Dynamics of Limit Cycle Oscillator Subject to General Noise

The phase description is a powerful tool for analyzing noisy limit cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to the Gaussian noise while noise in the real world often has non-Gaussian statistics. Here, we provide the phase reduction for limit cycle oscillators subject to general, colored and non-Gaussian, noise including heavy-tailed noise. We derive quantifiers like mean frequency, diffusion constant, and the Lyapunov exponent to confirm consistency of the result. Applying our results, we additionally study a resonance between the phase and noise.Comment: main paper: 4 pages, 2 figure; auxiliary material: 5-7 pages of the document, 1 figur

Quantum System under Periodic Perturbation: Effect of Environment

In many physical situations the behavior of a quantum system is affected by interaction with a larger environment. We develop, using the method of influence functional, how to deduce the density matrix of the quantum system incorporating the effect of environment. After introducing characterization of the environment by spectral weight, we first devise schemes to approximate the spectral weight, and then a perturbation method in field theory models, in order to approximately describe the environment. All of these approximate models may be classified as extended Ohmic models of dissipation whose differences are in the high frequency part. The quantum system we deal with in the present work is a general class of harmonic oscillators with arbitrary time dependent frequency. The late time behavior of the system is well described by an approximation that employs a localized friction in the dissipative part of the correlation function appearing in the influence functional. The density matrix of the quantum system is then determined in terms of a single classical solution obtained with the time dependent frequency. With this one can compute the entropy, the energy distribution function, and other physical quantities of the system in a closed form. Specific application is made to the case of periodically varying frequency. This dynamical system has a remarkable property when the environmental interaction is switched off: Effect of the parametric resonance gives rise to an exponential growth of the populated number in higher excitation levels, or particle production in field theory models. The effect of the environment is investigated for this dynamical system and it is demonstrated that there existsComment: 55 pages, LATEX file plus 13 PS figures. A few calculational mistatkes and corresponding figure 1 in field theory model corrected and some changes made for publication in Phys. Rev.D (in press

Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations

We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein-Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site breathers represent excited oscillations at different sites of the lattice separated by a number of "holes" (sites at rest). The theorem describes how the stability or instability of a multi-site breather depends on the phase difference and distance between the excited oscillators. Previously, only multi-site breathers with adjacent excited sites were considered within the first-order perturbation theory. We show that the stability of multi-site breathers with one-site holes change for large-amplitude oscillations in soft nonlinear potentials. We also discover and study a symmetry-breaking (pitchfork) bifurcation of one-site and multi-site breathers in soft quartic potentials near the points of 1:3 resonance.Comment: 34 pages, 12 figure

Relaxation of classical many-body hamiltonians in one dimension

The relaxation of Fourier modes of hamiltonian chains close to equilibrium is studied in the framework of a simple mode-coupling theory. Explicit estimates of the dependence of relevant time scales on the energy density (or temperature) and on the wavenumber of the initial excitation are given. They are in agreement with previous numerical findings on the approach to equilibrium and turn out to be also useful in the qualitative interpretation of them. The theory is compared with molecular dynamics results in the case of the quartic Fermi-Pasta-Ulam potential.Comment: 9 pag. 6 figs. To appear in Phys.Rev.

New Kinetic Equation for Pair-annihilating Particles: Generalization of the Boltzmann Equation

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic abundance is possible using this new equilibrium abundance in the sudden freeze-out approximation.Comment: 19 pages, LATEX file with 2 PS figure

Dynamical description of the buildup process in resonant tunneling: Evidence of exponential and non-exponential contributions

The buildup process of the probability density inside the quantum well of a double-barrier resonant structure is studied by considering the analytic solution of the time dependent Schr\"{o}dinger equation with the initial condition of a cutoff plane wave. For one level systems at resonance condition we show that the buildup of the probability density obeys a simple charging up law, $| \Psi (\tau) / \phi | =1-e^{-\tau /\tau_0},$ where $\phi$ is the stationary wave function and the transient time constant $\tau_0$ is exactly two lifetimes. We illustrate that the above formula holds both for symmetrical and asymmetrical potential profiles with typical parameters, and even for incidence at different resonance energies. Theoretical evidence of a crossover to non-exponential buildup is also discussed.Comment: 4 pages, 2 figure

Disorder Induced Ferromagnetism in CaRuO3

The magnetic ground state of perovskite structure CaRuO3 has been enigmatic for decades. Here we show that paramagnetic CaRuO3 can be made ferromagnetic by very small amounts of partial substitution of Ru by Ti. Magnetic hysteresis loops are observed at 5 K for as little as 2% Ti substitution. Ti is non-magnetic and isovalent with Ru, indicating that the primary effect of the substitution is the disruption of the magnetic ground state of CaRuO3 through disorder. The data suggest that CaRuO3 is poised at a critical point between ferromagnetic and paramagnetic ground states

Quantum Dissipation and Decay in Medium

Quantum dissipation in thermal environment is investigated, using the path integral approach. The reduced density matrix of the harmonic oscillator system coupled to thermal bath of oscillators is derived for arbitrary spectrum of bath oscillators. Time evolution and the end point of two-body decay of unstable particles is then elucidated: After early transient times unstable particles undergo the exponential decay, followed by the power law decay and finally ending in a mixed state of residual particles containing contributions from both on and off the mass shell, whose abundance does not suffer from the Boltzmann suppression.Comment: 19 pages, LATEX file. Substantially expanded and revised for publication, including more complete description of application to unstable particle decay in thermal medium. Some minor mistake of numerical factors correcte