Bilinear Coupling Terms Research Articles

Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator

Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle number. We determine the eigenvalues and eigenvectors, and expose the appearance of exceptional points where two of the eigenstates coalesce with the corresponding eigenvectors exhibiting self-orthogonality with respect to the bi-orthogonal inner product. The model admits a quantum phase transition—we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump indicating the transition between the two phases.

Hyper-Rayleigh Scattering and Third-Harmonic Scattering in Chiral Liquids: Basic Evidences and Differences with Linear Chiroptical Techniques.

Nonlinear chiroptical methods like hyper-Rayleigh optical activity (HROA) and third-harmonic optical activity (THOA) have a great potential in characterizing structure-chiroptical properties of molecular systems. Here, with these methods, we bring for the first time experimental and theoretical evidence of nonlinear chiroptical differences between enantiomers of simple chiral molecules, using exclusively linearly polarized incident light. The origin of these unexpected nonlinear chiroptical contributions comes from a new nonlinear source term of the form βOA(∇×μ(nω)), which is a bilinear coupling term including the linear chirality parameter, βOA, and the curl of the nonlinear induced electric dipole moment, μ(nω), both involving dipolar magnetic interactions. Through a simple nonlinear chiroptical model that we propose, we show that specific nonlinear chiroptical parameters can be quantified, thus bringing new insights into stereochemical and electronic structural features of molecular and supramolecular systems.

De Broglie-Bohm analysis of a nonlinear membrane: From quantum to classical chaos.

Within the de Broglie-Bohm theory, we numerically study a generic two-dimensional anharmonic oscillator including cubic and quartic interactions in addition to a bilinear coupling term. Our analysis of the quantum velocity fields and trajectories reveals the emergence of dynamical vortices. In their vicinity, fingerprints of chaotic behavior such as unpredictability and sensitivity to initial conditions are detected. The simultaneous presence of the off-diagonal -kxy and nonlinear terms leads to robust quantum chaos very analogous to its classical version.

Dynamic nuclear polarization pulse sequence engineering using single-spin vector effective Hamiltonians.

Dynamic nuclear polarization (DNP) has proven to be a powerful technique to enhance nuclear spin polarization by transferring the much higher electron spin polarization to nuclear spins prior to detection. While major attention has been devoted to high-field applications with continuous microwave irradiation, the introduction of fast arbitrary waveform generators is gradually increasing opportunities for the realization of pulsed DNP. Here, we describe how static-powder DNP pulse sequences may systematically be designed using single-spin vector effective Hamiltonian theory. Particular attention is devoted to the intricate interplay between two important parts of the effective first-order Hamiltonian, namely, linear field (single-spin) terms and Fourier coefficients determining scaling of the bilinear coupling terms mediating polarization transfer. We address two cases. The first case operates in the regime, where the microwave field amplitude is lower than the nuclear Larmor frequency. Here, we illustrate the predictive strength of a single-spin vector model by comparing analytical calculations with experimental DNP results at 9.8 GHz/15 MHz on trityl radicals at 80 K. The second case operates in the high-power regime, where we combine the underlying single-spin vector design principles with numerical non-linear optimization to optimize the balance between the linear terms and the bilinear Fourier coefficients in a figure of merit function. We demonstrate, numerically and experimentally, a broadband DNP pulse sequence PLATO (PoLarizAtion Transfer via non-linear Optimization) with a bandwidth of 80 MHz and optimized for a microwave field with a maximum (peak) amplitude of 32 MHz.

