Breather Modes Research Articles

Quantum control of Bose–Einstein condensates using Feshbach resonance

We present a method to execute quantum control in Bose–Einstein condensates via Feshbach resonance. By switching an initially positive scattering length to zero, it is possible to generate a breather mode that results from quantum interference. The density oscillation is accompanied by a periodic enhancement of the quantum mechanical squeezing in the amplitude quadrature.

Discrete breather modes associated with vertical dust grain oscillations in dusty plasma crystals

Accounting for the lattice discreteness and the sheath electric field nonlinearity in dusty plasma crystals, it is demonstrated that highly localized structures (discrete breathers) involving vertical (transverse, off-plane) oscillations of charged dust grains may exist in a dust lattice. These structures correspond to either extremely localized bright breather excitations (pulses) or dark excitations composed of dips/voids. Explicit criteria for selecting different breather modes are presented.

Inhomogeneity, local mode formation, and the breakdown of the Bloch theorem in complex charge transfer systems as a consequence of discrete breather formation

Charge transfer and valence unstable materials exhibit numerous ground states as functions of doping, pressure, and temperature. Multiscale inhomogeneity is typical for most of these materials, e.g., relaxor ferroelectrics, manganites, cuprates, tungstates, and related compounds. Here, we show that the strong anharmonicity in all these systems allows for a distinct form of inherent, dynamic inhomogeneity dictated by ``discrete breather'' formation, where lattice, charge, and elasticity are intimately coupled. The spatial extent of the breather is governed by the strength of anharmonicity it carries and can vary considerably, defining length scales of inhomogeneity. The coupling of the breather to the host lattice prevents a lattice instability and induces a collapse of the elastic constants and an excess specific heat and entropy as soon as the discrete breather modes emerge from the continuum of the optic modes. Then a coexistence of local, dynamically distorted patterns with the regular lattice is manifested, defining a two-component system with very different dynamics and a strong analogy to glasses: A self-organization of multiple breathers into patterns takes place as a function of temperature and breather density.

Interfacial structure at a two-dimensional wedge filling transition: Exact results and a renormalization group study.

Interfacial structure and correlation functions near a two-dimensional wedge filling transition are studied using effective interfacial Hamiltonian models. An exact solution for short range binding potentials and results for Kratzer binding potentials show that sufficiently close to the filling transition a new length scale emerges and controls the decay of the interfacial profile relative to the substrate and the correlations between interfacial positions above different positions. This new length scale is much larger than the intrinsic interfacial correlation length, and it is related geometrically to the average value of the interfacial position above the wedge midpoint. The interfacial behavior is consistent with a breather mode fluctuation picture, which is shown to emerge from an exact decimation functional renormalization group scheme that keeps the geometry invariant.

Recent high field ESR studies of low-dimensional quantum spin systems in Kobe

Recent advances in the high-field ESR studies of low-dimensional quantum spin systems in Kobe are presented. Among many systems studied, the results of S= 1 2 quasi-one-dimensional (1D) antiferromagnet BaCu 2(Si 1− x Ge x ) 2O 7 with the staggered field and S= 1 2 diamond chain system Cu 3OH 2(CO 3) 2 are discussed. As the interchain interaction is almost canceled in the BaCu 2(Si 1− x Ge x ) 2O 7 ( x=0.65) system, we have found that the field and temperature dependences of the linewidth and the resonance field obey the Oshikawa–Affleck (OA) ESR theory of 1D antiferromagnet. The effect of the interchain interaction from the x dependence measurement and the existence of the breather mode at low temperature are also discussed. On the other hand, the high-field ESR measurements at 1.8 K revealed the direct transition in Cu 3OH 2(CO 3) 2. The direct transition turned out to be anisotropic and it will be discussed in connection with the 1 3 magnetization plateau which is also anisotropic.

Wave mixing of hybrid Bogoliubov modes in a Bose-Einstein condensate

Mode-mixing of coherent excitations of a trapped Bose-Einstein condensate is modelled using the Bogoliubov approximation. Hybridization of the modes of the breather ($l=0$) and surface ($l=4$) states leads to the formation of a Bogoliubov dark state. Calculations are presented for second-harmonic generation between the two lowest-lying even-parity $m=0$ modes in an oblate spheroidal trap. Two hybrid modes are strongly excited near second-harmonic resonance, and the coupling strength, and hence conversion rate, to the breather mode is half that given by an equivalent hydrodynamic estimate.

Electron spin resonance measurements at ultralow temperatures

An electron spin resonance (ESR) measurement system for use at ultralow temperatures using a 3 He– 4 He dilution refrigerator has been developed down to 160 mK . As the first experiment, the ESR was measured on a quantum spin chain Cu benzoate, in which a field-induced gap was recently found. The evaluation of a new ESR mode, so-called breather mode, was found at the lowest temperatures. In the present work, we observed a smaller gap in H|| b by suppressing of the thermal excitation.

