Quantum-statistical mechanics of non-linear excitations in the one-dimensional antiferromagnet

We study the quantum-statistical mechanics, at low temperatures, of a one-dimensional antiferromagnetic Heisenberg model with two anisotropies. In the weak-coupling limit, the temperature dependences of the soliton energy, and the soliton density are determined. At temperaturesT<m ₁ c (wherem ₁ c is the energy of the lowest energy magnon) the soliton density agrees with the classical statistical-mechanics results if the soliton energy in the classical theory is replaced by the renormalized one of the present theory.     

Lattice vibrations as particle hole excitations

Lattice vibrations are treated in analogy to excitons in the electron system. In zeroth order the lattice is described by a system of uncoupled oscillators. The two particle interaction is taken into account in the random phase approximation. No power expansion of the potential is needed and the Pauli principle can be fulfilled at each step. Neglecting exchange terms the resulting secular equation is identical with the one inBorn's lattice theory.     

Interplay of low-energy phonons and magnetic excitations in the Kondo insulator YbB12

Peculiarities in the lattice dynamics of the Kondo insulator Y bB(12) have been studied by inelastic neutron scattering. Selected phonon modes were traced above and below the temperature region (T ~ 50 K) where the gap opens in the electron density of states. The intensities of some low-energy modes exhibit an anomalous temperature dependence for q vectors close to the Brillouin zone boundary, suggesting a renormalization of the phonon eigenvectors. This effect is thought to arise from a coupling with magnetic excitations of the same symmetry, which exist at nearby energies. It is argued that this magnetovibrational coupling may in turn play a role in the steep temperature crossover existing in Y bB(12) between the low-temperature (Kondo insulator) and high-temperature (incoherent spin-fluctuation) regimes, which is rapidly suppressed by lighter Zr substitution.     

A non-linear analysis of the interactions between parametric and external excitations

Solutions of a non-linear equation having a form often encountered in the study of structural dynamics and in which both parametric and external excitation is present have been obtained analytically and numerically. All the asymptotic (analytical) results can be verified by numerical integration for small values of ϵ. Some other solutions, obtained numerically, cannot be approximated by conventional asymptotic methods. Both types of solutions can exist simultaneously; in these situations the initial conditions determine which solution describes the actual response of the system. The solutions that can be predicted only by numerical means exhibit period multiplications (i.e., the response has a period that is an integral multiple of the period of the excitation) and chaos. In fact, in a certain range of ϵ, one set of initial conditions can lead to period doubling in the response while another set can lead to a response very close to the asymptotic prediction. Very flexible structures can exhibit non-linear characteristics in their response at very small amplitudes of the excitation. The present results serve to illustrate some of the extraordinary behavior that such structures can exhibit and suggest that it may be extremely difficult to develop control systems for them.     

Nuclear spin-lattice relaxation due to non-linear excitations in magnetic chains

A simple classical model for nuclear spin-lattice relaxation due to solitons in XY one-dimensional magnetic chains in an external magnetic field is discussed. The results show that one should expect opposite behavior for the H/T dependence of T^-1₁ for the ferromagnetic and the antiferromagnetic case.     

Response of a strongly non-linear oscillator to narrowband random excitations

The principal resonance of a van der Pol-Duffing oscillator subject to narrowband random excitations has been studied. By introducing a new expansion parameter the method of multiple scales is adapted for the strongly non-linear system. The behavior of steady state responses, together with their stability, and the effects of system damping and the detuning, and magnitude of the random excitation on steady state responses are analyzed in detail. Theoretical analyses are verified by some numerical results. It is found that when the random noise intensity increases, the steady state solution may change form a limit cycle to a diffused limit cycle, and the system may have two different stable steady state solutions for the same excitation under certain conditions. The results obtained for the strongly non-linear oscillator complement previous results in the literature for weakly non-linear systems.     

Raman scattering from phonons and electronic excitations in UO2 with different oxygen isotopes

Comparison of the phonons and electronic excitations of UO₂ with different oxygen isotopes (¹⁶O, ¹⁸O), two purely electronic excitations at 4162 and 5778 cm⁻¹ have been evidenced by their limited shift, when ¹⁶O is replaced by ¹⁸O. The bands observed at 570, 1144 and 2300 cm⁻¹ in U¹⁶O₂ shift to 545, 1091 and 2190 cm⁻¹ for U¹⁸O₂. The wavenumbers and the isotope shifts of these bands exhibit multiple relationships. It supports the assignments of the 1LO (~570 cm⁻¹) and 2LO (~1144 cm⁻¹) phonons for U¹⁶O₂. Both bands exhibit marked decrease for increasing O/U ratio. The observed phenomenon is regarded as a good estimation of the stoichiometry of a uranium oxide. In addition, by analyzing the intensity ratios of the 2LO to 1LO phonons for various UO₂ samples, the 2LO band is assigned to the Fröhlich interaction. Defect‐induced and/or deformation potential mechanisms play a dominant role for the 1LO band. Copyright © 2015 John Wiley & Sons, Ltd.     

Fractionally charged excitations in the charge density wave state of a quarter-filled t-J chain with quantum phonons

Elementary excitations of the 4k _F charge density wave state of a quarter-filled strongly correlated electronic one-dimensional chain are investigated in the presence of dispersionless quantum optical phonons using Density Matrix Renormalization Group techniques. Such excitations are shown to be topological solitons carrying charge e/2 and spin zero. Relevance to the 4k _F charge density wave instability in (DI - DCNQI)₂ A g or recently discovered in (TMTTF)₂X ( X=PF ₆, AsF₆) is discussed. Received 30 March 2001 and Received in final form 11 May 2001     

Resonant coupling of optical phonons to J-multiplet excitations in intermediate valent Sm0.75Y0.25S

An anomalous splitting of theJ=0J=1 multiplet transition has been observed by magnetic neutron scattering from intermediate valent Sm_0.75Y_0.25S. The splitting is discussed in terms of a resonant coupling of optical phonons to the magnetic exciton built from the localizedJ=0J=1 multiplet transition by magnetic intersite coupling.