretty niche notation, and it is indeed not defined in the paper, but the name "vector-coupled product" does seem to be used by a few people beyond Varga and Suzuki. In essence, $$ [\mathcal Y_{l_1}(\mathbf x_1)\mathcal Y_{l_2}(\mathbf x_2)]_{LM} $$ is a coupled wavefunction with total angular momentum $L$ that's made up of the single-particle ...


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I think the answer would have to depend on the nature of the simulation. I'm guessing it is some sort of flow simulation in which fluid "enters the system" at some point and exits at some other point. If so, there must be parameters to do with the fluid at the intake which you have control over. Is $\rho(\mathbf{x})$ (fluid density as a function of ...



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