Photonic spectral density of coupled optical cavities

We study a pair of anharmonic optical cavities that is connected by an optical fiber. The photonic spectral density characterizes the evolution of the coupled cavities after the system has been prepared in a Fock or N00N state. We evaluate the photonic spectral density within the recursive projection method and find that the anharmonicity leads to a collapse of the low-energy spectrum. The level spacing of the remaining spectrum agrees quite well with that of the harmonic cavities, whereas the spectral weights are strongly affected by the anharmonicity.     

Computer Simulation Study of Thermal Conduction in 1D Chains of Anharmonic Oscillators

In this work thermal conduction in one-dimensional(1D) chains of anharmonic oscillators are studied using computer simulation.The temperature profile,heat flux and thermal conductivity are investigated for chain length N = 100,200,400,800 and 1600.In the computer simulation anharmonicity is introduced due to Fermi-Pasta-Ulam-β(FPU-β) model.For substrate interaction,an onsite potential due to Frenkel-Kontorova(FK) model has been used.Numerical simulations demonstrate that temperature gradient scales behave as N-1 linearly with the relation J = 0.1765/N.For the thermal conductivity K,KN to N obey the linear relation of the type KN = 0.8805N.It is shown that thermal transport is dependent on phonon-phonon interaction as well as phonon-lattice interaction.The thermal conductivity increases linearly with increase inanharmonicity and predicts relation κ = 0.133 + 0.804β.It is also concluded that for higher value of the strength of the onsite potential system tends to a thermal insulator.     

Dynamics of a three level atom interacting with a detuned SU (1,1) quantum system

We study the stability of attractive atomic Bose-Einstein condensate and the macroscopic quantum many-body tunneling (MQT) in the anharmonic trap. We utilize correlated two-body basis function which keeps all possible two-body correlations. The anharmonic parameter (λ) is slowly tuned from harmonic to anharmonic. For each choice of λ the many-body equation is solved adiabatically. The use of the van der Waals interaction gives realistic picture which substantially differs from the mean-field results. For weak anharmonicity, we observe that the attractive condensate gains stability with larger number of bosons compared to that in the pure harmonic trap. The transition from resonances to bound states with weak anharmonicity also differs significantly from the earlier study of [N. Moiseyev, L.D. Carr, B.A. Malomed, Y.B. Band, J. Phys. B 37, L193 (2004)]. We also study the tunneling of the metastable condensate very close to the critical number N _cr of collapse and observe that near collapse the MQT is the dominant decay mechanism compared to the two-body and three-body loss rate. We also observe the power law behavior in MQT near the critical point. The results for pure harmonic trap are in agreement with mean-field results. However, we fail to retrieve the power law behavior in anharmonic trap although MQT is still the dominant decay mechanism.     

Interaction of phonons with discrete breathers in one-dimensional chain with tunable type of anharmonicity

In this paper, we consider the interaction of small amplitude waves (phonons) with standing discrete breather (DB) in the one-dimensional chain of harmonically coupled particles interacting with the anharmonic one-site potential, which can be of hard-type or soft-type anharmonicity. The coefficients of phonon reflection and transmission are calculated numerically. It is found that for the case of hard-type anharmonicity (soft-type anharmonicity) DBs are more transparent for short-wavelength (long-wavelength) phonon waves, while they efficiently reflect long-wavelength (short-wavelength) phonons. In thermal equilibrium, when all phonons have equal energy density, it is found that for the same width of the transparency window, DB transmits less energy in the case of the hard-type anharmonicity. This is so because, in this case, DB reflects long-wavelength phonons, which have larger group velocity and hence greater contribution to the net energy flux through the DB. In this sense, DBs more efficiently suppress thermal conductivity in the chain with hard-type anharmonicity. Our results contribute to a better understanding of the role of discrete breathers in the heat flow in nonlinear chains.     

