Results For Susceptibilities Research Articles

Analyzing coherent and incoherent optical susceptibilities in four-wave mixing: stochasticity, symmetry, and intramolecular coupling

The nonlinear optical susceptibilities are analyzed in their optical propagation length considering the incoherent-coherent contributions with the dependence on the relaxation times. In addition, some symmetry properties of the Four-Wave mixing (FWM) signal concerning the frequency detuning exchange are used in the study, without restricting ourselves to the maxima of population oscillations. We analyze the behaviors of these optical responses in a vibronic coupling scheme using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in position and nuclear energies. The solvent effect in our model is treated through the natural Bohr frequency shift to a time-dependent function, with explicit manifestations in its comparison as if the upper state were broadened. Our results for both FWM signal propagation and nonlinear optical susceptibilities are sensitive to the intramolecular coupling parameters, solvent stochasticity, and perturbation order for the treatment of the weak probe beam. The consideration of a second-order probe beam in FWM would not represent a significant contribution to the predicted results, since its percentage contribution is negligible within the model development framework; however, this contribution becomes important when increasing the ratio between longitudinal and transverse relaxation times.

Schwarzschild quasi-normal modes of non-minimally coupled vector fields

We study perturbations of massive and massless vector fields on a Schwarzschild black-hole background, including a non-minimal coupling between the vector field and the curvature. The coupling is given by the Horndeski vector-tensor operator, which we show to be unique, also when the field is massive, provided that the vector has a vanishing background value.We determine the quasi-normal mode spectrum of the vector field, focusing on the fundamental mode of monopolar and dipolar perturbations of both even and odd parity, as a function of the mass of the field and the coupling constant controlling the non-minimal interaction. In the massless case, we also provide results for the first two overtones, showing in particular that the isospectrality between even and odd modes is broken by the non-minimal gravitational coupling.We also consider solutions to the mode equations corresponding to quasi-bound states and static configurations. Our results for quasi-bound states provide strong evidence for the stability of the spectrum, indicating the impossibility of a vectorization mechanism within our set-up. For static solutions, we analytically and numerically derive results for the electromagnetic susceptibilities (the spin-1 analogs of the tidal Love numbers), which we show to be non-zero in the presence of the non-minimal coupling.

Domino cooling of a coupled mechanical-resonator chain via cold-damping feedback

We propose a domino-cooling method to realize simultaneous ground-state cooling of a coupled mechanical-resonator chain through an optomechanical cavity working in the unresolved-sideband regime. This domino-effect cooling is realized by combining the cold-damping feedback on the first mechanical resonator with nearest neighbor couplings between other neighboring mechanical resonators. We obtain analytical results for the effective susceptibilities, noise spectra, final mean phonon numbers, and cooling rates of these mechanical resonators, and find the optimal cooling condition for these resonators. In particular, we analyze a two-mechanical-resonator case and find that by appropriately engineering either the laser power or the feedback, a flexible switch between symmetric and asymmetric ground-state cooling can be achieved. This could be used for preparing symmetric quantum states in multimode mechanical systems. We also simulate the cooling performance of a coupled $N$-mechanical-resonator chain and confirm that these resonators can be simultaneously cooled to their quantum ground states in the unresolved-sideband regime. Under proper parameter conditions, the cooling of the mechanical-resonator chain shows a temperature gradient along the chain. This study opens a route to quantum manipulation of multiple mechanical resonators in the bad-cavity regime.

Boundary conformal field theory at the extraordinary transition: The layer susceptibility to O(\u03b5)

We present an analytic calculation of the layer (parallel) susceptibility at the extraordinary transition in a semi-infinite system with a flat boundary. Using the method of integral transforms put forward by McAvity and Osborn [Nucl. Phys. B455 (1995) 522] in the boundary CFT, we derive the coordinate-space representation of the mean-field propagator at the transition point. The simple algebraic structure of this function provides a practical possibility of higher-order calculations. Thus we calculate the explicit expression for the layer susceptibility at the extraordinary transition in the one-loop approximation. Our result is correct up to order O(ε) of the ε = 4 − d expansion and holds for arbitrary width of the layer and its position in the half-space. We discuss the general structure of our result and consider the limiting cases related to the boundary operator expansion and (bulk) operator product expansion. We compare our findings with previously known results and less complicated formulas in the case of the ordinary transition. We believe that analytic results for layer susceptibilities could be a good starting point for efficient calculations of two-point correlation functions. This possibility would be of great importance given the recent breakthrough in bulk and boundary conformal field theories in general dimensions.

