In (quant–ph/0701141) Rajeev studied quantization of the damped simple harmonic oscillator and introduced a complex–valued Hamiltonian (which is normal). In this note we point out that the quantization is interpreted as a quantum mechanics with complex time. We also present a problem on quantization of classical control systems. In the paper [1] Rajeev studied a quantization of the damped simpl...

Abstract We discuss some frequency-domain criteria for the exponential stability of nonlinear feedback systems based on Popov’s hyperstability theorem. The main results are new bounds convergence rates perturbations damped harmonic oscillator, including Hessian-damped case, when satisfy certain sectoriality or convexity hypotheses. also include a simplified proof theorem in its general form, wh...

We model theoretically the response of the widely studied circadian oscillator of Neurospora crassa to inactivation of the frq gene. The resulting organism has been termed "arrhythmic" under constant conditions. Under entrainment to periodic temperature cycles Roenneberg, Merrow and coworkers have shown that the phase angle at which spore formation occurs depends on the entrainment period, curi...

The present work discusses symmetry-breaking-induced bidirectional escape from a symmetric metastable potential well by the application of zero-average periodic forces in presence dissipation. We characterized interplay between heteroclinic instabilities leading to chaotic and breaking generalized parity symmetry directed ratchet an attractor either at $\ensuremath{\infty}$ or $\ensuremath{-}\e...

We model solar activity cycle as a forced and damped harmonic oscillator consisting of two parts, sinusoidal and transient. The amplitudes, frequencies, phases and decay factors of such a harmonic oscillator are determined by fitting the equation of the sinusoidal and transient parts to the sunspot data for the years 1755–1996 (cycles 1–22) with the results: (i) there is a long-term decreasing ...

We investigate how the kinetic energy acquired by a dense granular system driven an external vibration depends on input energy. Our focus is dependence of behavior two main parameters: frequency and amplitude. find that there exists optimal forcing frequency, at which reaches maximal energy: if increased beyond such threshold, dissipates more recovers colder viscous state. Quite surprisingly, n...

The de Broglie-Bohm quantum trajectories are found in analytically closed forms for the eigenstates and the coherent state of the Lewis-Riesenfeld (LR) invariant of a time-dependent harmonic oscillator. It is also shown that an eigenstate (a coherent state) of an invariant can be interpreted as squeezed states obtained by squeezing an eigenstate (a coherent state) of another invariant. This pro...

In this paper we study to what extent the canonical equivalence and the identity of the geometric phases of dissipative and conservative linear oscillators, established in a preceeding paper, can be generalized to nonlinear ones. Considering first the 1-D quartic generalized oscillator we determine, by means of a perturbative time dependent technic of reduction to normal forms, the canonical tr...

Abstract El Niño Southern Oscillation (ENSO) dynamics are best described by the recharge oscillator model, in which eastern tropical Pacific sea surface temperatures ( T ) and subsurface heat content (thermocline depth; h have an out-of-phase relationship. This defines a 2-dimensional phase space diagram between . In idealized, stochastically forced damped oscillator, mean should be perfectly s...