Quantum States in Templated Biological Processes

Living matter is characterized by its variegated potential energy landscape possessing a proneness to continually absorb externally supplied energy. This enables it to ascend from its momentary energy minimum state to one of its myriad barriers only to subsequently descend to a new minimum with a potentiality to perform new functions or processes, in the while exuding energy (mainly in the form of heat). As in studies of molecular intersystem crossing, the jumping processes are describable in terms of quantum states. In this work we derive the low energy quantum states for those three templated self-assembling processes, self-replication, metabolism and self-repair that are commonly regarded as distinguishing animate from inanimate substance. The outcome of each process is a new, long-living, stable molecular aggregate characterized by its specific conformation, comprising a host of micro-states associated with sub-conformations and patterned upon the template. The provenance of these newly-formed states is obtained here by a unified formalism for all three processes, based on a Hamiltonian, constructed in an abstract Hilbert-space framework, whose essences are bilinear coupling terms in the Hamiltonian between the template and the bath, as well as between the reactants and the bath. Treating these terms by second order perturbation, one finds in low lying quantum states an alignment between the template and the product, somewhat analogous to the Kramers-Anderson superexchange mechanism, with the bath replacing the bridging anion and by exploitation of the decohering due to the randomness of the bath. The idea underlying this work, recurrent in the biological literature and here expressed in a Physics, Hamiltonian framework, is the correlative unity of the whole biological system comprising multiple organs.

Finite temperature effects in quantum systems with competing scalar orders

The study of the competition or coexistence of different ground states in many-body systems is an exciting and actual topic of research, both experimentally and theoretically. Quantum fluctuations of a given phase can suppress or enhance another phase depending on the nature of the coupling between the order parameters, their dynamics and the dimensionality of the system. The zero temperature phase diagrams of systems with competing scalar order parameters with quartic and bilinear coupling terms have been previously studied for the cases of a zero temperature bicritical point and of coexisting orders. In this work, we apply the Matsubara summation technique from finite temperature quantum field theory to introduce the effects of thermal fluctuations on the effective potential of these systems. This is essential to make contact with experiments. We consider two and three-dimensional materials characterized by a Lorentz invariant quantum critical theory, i.e., with dynamic critical exponent z = 1, such that time and space scale in the same way. We obtain that in both cases, thermal fluctuations lead to weak first-order temperature phase transitions, at which coexisting phases arising from quantum corrections become unstable. We show that above this critical temperature (Tc), the system presents scaling behavior consistent with that approaching a quantum critical point. Below the transition the specific heat has a thermally activated contribution with a gap related to the size of the domains of the ordered phases. We obtain that Tc decreases as a function of the distance to the zero temperature classical bicritical point (ZTCBP) in the coexistence region, implying that in our approach, the system attains the highest Tc above the fine tuned value of this ZTCBP.

Gravitational waves from nonlinear couplings of radial and polar nonradial modes in relativistic stars

The postbounce oscillations of newly-born relativistic stars are expected to lead to gravitational-wave emission through the excitation of nonradial oscillation modes. At the same time, the star is oscillating in its radial modes, with a central density variation that can reach several percent. Nonlinear couplings between radial oscillations and polar nonradial modes lead to the appearance of combination frequencies (sums and differences of the linear mode frequencies). We study such combination frequencies using a gauge-invariant perturbative formalism, which includes bilinear coupling terms between different oscillation modes. For typical values of the energy stored in each mode we find that gravitational waves emitted at combination frequencies could become detectable in galactic core-collapse supernovae with advanced interferometric or wideband resonant detectors.

Determination of the Landau potential of chiral enantiomer ferroelectric liquid crystal mixtures.

The full Landau potential was determined for mixtures of the two chiral configurations of ferroelectric liquid crystal enantiomers. Experimental temperature and electric field dependent tilt and polarisation data are analysed a multi-curve fitting procedure to determine all the parameters of the generalised Landau model for ferroelectric liquid crystals. The three Landau coefficients , and as well as the bilinear coupling, , biquadratic coupling, and dielectric susceptibility, , were obtained as a function of enantiomeric excess. The chirality dependent bilinear coupling term vanishes as the chirality of the system tends to zero on approaching the racemic mixture. All other terms remain constant within the limits of error, providing experimental evidence that the bilinear coupling term is the only chirality dependent term of the generalised Landau model.

