We study dipolarly coupled three dimensional spin systems in both the microcanonical and the canonical ensembles by introducing appropriate numerical methods to determine the microcanonical temperature and by realizing a canonical model of heat bath.
In the microcanonical ensemble, we show the existence of a branch of stable antiferromagnetic states in the low energy region. Other metastable ferromagnetic states exist in this region: by externally perturbing them, an effective negative specific heat is obtained. In the canonical ensemble, for low temperatures, the same metastable states are unstable and reach a new branch of more robust metastable states which is distinct from the stable one. Our statistical physics approach allows us to put some order in the complex structure of stable and metastable states of dipolar systems.
A simple mechanical analog describing Landau-Zener tunneling effect is proposed using two weakly coupled chains of nonlinear oscillators with gradually decreasing (first chain) and increasing (second chain) masses. The model allows to investigate non
linear generalization of Landau-Zener tunneling effect considering soliton propagation and tunneling between the chains. It is shown that soliton tunneling characteristics become drastically dependent on its amplitude in nonlinear regime. The validity of the developed tunneling theory is justified via comparison with direct numerical simulations on oscillator ladder system.
A conceptual mechanism of amplification of phonons by phonons on the basis of nonlinear band-gap transmission (supratransmission) phenomenon is presented. As an example a system of weakly coupled chains of anharmonic oscillators is considered. One (s
ource) chain is driven harmonically by boundary with a frequency located in the upper band close to the band edge of the ladder system. Amplification happens when a second (gate) chain is driven by a small signal in the counter phase and with the same frequency as first chain. If the total driving of both chains overcomes the band-gap transmission threshold the large amplitude band-gap soliton emerges and amplification scenario is realized. The mechanism is interpreted as nonlinear superposition of evanescent and propagating nonlinear modes manifesting in a single or double soliton generation working in band-gap or band-pass regimes, respectively. The results could be straightforwardly generalized for all-optical or all-magnonic contexts and has all the promises for logic gate operations.
We introduce a weakly coupled photonic crystal waveguide as a promising and realistic model for all-optical amplification. A symmetric pillar type coupled photonic crystal waveguide consisting of dielectric rods periodically distributed in a free spa
ce is proposed as all-optical amplifier. Using the unique features of the photonic crystals to control and guide the light, we have properly chosen the frequency at which only one mode (odd mode) becomes the propagating mode in the coupled photonic crystal waveguide, whereas another mode (even mode) is completely reflected from the guiding structure. Under this condition, the all-optical amplification is fully realized. The amplification coefficient for the continuous signal and the Gaussian pulse is calculated.
All-optical amplification of the light pulse in a weakly coupled two nonlinear photonic crystal waveguides (PCWs) is proposed. We consider pillar-type PCWs, which consist of the periodically distributed circular rods made from a Kerr-type dielectric
material. Dispersion diagrams of the symmetric and antisymmetric modes are calculated. The operating frequency is properly chosen to be located at the edge of the dispersion diagram of the modes. In the linear case no propagation modes are excited at this frequency, however, in case of nonlinear medium when the amplitude of the injected signal is above some threshold value, the solitons are formed and they are propagating inside the coupled nonlinear PCWs. Near field distributions of the light pulse propagation inside the coupled nonlinear PCWs and the output powers of the registered signals are studied in a detail. The amplification coefficient is calculated at the various amplitudes of the launched signal. The results vividly demonstrate the effectiveness of the weakly coupled nonlinear PCWs as all-optical digital amplifier.
Proposed all optical amplification scenario is based on the properties of light propagation in two coupled subwavelength metallic slab waveguides where for particular choice of waveguide parameters two propagating (symmetric) and non-propagating (ant
isymmetric) eigenmodes coexist. For such a setup incident beams realize boundary conditions for forming a stationary state as a superposition of mentioned eigenmodes. It is shown both analytically and numerically that amplification rate in this completely linear mechanism diverges for small signal values.
We propose the method for optical visualization of Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by differe
nt refractive index than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over direction of propagation for both ordered and disordered cases, exploring sensitivity of the averaged picture with respect to the beam injection position. For our finite systems the resulting patterns reminiscent the ones set in billiards and therefore we introduce a definition of discrete quantum billiard discussing the possible relevance to its well established continuous counterpart.
Experiments on a chain of coupled pendula driven periodically at one end demonstrate the existence of a novel regime which produces an output frequency at an odd fraction of the driving frequency. The new stationary state is then obtained on numerica
l simulations and modeled with an analytical solution of the continuous sine-Gordon equation that resembles a kink-like motion back and forth in the restricted geometry of the chain. This solution differs from the expressions used to understand nonlinear bistability where the synchronization constraint was the basic assumption. As a result the short pendula chain is shown to possess tristable stationary states and to act as a frequency divider.
Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous e
xistence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to make suggestions on possible experiments using Bose-Einstein condensates in engineered optical lattices or weakly coupled optical waveguide arrays.
A two-level medium, described by the Maxwell-Bloch (MB) system, is engraved by establishing a standing cavity wave with a linearly polarized electromagnetic field that drives the medium on both ends. A light pulse, polarized along the other direction
, then scatters the medium and couples to the cavity standing wave by means of the population inversion density variations. We demonstrate that control of the applied amplitudes of the grating field allows to stop the light pulse and to make it move backward (eventually to drive it freely). A simplified limit model of the MB system with variable boundary driving is obtained as a discrete nonlinear Schroedinger equation with tunable external potential. It reproduces qualitatively the dynamics of the driven light pulse.