Effects of transverse perturbations on the motion of an edge dislocation

The influence of transverse perturbations on the motion of an edge dislocation is studied using the averaged Lagrangian of the Ritz-Whitham type. The dislocation is described by the Frenkel-Kontorova model with inclusion of elastic anharmonicity and lattice discreteness (acoustic dispersion). The quadratic anharmonicity and acoustic dispersion are shown to promote self-focusing of the dislocation and microcrack formation. Under certain conditions, cubic anharmonicity can stabilize transverse compression of the dislocation, which can bring about the development of “ crowdion droplets.”     

Evidence for intra-ionic anharmonicity in the Raman spectra of cubic ionic crystals

The importance of intra-ionic anharmonicity for Raman spectra in cubic ionic crystals is discussed. A calculation of the second order Raman spectra of of MgO assuming such an anharmonicity is presented and a satisfactory agreement with experiment is obtained.     

Hamiltonians with quartic anharmonicities: Comparison with EPR measurements in SrTiO3

Rigorous bounds have been found for Hamiltonians with quartic anharmonicity in the single particle potential. They reveal that EPR measurements in SrTiO₃ can only be explained by use of those Hamiltonians alone, when there exists a strong cubic anisotropy in the anharmonicity.     

On the effect of the cubic anharmonicity of the interatomic interaction on the low-temperature phase of a peierls system

The low-temperature phase of a Peierls system is studied theoretically taking into account the cubic anharmonicity of the interatomic interaction. It is shown that at a transition into the semiconductor phase a uniform deformation of the system occurs simultaneously with the atoms approaching one another in pairs. The cubic anharmonicity of the interatomic interaction (with a negative anharmonicity constant) produces a large increase in the band gap in the electronic spectrum and the order parameters—the reduced amplitude of the static phonon at the edge of the Brillouin zone and the relative uniform deformation of the atomic chain—of the metal-semiconductor phase transition. An interpretation of the experimental data on the metal-semiconductor phase transition in vanadium dioxide is given on the basis of the results obtained.     

Single-particle model for the frequency dependence of weak infrared absorption in crystals and molecules at T = 0 K

We obtain a simple expression for the infrared absorption coefficient α within the single-particle model at zero temperature. For potentials admitting harmonic approximation, α is found to decrease nearly exponentially with increasing frequency for small anharmonicity, with departures for larger anharmonicity. Potentials which do not admit harmonic approximation display a frequency dependence of the power-law variety. The present results in the quantum limit are similar to those obtained in the classical limit by Mills and Maradudin.     

Vibrational anharmonicity and the inversion potential function of NH3

The nonrigid bender formulation of the vibration-inversion-rotation Hamiltonian for an XY₃ pyramidal molecule (V. ?pirko, J. M. R. Stone, and D. Papou?ek, J. Mol. Spectrosc.60, 159 (1976)) is improved by allowing for anharmonicity in all the vibrations. To model the anharmonic potential function of an XY₃ molecule with a low barrier to inversion a Plíva-type empirical potential (J. Plíva, Collect. Czech. Chem. Commun.23, 777 (1958)) is used. A fitting procedure that involves the numerical integration of the effective inversion Schrödinger equation (the nonrigid bender equation) and diagonalization of some resonance matrices is used to determine the equilibrium structure and the anharmonic potential function of the ammonia molecule.     

High Resolution FTIR Study on NH(2)Cl Molecule: Inversion and Anharmonicity

The high-resolution FTIR absorption spectra of the NH(2)Cl molecule have been measured in the region 500-3600 cm(-1). The rotational structures of all the fundamental bands and a number of overtone and combination bands have been analyzed. Every rotational line of the observed bands except the NH(2) twisting and stretching fundamental bands splits into two components due to the amino inversion motion. The vibrational anharmonicity and the direction of the transition moments have been studied with the help of B3LYP/6-31++G(**) calculations. The amount of inversion splitting depends on the molecular rotation, and the J,K-dependence of the inversion splitting has been determined. Copyright 2001 Academic Press.     

