We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of the well known pathologies which appear in quantum field theory due to the sharp cutoff. We show that for an arbitrary background path the usual local form o...

1 We consider the Kac equation with a thermostatted force field and prove the existence of a global in time solution that converges weakly to a stationary state. As there is no an obvious candidate for the entropy functional, in this case, the convergence result is obtained via Fourier transform techniques.

The magnetic field integral equation for axially symmetric cavities with perfectly conducting piecewise smooth surfaces is discretized according to a high-order convergent Fourier–Nyström scheme. The resulting solver is used to accurately determine eigenwavenumbers and normalized electric eigenfields in the entire computational domain.

An almost-Markovian model equation is proposed for Fourier modes of velocity field of isotropic turbulence whose statistical properties are identical to those governed by equations of Local Energy Transfer theory of turbulence [McComb et. al., J. Fluid Mech. 245, 279 (1992)] compatible with the Kolmogorov spectrum.

An autoresonance relativistic motion of 0.1 mA electron beam in a combined steady-state inhomogeneous magnetic field and a stationary microwave field is studied. The space profile of the axially symmetric magnetic field is fitted to maintain the interaction of electrons with the microwave field of cyclotron resonance type on all their trajectories. The Newton-Lorentz equation is simulated simul...

We develop a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic Smoluchowski equation governing the evolution of the fluctuating density field of the Brownian particles, we determine the expression of the correlation function of th...

In recent years, Fourier spectral methods have been widely used as a powerful tool for solving phase-field equations. To improve its effectiveness, many researchers have employed stabilized semi-implicit Fourier spectral (SIFS) methods which allow a much larger time step than a usual explicit scheme. Our mathematical analysis and numerical experiments, however, suggest that an effective time st...

In the paper, we derive a multi-symplectic Fourier pseudospectral method for Zhiber-Shabat equation. The Zhiber-Shabat equation, which describes many important physical phenomena, has been investigated widely in last several decades. The multi-symplectic geometry and multi-symplectic Fourier pseudospectral method for the Zhiber-Shabat equation is presented. The numerical experiments are given, ...