We introduce a Langevin equation describing the pinning-depinning phase transition experienced by Kardar-Parisi-Zhang interfaces in the presence of a bounding “lower-wall”. This provides a continuous description for this universality class, complementary to the different and already well documented one for the case of an “upper-wall”. The Langevin equation is written in terms of a field that is...

Telecommunication network topologies are changing nowadays. The core telecommunication networks are based on fiber optics infrastructure. WDM technology is used to transmit multiple flows of traffic over a single fiber. Virtual network topology (VNT) is used to route IP traffic over WDM networks. VNT control system must be adaptive to traffic changes and dynamically reconfigure VNT. Langevin eq...

We extend the Langevin approach to a class of driving noises whose generating processes have independent increments with super-heavy-tailed distributions. The time-dependent generalized Fokker–Planck equation that corresponds to the first-order Langevin equation driven by such a noise is derived and solved exactly. This noise generates two probabilistic states of the system, survived and absorb...

We derive the linear Langevin equation that describes the behavior of the fluctuations of the order parameter of the chiral phase transition above the critical temperature by applying the projection operator method to the Nambu-Jona-Lasinio model at finite temperature and density. The Langevin equation relaxes exhibiting oscillation, reveals thermalization and converges to the equilibrium state...

Quaternion measurable processes are introduced and the Dirac equation is derived from the Langevin equation associated with a two-valued process.

A new type of Langevin equation exhibiting a nontrivial phase transition associated with the presence of multiplicative noise is discussed. The equation is derived as a mesoscopic representation of the microscopic annealed Ising model ~AIM! proposed by Thorpe and Beeman, and reproduces perfectly its basic phenomenology. The AIM exhibits a nontrivial behavior as the temperature is increased, in ...

We analyze two different confining mechanisms for Lévy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Lévy-Schrödinger semigroups which induce so-called topological Lévy processes (Lévy flights with locally modified jump rates in the master equation). Given a stationary probability func...

A Stochastic Quantization Method (in short, SQM)l) was first introduced by Parisi and Wu) as the third quantization method of gauge theories. Their statement is as follows: In this scheme there is no need to fix the gauge degrees of freedom, i.e., no need to introduce any artificial auxiliary fields (ghost and multiplier fields). It is the main advantage of the SQM. It is essentially governed b...

An attempt to generalize the Langevin dynamics simulation method is presented based on the generalized Langevin theory of liquids, in which the dynamics of both solute and solvent is treated by the generalized Langevin equations, but the integration of the equation of motion of solute is made in the manner similar to the ordinary molecular dynamics simulation with discretized time steps along a...

Standard damping theory is generalized to incorporate the effects of finite mirror transmittivity. The correction to the standard Langevin equation for the quasimode annihilation operator is determined in first order in the transmittivity of the mirrors. From the Langevin equation an effective master equation is derived. As an example, we study the decay of a single two-level atom at a fixed po...