Slow electron velocity-map imaging photoelectron spectra of the methoxide anion

High resolution anion photodetachment spectra are presented for the methoxide anion and its fully deuterated counterpart. The spectra were obtained with slow electron velocity-map imaging. Improved electron affinities are determined for CH3O as 1.5690+/-0.0019 eV and for CD3O as 1.5546+/-0.0019 eV. The spectra resolve many features associated with spin-orbit and vibronic coupling that were not seen in previous photodetachment studies. Photoelectron angular distributions taken as a function of detachment wavelength for the ground vibronic state transitions are recorded and are consistent with the removal of a nonbonding, p-type electron localized on the oxygen atom. Several hot bands and sequence bands are observed for the first time, providing insight into the vibrational structure of the methoxide anion. The results are compared to recent calculations of the anion photoelectron spectra that incorporate bilinear coupling terms among the methoxy vibrational modes and are found to be in reasonable agreement.

Quantitative experimental determination of the Landau-potential of chiral enantiomer doped ferroelectric liquid crystals

The full Landau potential was determined for a ferroelectric liquid crystal doped with varying concentrations of the chiral dopant R1011 and its enantiomer S1011. A multi-curve fitting procedure using temperature and electric field dependent tilt angle and polarization data was employed to the generalized Landau model of ferroelectric liquid crystals. From this analysis the three Landau coefficients as well as the polarization-tilt coupling parameters were obtained as a function of dopant concentration and configuration. It is shown that the two most varied parameters are those of the first Landau coefficient alpha and the (chiral) linear polarization-tilt coupling constant C. The effect on the first Landau term is equivalent for the two dopants of opposite handedness indicating its achiral nature, while the effect on the (chiral) bilinear coupling term differs for the R1011 and S1011 dopant, increasing and decreasing the coupling between tilt and polarization respectively. This difference in the bilinear coupling term quantifiably evidences that the R1011 dopant increases and S1011 dopant reduces the inherent chirality in this system.

Bilinear Jahn–Teller coupling effects in the methoxy radical: impact on photoelectron spectra and spin–orbit splittings

A previous theoretical investigation of the multimode dynamical Jahn–Teller effect in the methoxy radical is extended to calculate the vibrational structure of the first bands of the photoelectron spectra of CH 3O − and CD 3O − and to include the effects of spin–orbit coupling. Bilinear coupling terms between the e and a 1 vibrational modes are shown to be of major importance for the spectral intensities; they also lead to a marked dependence of the spin–orbit splittings on the quantum numbers of the a 1 modes in the electronic ground state of the radical.

Temperature-dependent biquadratic coupling in antiferromagnetically coupled Fe/FeSi multilayers.

Fe/FeSi multilayers are known to exhibit a strong antiferromagnetic interlayer coupling peak centered at a nominal FeSi spacer thickness of \ensuremath{\sim}15\ifmmode\pm\else\textpm\fi{}2 \AA{} at room temperature, and to develop remanence in the magnetic hysteresis loop upon cooling to \ensuremath{\sim}100 K. An analysis of the hysteresis loops is found to require the inclusion of a temperature-dependent biquadratic (90\ifmmode^\circ\else\textdegree\fi{} coupling) in addition to the bilinear coupling term in the energetics. The temperature dependence of the Fe/FeSi multilayer coupling can then be understood in terms that are applicable to conventional metallic multilayer systems such as Fe/Cr.

Orthogonally spin-adapted multi-reference Hilbert space coupled-cluster formalism: diagrammatic formulation

The problem of spin-adaptation of the multi-reference (MR) coupled-cluster (CC) formalism, employing Jeziorski-Monkhorst ansatz, is addressed. The diagrammatic technique based on graphical methods of spin algebras is generalized to the MR case, so that both direct and coupling terms can be determined. Usefulness of this fully diagrammatic spin-adaptation approach is illustrated on a derivation of explicit expressions for the linear and bilinear coupling terms that are required in the special two-reference MR-CC theory involving singly and doubly excited states (MR-CCSD formalism). Results obtained with the diagrammatic approach are compared with those derived earlier using the algebraic technique and relative advantages of both procedures are compared.