Nonlinear optical studies and structure-activity relationship of chalcone derivatives with in silico insights

Nine chalcones were prepared via Claisen-Schmidt condensation, and characterized by UV–vis, IR, 1H NMR, 13C NMR and mass spectrometry. One of the representative member 4-NDM-TC has been studied via single crystal XRD and the TGA/DTA technique. SHG efficiency and NLO susceptibilities of the chalcones have been evaluated by the Kurtz and Perry method and Degenerate Four Wave Mixing techniques respectively. 3-Cl-4′-HC was noted to possess SHG efficiency 1.37 times that of urea while 4-NDM-TC returned the highest third order NLO susceptibilities with respect to CS2. In silico studies help evaluate various physical parameters, in correlating the observed activities. In conclusion, the structure-activity relationship was derived based on the in silico and experimental results for the third order NLO susceptibilities.

Effects of dielectric screening and position dependent effective mass on donor binding energies and on diamagnetic susceptibility in a quantum well

Abstract The binding energies of a shallow hydrogenic donor in the GaAs quantum well have been calculated using five different screening functions within the effective mass approximation. Both the infinite and finite confinements are used. Though all the screening functions yield results, which are nearly the same for all well dimensions studied, it is observed that the Resta dielectric function leads to smaller binding energies for well dimensions ≤100 A. The diamagnetic susceptibility of a hydrogenic donor has also been estimated and the results are in good agreement with the recently reported values. In addition, the position dependent effective masses are used for both confinements and the results for donor ionization energies and diamagnetic susceptibilities are shown to be appreciable for narrow well dimensions. Using the Resta dielectric function, pressure effects on donor ionization energies and diamagnetic susceptibilities are estimated for Q2D GaAs. It is found that while the ionization energies increase with pressure, | χ dia | decreases with pressure.

53-Year-Old Man With a Swollen Finger

53-Year-Old Man With a Swollen Finger

Susceptibilities and screening masses in two flavor QCD

We studied QCD with two flavors of dynamical staggered quarks at finite temperature, with a bare sea quark mass of about 17 MeV. We report investigations of baryon, isospin, charge and strangeness susceptibilities, as well as screening masses obtained from correlators of local and one-link separated meson operators. These were studied as functions of valence quark mass at several temperatures. Our results for susceptibilities deviate significantly from ideal gas values, and even more from the weak coupling series. We also report the first measurement of off-diagonal quark number susceptibilities below the transition temperature, Tc, where they are the main contribution to charge fluctuations. We present evidence for a close connection between the susceptibilities and the screening masses.

Nonlinear optical susceptibilities of fullerenes in the condensed phase

We present results for nonlinear optical susceptibilities of fullerenes, including C-60, C-70, and C-84, in the condensed phase from large-scale nb initio calculations using self-consistent reactio ...

Exact results for a linear chain of classical spins with Dzyaloshinski–Morya interaction

We calculate the exact partition function and two-spin correlation functions for the one-dimensional classical anisotropic antiferromagnetic Heisenberg model with antisymmetric Dzyaloshinski–Morya interaction. We present results for the magnetic susceptibilities and the shift in the EPR frequency.

Initial static susceptibilities of nonuniform and random Ising chains

Within the conventional framework of standard linear response theory we have derived exact results for the initial static susceptibilities of nonuniform spin- 1 2 Ising chains. The results obtained permit one to study regularly alternating-bond and random-bond Ising chains. The influence of several types of nonuniformity and disorder on the temperature dependence of the initial longitudinal and transverse static susceptibilities is discussed.

