By the method of eigenfunction expansion, we study the linear response to a time-dependent external field for stochastic systems described by the one-dimensional subdiffusive fractional Fokker–Planck equation with a general confining potential and natural boundary conditions; an expression for...

We study the dynamical properties of bistable systems described by the one-dimensional subdiffusive fractional Fokker–Planck equation, for the natural boundary conditions as well as the absorbing boundary conditions. We have investigated the propagators, the auto-correlation function, the...

We study the dynamics of stochastic systems obeying the one-dimensional diffusive Fokker–Planck equation (FPE), as well as systems described by the subdiffusive fractional Fokker–Planck equation (SFFPE), with a confining potential U(x) and in the presence of delta-function sinks. For the...

We study the response of a stochastic system described by the one-dimensional Fokker–Planck equation with a sextic double-well potential U6(x)=(−c4x4+c6x6) to a weak sinusoidal periodic signal. Two types of boundary conditions have been investigated: (i) absorbing boundary conditions, and...

We study the statistical mechanics of two models of nonlinear Klein–Gordon chain: the ‘φ8-chain’ with the single-site potential v(y)=a(y2−1)4, and the Gaussian double-well model with v(y)=12ky2+bexp(−12cy2) where a,b,c and k are positive constants. The thermodynamics of the classical...

We study the Fokker–Planck equation of one-dimensional bistable systems with symmetric as well as asymmetric potentials. In this work, the method of state-dependent diagonalization (SDD) is proposed for solving the eigenvalue problem of the associated Schrödinger equation. The example of a...

We have investigated the eigenenergy spectrum of the intensity-dependent Jaynes–Cummings (JC) model with and without the rotating-wave approximation (RWA). Our analysis has indicated that the counter-rotating term dramatically changes the nature of the RWA energy spectrum and that the non-RWA...

In this paper we have investigated the eigen energy spectrum of the k-photon intensity-dependent Jaynes–Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis shows that for k⩾2 the k-photon intensity-dependent JC model without the RWA does not have eigenstates in...

In this paper we have investigated the eigenenergy spectrum of the k-quantum q-deformed Jaynes–Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis has shown that the k-quantum q-deformed JC model without the RWA does not have eigenstates in the Hilbert space spanned...