Impact of totally symmetric vibrations on the e⊗e Jahn-Teller effect

The influence of totally symmetric modes on the E⊗e Jahn-Teller effect is investigated. Within a model Hamiltonian containing up to second-order terms in the nuclear displacements the relevant interaction is provided by a bilinear vibronic coupling term, involving both the coordinates of a degenerate (e) and a totally symmetric (a 1) vibration. Concerning the adiabatic potential energy surfaces this leads to an effective frequency in the equations for the stationary points, and to the appearance of an additional manifold of conical intersections between the upper and lower surfaces. Dynamical calculations on the vibronic structure of an E←A electronic transition have been performed for selected values of the parameters. If the frequencies of the e and the a 1 mode are sufficiently different, the results can be well understood within a vibrationally adiabatic picture whereby the eigen-values of the faster mode act as additional potential of the slower motion. The importance of the bilinear coupling term is estimated by an analysis of the ground state potential energy surface of the sodium trimer.

Vibronic model leading to orthorhombic Jahn-Teller distortions

The eigenvalue problem for the dynamic Jahn-Teller system of an orbital triplet in cubic symmetry coupled to $e$ and ${t}_{2}$ vibrational modes has been solved numerically with the simultaneous inclusion of both the linear and quadratic coupling terms. The possibility of orthorhombic Jahn-Teller distortion has been found from the appearance of a nearly-sixfold-degenerate (${T}_{1}+{T}_{2}$) ground state in the case when an $E$-type quadratic coupling term or a bilinear coupling term has been considered. The computed result of Ham's reduction factors in the ground state shows the orthorhombic property.

On the phase transition in benzil

The phase transition in crystalline benzil [(C6H5CO)2] at 84 K is investigated through Brillouin scattering. The major experimental findings are two transverse acoustic phonon modes exhibiting softening near the phase transition, a longitudinal acoustic mode that is temperature sensitive, and the ratio of the Rayleigh peak intensity to the soft mode intensity behaves anomalously. These results are discussed using a theory developed for an elastic phase transition in sym-triazine (C3N3H3). It is found that bilinear-coupling terms involving strains and the order parameter can explain transverse mode behavior but not that of the longitudinal acoustic mode.

Metal pair spectra and exchange coupling parameters of di-μ-hydroxo-bis [tetraamine chromium (III)] bromide

The absorption, luminescence, and far i.r. spectra of the title compound have been recorded at various temperatures. A computer-assisted assignment of all peaks measured in the vibronic spectra has been carried out using an energy level scheme for the exchange coupled 4 A 2 g 4 A 2 g and 4 A 2 g 2 E g manifolds, calculated from a model considering only bilinear coupling terms in the excited states. Optimal agreement with the experiment is obtained if the energy levels are calculated from the exchange coupling parameters (in cm −1) J = 30, j = −0.3 for the ground state, J 11 = 0, J 12 = 125, J 13 = −48, J 33 = 186 for the excited state manifold, from the low symmetry ligand field parameter V = 46, and an energy gap of Δ E = 14 445. The importance of vibronically induced transitions in the assignment of band peaks is emphasized: frequencies due to this transition mechanism are obtained by comparison with the i.r. spectrum and with the electronic transition energies calculated from the model.

On the phase transition in alkali cyanides

The phase transition in alkali cyanides is studied starting from a Hamiltonian containing a bilinear coupling term between translational and rotational degrees of freedom, thus leading to an effective rotational interaction. It is shown that the problem can be reformulated in terms of elasticity theory and the effective rotational interaction then becomes an interaction between elastic dipoles. It is demonstrated that the phase transition is of first order. The long range nature of the elastic dipole forces which would lead to a shape dependence of the system for monodomain samples is responsible for the breakup of the ordered phase into domains.