Nonlinear Excitations in Hydrogen-Bonded Chains with Anharmonic Interatomic Interactions

We discuss the nonlinear excitations and the motion of a kink soliton pair in hydrogen-bonded chains with anharmonic interatomic interactions, based on a two-component soliton model, using a direct perturbation method. The expression for the asymmetric solutions of the kink soliton pair is found because of anharmonicity, and the energy, the momentum and the effective mass of a kink pair for cubic and quartic anharmonicity are calculated, which are in good agreement with the experimental data.     

Absence of Critical Points for a Class of Quantum Hierarchical Models

Hierarchical models of quantum anharmonic oscillators with a polynomial anharmonicity and interaction decaying as (distance)^-1-λ are considered. For a class of such models (including ϕ⁴-type anharmonicity ones), it is shown that the critical fluctuations of the position operator are absent, for all λ > 0 and all temperatures, provided the oscillators mass in less than some threshold value depending on the anharmonicity parameters. This result may be interpreted as a rigorous mathematical justification of physical arguments showing that quantum fluctuations can damp phase transitions. Received: 12 April 1996 / Accepted: 25 October 1996     

Relation between the Grüneisen constant and Poisson’s ratio of vitreous systems

The lattice Grüneisen constant is calculated for amorphous polymers and glasses by using the data on Poisson’s ratio. While the thermodynamic Grüneisen constant of vitreous polymers characterizes the anharmonicity averaged over intrachain and other vibration modes, the lattice Grüneisen constant describes the anharmonicity of interchain vibrations associated with intermolecular interaction. For alkali-silicate glasses, the lattice Grüneisen constant characterizes the anharmonicity of vibrations of the ionic sublattice, which is formed by alkali metal ions and nonbridge oxygen ions.     

Stability and Collective Excitation of Two-Dimensional BECs with Two- and Three-Body Interactions in an Anharmonic Trap

The stability and collective excitation of Bose-Einstein condensates with both two- and three-body interactions in a two-dimensional anhaxmonic trap （i.e., harmonic plus quartic trap） are investigated. By using the variational method, the influence of the three-body interaction and the anharmonicity on the stability axe discussed in detail. It is found that the anhaxmonicity of the trap and the three-body interaction have significant effect on the stability and collective excitations of the system.     

Role of weak transitions in multiphoton excitation of molecules by IR laser radiation

Simultaneous excitation of a considerable part of molecules from many rotational levels of the ground state to higher vibrational states by IR laser radiation can be explained by considering weak transitions in a rotational band structure as it is shown at the example of SF₆ molecule. Very accurate compensation of anharmonicity in relatively wide spectral interval at comparatively low intensity of laser radiation can be explained on this basis. The considered scheme can be applied to the molecules of various symmetry with arbitrary anharmonicity.     

Equations of state of crystals with strong sixth-order anharmonicity

In a nonsymmetrized approximation of a self-consistent field, the equations of state of densely packed crystals with strong anharmonicity of up to sixth order are considered. These equations include two coefficients which are implicit functions of two dimensionless combinations of the temperature and force parameters of second, fourth, and sixth order. The properties of these functions are investigated; their values are tabulated for broad ranges of variation of the arguments. In particular, it follows from these properties that, as the temperature is reduced, sixth-order anharmonicity is first switched off, and the equations pass over into the already studied equations of state of crystals with strong fourth-order anharmonicity, which is switched off at still lower temperature. The method of obtaining corrections to the given approximation is also considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 77–82, August, 1979.     

Change of decoherence scenario and appearance of localization due to reservoir anharmonicity

Although coupling to a super-Ohmic bosonic reservoir leads only to partial dephasing on short time scales, exponential decay of coherence appears in the Markovian limit (for long times) if anharmonicity of the reservoir is taken into account. This effect not only qualitatively changes the decoherence scenario but also leads to localization processes in which superpositions of spatially separated states dephase with a rate that depends on the distance between the localized states. As an example of the latter process, we study the decay of coherence of an electron state delocalized over two semiconductor quantum dots due to anharmonicity of phonon modes.