Chain Of Classical Oscillators Research Articles

Energy transport in boundary driven quantum spin systems: One-way street phenomenon in models with long range interactions

We address the investigation of non trivial properties of the energy current in boundary driven XXZ quantum spin models. In specific, we focus on the occurrence of the one-way street phenomenon in asymmetrical chains, a phenomenon stronger than rectification, which establishes the existence of a unique way for the energy current in the absence of external magnetic field, that is, the magnitude and direction of the energy flow does not change as we invert the baths at the boundaries. For general target polarizations at the boundaries, we show that such a phenomenon holds in the presence of long range interactions, ingredient which increases the flow and the rectification in chains of classical oscillators, and so, of interest in the study of manipulation and control of the energy flow.

Momentum autocorrelation function of an impurity in a classical oscillator chain with alternating masses III. Some limiting cases

The momentum autocorrelation function of a mass impurity in a classic diatomic chain is studied using the recurrence relations method. General expressions for the contributions of branch cuts and resonant poles have been derived and illustrated in previous papers I and II, respectively. In the present paper a series of limiting cases that any one of the three masses m0,m1,m2 approaches to zero or infinity are analyzed. It is found that the cases m0→0 and →(2m2)+ are closely related to each other and that the general expressions for the amplitudes are valid also in the limits λ→0 and ∞. The ergodicity in the case m2→0 is studied and the ratio of two specific infinite products is obtained.

Momentum autocorrelation function of an impurity in a classical oscillator chain with alternating masses II. Illustrations

A classic diatomic chain with a mass impurity is studied using the recurrence relations method. The dependence of frequency and amplitude upon two mass ratios is illustrated in detail. By examining the figures we can learn a lot about the model, such as the widths of the acoustic and optical branches as well as the gap between them, the frequency and amplitude of the resonant modes, etc. The momentum autocorrelation functions of the impurity in different regions of the configuration space are numerically calculated and illustrated. A theorem is obtained governing the upper and lower frequencies of the acoustic and optical branches. The envelope of the integrand of the cut contribution is determined. The convergence of numerical calculations of time integration for parameter W to its theoretical value is confirmed.

Momentum autocorrelation function of an impurity in a classical oscillator chain with alternating masses— I. General theory

A chain composed of classic harmonic oscillators with alternating masses and one mass impurity is studied using the recurrence relations method. The dynamics of the momentum autocorrelation function of the impurity mass is contributed by three branch cuts corresponding to acoustic and optic modes and by two pairs of poles for resonant modes. One pair of the poles are located beyond the optic branch and the other in the gaps between the branches. Criteria for the resonances are established. General expressions for frequencies and amplitudes of the resonant modes are derived. Ergodic behavior of the momentum of the impurity is analyzed.

Momentum autocorrelation function of a classical oscillator chain with alternating masses

A classical harmonic oscillator chain with alternating masses is studied using the recurrence relations method. The momentum autocorrelation function changes from combination of cosines to Bessel functions when the number of oscillators increases from finite to infinite bringing about irreversibility. Optic and acoustic branches of the momentum autocorrelation function are expanded in terms of even-order Bessel functions and are shown to be finite and well behaved. Irreversibility and ergodicity are discussed.

On physics at the Planck scale: Space as a network

It is shown that the one-dimensional quantum field theory can be modeled as a chain of classical oscillators in a thermal bath provided that the Gibbs measure is identified with the phase-space volume measure, the chain being in a nonequilibrium state. Quantized strings and p-branes are also modeled by ordered systems of oscillators. The model of a one-dimensional superspace is constructed. It is shown that the Ramond-Neveu-Schwarz superstring is modeled by a helix formed of a bosonic-string in a multidimensional space. The physical 3D space is represented by a superstring structure (3D “network”), which is described by some Lagrangian. Thus, the unified description of all interactions including gravity is achieved because the superstring excitations involve all fields. In view of the discrete character of the initial structure, the theory is free of ultraviolet divergences. The essential element of the model is the occurrence of the cosmological constant in the gravity equations. A black hole model giving reasonable values for its temperature and entropy is proposed.

Many-bodysymbolic dynamics of a classical oscillator chain

We study a certain type of the celebrated Fermi-Pasta-Ulam particlechain, namely the inverted FPU model, where the interparticle potentialhas the form of a quartic double well. Numerical evidence is given insupport of a simple symbolic description of dynamics (in the regime ofsufficiently high potential barrier between the wells) in terms of an(approximate) Markov process. The corresponding transition matrix isformally identical to a ferromagnetic Heisenberg quantum spin-1/2chain with long-range coupling, whose diagonalization yields accurateestimates for a class of time correlation functions of the model.