Wesp Christian, van Hees Hendrik, Meistrenko Alex, Greiner Carsten
Institut für theoretische Physik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Straße 1, 60438 Frankfurt, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):043302. doi: 10.1103/PhysRevE.91.043302. Epub 2015 Apr 8.
Particles and fields are standard components in numerical calculations like transport simulations in nuclear physics and have well-understood dynamics. Still, a common problem is the interaction between particles and fields due to their different formal description. Particle interactions are discrete, pointlike events while field dynamics is described with continuous partial-differential equations of motion. A workaround is the use of effective theories like the Langevin equation with the drawback of energy conservation violation. We present a method, which allows us to model noncontinuous interactions between particles and scalar fields, allowing us to simulate scattering-like interactions which exchange discrete "quanta" of energy and momentum between fields and particles while obeying energy and momentum conservation and allowing control over interaction strengths and times. In this paper we apply this method to different model systems, starting with a simple harmonic oscillator, which is damped by losing discrete energy quanta. The second and third system consists of an oscillator and a one-dimensional field, which are damped via discrete energy loss and are coupled to a stochastic force, leading to equilibrium states which correspond to statistical Langevin-like systems. The last example is a scalar field in (1 + 3) space-time dimensions, which is coupled to a microcanonical ensemble of particles by incorporating particle production and annihilation processes. Obeying the detailed-balance principle, the system equilibrates to thermal and chemical equilibrium with dynamical fluctuations on the fields, generated dynamically by the discrete interactions.
粒子和场是数值计算中的标准组件，例如核物理中的输运模拟，并且具有易于理解的动力学。然而，由于它们不同的形式描述，粒子与场之间的相互作用仍是一个常见问题。粒子相互作用是离散的、点状事件，而场动力学则由连续的运动偏微分方程描述。一种解决方法是使用像朗之万方程这样的有效理论，但存在违反能量守恒的缺点。我们提出了一种方法，它使我们能够对粒子与标量场之间的非连续相互作用进行建模，从而能够模拟类似散射的相互作用，这种相互作用在场和粒子之间交换离散的能量和动量“量子”，同时遵守能量和动量守恒，并允许控制相互作用强度和时间。在本文中，我们将这种方法应用于不同的模型系统，首先是一个简谐振子，它通过损失离散的能量量子而受到阻尼。第二个和第三个系统由一个振子和一个一维场组成，它们通过离散的能量损失受到阻尼，并耦合到一个随机力，导致对应于统计类朗之万系统的平衡态。最后一个例子是(1 + 3)时空维度中的标量场，它通过纳入粒子产生和湮灭过程与粒子的微正则系综耦合。遵循细致平衡原理，该系统通过离散相互作用动态产生的场的动态涨落，达到热平衡和化学平衡。