High-order nonlinear susceptibilities of helium

With the goal of providing critically evaluated atomic data for modeling high harmonic generation processes in noble gases, we present calculations of frequency-dependent nonlinear susceptibilities of the ground state of helium, within the framework of Rayleigh-Schr\"odinger perturbation theory at lowest applicable order. The nonrelativistic, infinite-nuclear-mass, atomic Hamiltonian is decomposed in terms of Hylleraas coordinates and spherical harmonics, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. The mixed Hylleraas and Frankowski basis functions are employed to represent accurately the ground-state and perturbed wave functions. We believe our results for nonlinear susceptibilities of helium are the most accurate (and in many cases, the only) available to date, and they are offered as benchmark data for design of future multiphoton experiments.

Fractional Exclusion Statistics for thet-JModel with Long Range Exchange and Hopping

We construct thermodynamics of the one-dimensional supersymmetric t-J model with the 1/sin 2 interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component t-J model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.

Spin waves and static susceptibility in the weakly doped t‐J model

AbstractWe investigate the spin dynamics in weakly doped high‐temperature superconductors. The system is described by the two‐dimensional t‐J model. Our focus is on the interaction between mobile holes and spin waves. The calculations are based on a recently introduced cumulant method for computing the ground state energy of correlated electronic systems. Contrary to previous works using dynamical quantities like correlation functions or spectral densities our approach contains a static view to the system. This new method treats spin and hole dynamics on the same basis and allows for the calculation of static and dynamical quantities. We present results for spin‐wave energies and transverse static susceptibilities for small hole concentrations and various values of t/J. We find a strong renor‐malization of the spin‐wave energies due to the spin‐hole interaction. In agreement with neutron scattering experiments the spin‐wave velocity vanishes at a critical hole density of a few percent which is equivalent to the instability of the antiferromagnetic order.

Local mean field study of two-sublattice frustrated Ising systems

One- and two-sublattice frustrated Ising systems are studied by the local mean field method. Our results for linear and nonlinear susceptibilities suggest that the reentrancy phenomenon is absent in these systems. A decrease of the irreversibility temperature with the field in the magnetically ordered phases of the two-sublattice system is found to be weaker than in the one-sublattice case. The field-cooled susceptibility of a spin glass is influenced by the two-sublattice structure, but not as much as the mean field theory predicts. The intersublattice frustration is shown to decrease the compensation point in frustrated ferrimagnets whereas the intrasublattice frustration increases it.

Transient changes in polarizability for centrosymmetric linear molecules interacting at long range: Theory and numerical results for H2...H2, H2...N2, and N2...N2

Transient, collision-induced changes in polarizability Δα on the subpicosecond time scale affect Rayleigh and rototranslational Raman scattering by diatomic molecules in dense gases and liquids, induced birefringence, impulsive stimulated scattering, and dielectric and refractivity virial coefficients. For pairs of D∞h molecules, this work gives the long-range contributions to Δα complete through order R−6 in the intermolecular separation R, including the first- and second-order dipole–induced-dipole (DID) interactions, higher-multipole induction, effects of the nonuniformity in the local field, hyperpolarization, and dispersion. We have used spherical tensor methods to cast Δα into the symmetry-adapted form needed for spectroscopic line shape analysis. The polarization mechanisms included here give rise to isotropic rototranslational Raman scattering and to simultaneous rotational transitions on two interacting molecules; both are collision-induced phenomena. Transitions with ΔJ up to ±4 are produced by the R−5 and R−6 polarization mechanisms treated in this work (and the isotropic part of the pair potential). For the pairs H2...H2, H2...N2, and N2...N2, we have used ab initio results for permanent multipoles and susceptibilities to evaluate the classical induction contributions to Δα. For the dispersion contributions, we have derived exact results in the form of integrals of the polarizability and γ hyperpolarizability over imaginary frequencies, and we have approximated these numerically in terms of the static α and γ values, together with van der Waals energy coefficients. For the pairs and configurations studied, the first-order DID terms give the dominant contributions to Δα; the agreement between these terms and the full long-range results tends to be better for the anisotropic collision-induced polarizability ΔαM2 than for the isotropic part Δα00, particularly for T-shaped pairs. The relative contributions to Δα from the other polarization mechanisms reach as high as 29% for second-order DID terms, 27% for E-tensor terms (higher-multipole induction and local field nonuniformity), 21% for dispersion, and 8% for hyperpolarization effects, for R values ∼0.5–1.0 a.u. outside the isotropic van der Waals minimum.