Vibrational spectra of Fe3P and Fe2P metal-metalloid compound crystallites: Phonon and breather excitations

The spectra of small-amplitude single-phonon vibrations and large-amplitude nonlinear multiphonon vibrations of Fe3P and Fe2P metal-metalloid compound crystallites are investigated. The vibrational spectra of 3D crystallites of gradually increasing volumes are calculated within a microscopic approach using previously tested interatomic interaction potentials. The calculated energy of the main low-frequency peak is closer to its experimental value in comparison with previous calculations, which reduces the significant discordance between the experimental and theoretical spectra. The fine structure of the high-frequency part of the vibrational spectrum is discussed. A study of large-amplitude nonlinear vibrations (which determine the diffusion of atoms and dispersive processes in materials) showed that a specific nonlinear breather mode of vibration can be generated in the crystallites in question, which is a genetic precursor of nonlinear self-localized vibrations.

ESR Measurements at Ultra-Low Temperatures Using a Dilution Refrigerator

An ESR measurement system with a high sensitivity vector network analyzer has been developed for use at ultralow temperatures below 1 K. The microwave frequency can be varied between 45 GHz and 110 GHz. The resonant cavity was installed in a bottom of a 3 He- 4 He dilution refrigerator, which realizes the temperatures down to 160 mK. In order to avoid a heating of the cavity and sample by microwaves or heat leaks, attenuators and thermal anchors were placed at suitable positions. As the first experiment, the ESR was measured on a quantum spin chain Cu benzoate down to 160 mK, in which a field-induced gap was recently found. The evaluation of a new ESR mode, so called breather mode, was found at the lowest temperatures. In the previous ESR down to 0.5 K, this mode was clearly found for H||c, in which the magnitude of the gap is largest. In the present work, the achievement of low temperatures enabled us to observe a smaller gap in H||b by suppressing of the thermal excitation.

Exploration of a rich variety of breather modes in Josephson ladders.

We report on systematic measurements of localized rotational modes in Josephson junction arrays. These modes, also known as rotobreathers, persist under the action of uniform bias force. In contrast to previous experiments, here we focus on systems with strong coupling between rotators. In ladders with either open or periodic boundary conditions, we observe a very rich variety of stable dynamic states including symmetric, asymmetric, combined, hybrid, coupled, and truncated modes. The switching scenarios between different states are discussed in detail.

Interacting domain walls in an easy-plane ferromagnet

The Landau-Lifshitz equation for an anisotropic (easy-plane) ferromagnet is formulated as a Riemann-Hilbert problem on a Riemann surface of the spectral parameter. Exact multiple domain wall solutions can be obtained in a systematic and exhaustive manner by considering all possible pole arrangements on the Riemann surface. Explicit calculations for up to four poles have been carried out, yielding all possible double wall solutions, including states of colliding walls, breather modes of bound walls, and a set of solutions corresponding to marginally bound walls.

Electron spin resonance experiments at ultralow temperatures by means of a dilution refrigerator

An electron spin resonance (ESR) apparatus with a high sensitivity vector network analyzer has been developed for use at ultralow temperatures. The microwave frequency can be varied between 45 and 110 GHz. The resonant cavity was installed in a He3–4He dilution refrigerator which provides ultralow temperatures down to 160 mK. In order to avoid the heating of the cavity and the sample by microwaves or heat leaks in the cryostat, attenuators and thermal anchors were placed at the most suitable positions. As the first experiment, the ESR was measured for a quantum spin chain Cu benzoate. The breather mode, which is a new ESR mode caused by a field induced gap, has been clearly observed at the lowest temperatures.

Energy relaxation in nonlinear one-dimensional lattices.

We study energy relaxation in thermalized one-dimensional nonlinear arrays of the Fermi-Pasta-Ulam type. The ends of the thermalized systems are placed in contact with a zero-temperature reservoir via damping forces. Harmonic arrays relax by sequential phonon decay into the cold reservoir, the lower-frequency modes relaxing first. The relaxation pathway for purely anharmonic arrays involves the degradation of higher-energy nonlinear modes into lower-energy ones. The lowest-energy modes are absorbed by the cold reservoir, but a small amount of energy is persistently left behind in the array in the form of almost stationary low-frequency localized modes. Arrays with interactions that contain both a harmonic and an anharmonic contribution exhibit behavior that involves the interplay of phonon modes and breather modes. At long times relaxation is extremely slow due to the spontaneous appearance and persistence of energetic high-frequency stationary breathers. Breather behavior is further ascertained by explicitly injecting a localized excitation into the thermalized arrays and observing the relaxation behavior.

Electron Spin Resonance Study of Cu Benzoate Using a3He–4He Dilution Refrigerator

An electron spin resonance (ESR) measurement system for use at ultralow temperatures using a 3 He– 4 He dilution refrigerator has been developed. As the first experiment, the ESR was measured on a quantum spin chain Cu benzoate down to 160 mK, in which a field-induced gap was recently found. [rf_4] The evaluation of a new ESR mode, the so-called breather mode, was found at the lowest temperatures. In the previous ESR down to 0.5 K, this mode was clearly found for H ∥ c , in which the magnitude of the gap is largest. In the present work, the achievement of low temperatures enabled us to observe a smaller gap in H ∥ b by suppressing the thermal excitation. The magnitude of the field-induced gap evaluated from the nonlinear field dependence of the mode shows good agreement with that determined by previous specific heat measurements.