Quantum Monte Carlo study of spin correlations in the one-dimensional Hubbard model.

The one-dimensional Hubbard model is studied at and close to half-filling using a generalization of Handscomb's quantum Monte Carlo method. Results for spin-correlation functions and susceptibilities are presented for systems of up to 128 sites. The spin-correlation function at low temperature is well described by a recently introduced formula relating the correlation function of a finite periodic system to the corresponding T=0 correlation function of the infinite system. For the T\ensuremath{\rightarrow}0 divergence of the q=2${\mathit{k}}_{\mathit{F}}$ spin susceptibility, our results are consistent with the form \ensuremath{\chi}(2${\mathit{k}}_{\mathit{F}}$)\ensuremath{\sim}\ensuremath{\Vert}ln(T)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\sigma}}}$${\mathit{T}}_{\mathrm{\ensuremath{\rho}}}^{\mathit{K}}$-1, with \ensuremath{\sigma}=1/2.

Theory of the magnetization and exchange-enhanced susceptibility of alloys. I. Zero-temperature susceptibility of paramagnetic alloys in the random-phase approximation.

A new theoretical treatment of the magnetic susceptibility of substitutionally disordered alloys is presented. This treatment goes beyond the existing treatments of the susceptibility of alloys in several important respects, although in the present paper (I of this series) it is confined to zero temperature and the random-phase approximation (RPA). Unlike treatments based on the single-site approximation, it yields results for the exchange-enhanced local susceptibilities ${\ensuremath{\chi}}_{\mathrm{ij}}$(\ensuremath{\omega}) as a function of the local environment of sites i and j. Specifically, it includes the strong effects of the nonlinearity of the dependence of the ${\ensuremath{\chi}}_{\mathrm{ij}}$(\ensuremath{\omega}) on local environments and the effects of short-range order on the uniform susceptibility \ensuremath{\chi}(0,\ensuremath{\omega}). This treatment goes beyond all previous cluster treatments of the susceptibility by treating exactly the embedding of a cluster in a given effective medium. Even more important, it is the first cluster theory to include exchange-enhancement effects in the embedding medium. Disorder in the exchange enhancement and in the local band susceptibility are treated on an equal footing. Finally, the formal connection between alloy band theory and the random-phase-approximation theory of alloy susceptibilities is elucidated. In particular, the problem of choosing the best self-consistency condition for the determination of the susceptibility \ensuremath{\chi}\ifmmode\bar\else\textasciimacron\fi{}(q,\ensuremath{\omega}) of the effective medium is considered in detail in light of the known results of alloy band theory. In the following two papers of this series, the theory presented here is extended to treat the local magnetization of alloys and the susceptibility in the presence of moments, and to include the effects of quantum and thermal spin fluctuations in a manner consistent with the results of renormalization-group theory.

Absorption spectroscopy of strongly perturbed bound-continuum transitions.

Absorption properties of a system consisting of two autoionizing states coupled strongly either by internal interactions or by external fields are investigated. The autoionizing states may themselves correspond to those induced by laser fields as in resonant multiphoton ionization. The analysis is based on the density matrices and incoherent processes like spontaneous emission and radiative recombination are included. Optical susceptibilities exist in a number of special cases for autoionizing transitions. Exact results for such optical susceptibilities are obtained. Explicit numerical results for susceptibilities, corresponding traditionally to strong-field inverse Raman effect, are given with a view to recent work on dc-field-coupled autoionizing states and on laser-induced autoionization. The behavior of both absorptive and dispersive parts is discussed for a range of parameters.

Multiphoton processes in two-level atoms in two intense pump beams

The dynamical behavior of a two-level atom under the influence of two intense pump beams is examined. Exact equations for the nonlinear susceptibilities to all orders in the field strengths are derived. Numerical results for the nonlinear susceptibilities giving the absorption of the radiation from either of the pump beams and the generation of the four-wave mixing signal are given. The susceptibility for four-wave mixing, in addition to showing various saturation peaks, shows a peak at ω1 = ω2 even in the case of radiative relaxation. Higher-order multiphoton peaks in the absorption spectra are found to be extremely sensitive to the temporal fluctuations in the pumps.