Dynamic model of base pair breathing in a DNA chain with a defect.

We model and analyze a short section of a DNA chain with a defect, with the aim of understanding how the frequency, amplitude, and localization of breathing events depend on the strength of the bonds between base pairs, both along the chain and between the chains. Our results show that the presence of a defect in the chain permits the existence of a localized breather mode. The models we analyze are linear and hence solvable, with solvability extending to the statistical mechanics formulation of the problem. Parameter values for the interaction energy of a base with its nearest neighbors are obtained from AMBER. The results indicate good agreement with both the amplitude and the number of base pairs affected by defect-induced breathing motion.

ESR investigation on the breather mode and the spinon-breather dynamical crossover in Cu benzoate.

A "breather excitation" is observed directly by electron spin resonance in the quantum spin chain Cu benzoate, in which an unexpected field-induced gap has recently been found. The nonlinear field dependence of the resonance field agrees well with the formula based on a quantum sine-Gordon model. The power-law temperature dependence of the linewidth is observed in the gapless spinon regime while the width decreases exponentially for the gapped breather regime. In the intermediate range, a distinct anomaly is found, which is the manifestation of "the spinon-breather dynamical crossover."

Metastability of breather modes of time-dependent potentials

We study the solutions of linear Schrödinger equations in which the potential energy is a periodic function of time and is sufficiently localized in space. We consider the potential to be close to one that is time periodic and yet explicitly solvable. A large family of such potentials has been constructed and the corresponding Schrödinger equation solved by Miller and Akhmediev. Exact bound states, or breather modes, exist in the unperturbed problem and are found to be generically metastable in the presence of small periodic perturbations. Thus, these states are long-lived but eventually decay. On a time scale of order -2, where is a measure of the perturbation size, the decay is exponential, with a rate of decay given by an analogue of Fermi's golden rule. For times of order -1 the breather modes are frequency shifted. This behaviour is derived first by classical multiple-scale expansions, and then in certain circumstances we are able to apply the rigorous theory developed by Soffer and Weinstein and extended by Kirr and Weinstein to justify the expansions and also provide longer-time asymptotics that indicate eventual dispersive decay of the bound states with behaviour that is algebraic in time. As an application, we use our techniques to study the frequency dependence of the guidance properties of certain optical waveguides. We supplement our results with numerical experiments.

Nonlinear dynamics of a DNA chain affected by endogenous AC fields

In this paper we investigate the nonlinear dynamics of a DNA chain in the presence of endogenous AC fields (EACF) generated by the living cell itself. The dynamics of the DNA chain is described in the framework of the nonlinear breather mode. The transition of breather localized modes into open states, affected by AC fields is calculated by using Kubo's formalism for the linear response of the system.

Inelastic-neutron-scattering study of the sine-Gordon breather interactions in isotopic mixtures of 4-methyl-pyridine

The inelastic-neutron-scattering spectrum of totally hydrogenated 4-methyl-pyridine $(4\mathrm{MP}{\ensuremath{-}h}_{7})$ at 0.5 K reveals three bands whose widths are limited to the resolution function of the spectrometer: 9 \ensuremath{\mu}eV. Within the quantum sine-Gordon theory, these bands are assigned to in-phase (537 \ensuremath{\mu}eV) and out-of-phase (470 \ensuremath{\mu}eV) tunneling transitions and to the traveling transition of the breather mode (516 \ensuremath{\mu}eV). The spectra of isotopic mixtures with the totally deuterated analogue $(4\mathrm{MP}{\ensuremath{-}d}_{7}),$ containing 85%, 65%, and 50% of $4\mathrm{MP}{\ensuremath{-}h}_{7},$ respectively, were obtained at 1.8 K with the same resolution. The frequency of the breather traveling state is progressively shifted downwards to 506 \ensuremath{\mu}eV. The frequency shift is represented with the breather mode in clusters of hydrogenated molecules. Simultaneously, an additional band is observed between 490 and 497 \ensuremath{\mu}eV whose intensity is proportional to the amount of deuterated molecules. This band is attributed to the breather-mode interaction with isolated deuterated molecules. The breather wave form and the effective potential for the impurity are calculated. For the sample containing 50% of each isotopomer, new bands at 478 and 464 \ensuremath{\mu}eV are attributed to the breather mode in rather small hydrogenated clusters with deuterated clusters as reflective boundaries.

Frequency analysis of discrete breather modes using a continuous wavelet transform

Previous theoretical and numerical studies have shown the conditions for existence and stability properties of intrinsic localized modes (often refered to as discrete breathers) which exist in the gaps outside the linear dispersion bands in anharmonic lattices. We apply a continuous wavelet tranform to numerical simulations in order to verify some of the predicted frequency behaviour.