Spectrum Of Elementary Excitations Research Articles

Theory of the pseudogap in the elementary excitation spectrum of the normal phase of bilayer cuprates

Solutions of the integral equations for the pseudogap in the elementary excitation spectrum of current carriers in bilayer cuprates are found. In the general case, the pseudogap possesses s1id symmetry, where the s component is determined by the interaction of holes via the phonon field and the d component is due to the superexchange interaction of the copper spins and the Coulomb-repulsion screened holes. The s and d components exhibit different temperature dependences. This fact enabled us to explain the characteristic features of the temperature behavior of the normal-phase spin susceptibility of lightly doped cuprates, specifically, for the compound YBa 2Cu4O8 in the entire temperature interval T.Tc . The wave-number dependence of the pseudogap agrees with the photoemission data for Bi2Sr2CaCu2O81y .© 1997 American Institute of Physics. @S0021-3640~97!00520-3#

Elementary excitation spectrum of a trapped weakly interacting Bose-Einstein condensate

An analytic expression is presented for the elementary excitation spectrum of the Bose-Einstein condensate of a trapped boson system in the weakly interacting, low-density limit. Explicit analytic formulas for the elementary excitation spectrum are obtained for harmonic-oscillator traps. These formulas provide information about the behavior of the elementary excitation levels as a function of the number of atoms and their interaction strength for a given trap geometry. They also provide a low-density benchmark for results of fully numerical calculations.

Excitonic light-absorption and amplification bands in the presence of laser radiation

We examine the absorption and amplification bands of a weak probe signal in the presence of Bose-Einstein condensation of excitons that emerges in nonequilibrium conditions in the field of coherent laser radiation with a wave vector k0. We assume that the detuning \(\tilde \Delta \) from resonance between the energy ħω ex (k0)+L0 of the exciton level, which is shifted because of exciton-exciton interaction, and the laser photon energy ħω L , is generally nonzero. The elementary excitation spectrum consisting of the quasiexcitonic and quasienergy branches determines the optical properties of the system. When there is real induced Bose-Einstein condensation, at \(\tilde \Delta = 0\) the two branches touch, as they do in spontaneous Bose-Einstein condensation. In virtual induced Bose-Einstein condensation, when \(\tilde \Delta < 0\), instabilities emerge in the spectrum in certain regions of the k-space. These instabilities are caused by a real transformation of two laser photons into two extracondensate particles. Nonequilibrium extracondensate excitons strongly affect the absorption and amplification of the probe light signal. We show that light absorption is due to the quantum transition from the ground state of the crystal to the quasiexcitonic branch of the spectrum. On the other hand, amplification of the signal is caused by the transition from the quasienergy branch to the ground state of the crystal. The same transition can be explained by a real transformation of two laser photons into a vacuum photon of frequency ħcq and a crystal exciton with a wave vector 2k0−q. Finally, we show that the excitonic absorption and light-amplification bands are essentially anisotropic at \(\tilde \Delta \approx 0\) and depend on the orientation of the vectors q and k0.

DNA molecule as an elastic Heisenberg chain

A DNA molecule is simulated by an anisotropic elastic fiber which defines the configuration of the molecule central line and is supplemented with a chain of quantum two-level systems imitating hydrogen bonds between two polynucleotide chains in the DNA double helix. The system Hamiltonian consists of Kirchhoff’s classical elastic energy and the energy of a quantum anisotropic chain of “spins” 1/2. The two-level systems and macroscopic vector variables which determine the conformation of the central line are coupled by a classical vector field q, which is introduced to take into account the existence of two polynucleotide strands. Averaging over fast (microscopic) variables yields an effective potential U(q). In the approximation of weak coupling between the systems, the spectrum of elementary excitations and effective potential U(q) have been calculated in explicit form. The relation between elementary excitations in the “magnetic” subsystem and so-called breathing modes [C. Mandel, N. R. Kallenbach, and S. W. Englander, J. Mol. Biol. 135, 391 (1980); G. Manning, Biopolymers 22, 689 (1983)] corresponding to low-frequency excitations in DNA molecules is discussed.

Spectrum of Elementary Excitations of Mixed-Valence Molecular Crystals

The spectrum of elementary excitations of molecular crystals comprising mixed-valence d1–d2 clusters has been investigated. Depending on the number of phase transitions arising in the systems under consideration two types of temperature behaviour of the soft mode frequency are shown to be possible. An anomalous temperature dependence of the elastic modulus is predicted.

Static and dynamic properties of a two-dimensional charged Bose fluid

We investigate some static and dynamic properties of a two-dimensional charged Bose fluid interacting via ln (r) potential by using the self-consistent-field approximation of Singwi, Tosi, Land, and Sj\"olander. The static structure factor, the pair-correlation function, the energy spectrum of elementary excitations, and the static dielectric-response function are calculated over a wide density range (1\ensuremath{\leqslant}${\mathrm{r}}_{\mathrm{s}}$\ensuremath{\leqslant}10). Wherever available, the results for the structure factor are compared with the recent diffusion Monte Carlo calculation by Magro and Ceperley and a good agreement is found. A comparison is also made with the two-dimensional charged Bose fluid with 1/r interaction potential. It is noticed that the Bose fluid interacting with ln (r) potential becomes partially localized at ${\mathrm{r}}_{\mathrm{s}}$\ensuremath{\approx}10, which is closer to the Monte Carlo prediction of Wigner crystallization at ${\mathrm{r}}_{\mathrm{s}}$\ensuremath{\approx}12.

Convergent Expansions for Properties of the Heisenberg Model for CaV4 O9.

We have carried out a wide range of calculations for the $S=1/2$ Heisenberg model with nearest- and second-neighbor interactions on a two-dimensional lattice which describes the geometry of the vanadium ions in the spin-gap system CaV$_4$O$_9$. The methods used were convergent high-order perturbation expansions (``Ising'' and ``Plaquette'' expansions at $T=0$, as well as high-temperature expansions) for quantities such as the uniform susceptibility, sublattice magnetization, and triplet elementary excitation spectrum. Comparison with the data for CaV$_4$O$_9$ indicates that its magnetic properties are well described by nearest-neighbor exchange of about 200K in conjunction with second-neighbor exchange of about 100K.

Bose commutation rule approximation in the theory of spin systems and elementary excitation spectrum

AbstractThe Bose commutation rule approximation for spin operators has been examined using as a testing ground the 1D s = 1/2 generalized XY model. The conditions under which the dependence of the elementary excitation energy on quasi‐momentum is not changed after such an approximationhave been found.

Zero-temperature spin-wave spectrum of the critical two-layer S=1/2 antiferromagnet.

Series expansions about the interlayer dimer limit are calculated to eighth order in the intralayer coupling for the T=0 antiferromagnetic susceptibility and elementary excitation spectrum of the two-layer, S=1/2, square lattice Heisenberg antiferromagnet. Extrapolations of the susceptibility and the gap series yield an estimate of the critical interlayer/intralayer coupling ratio ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$=2.54\ifmmode\pm\else\textpm\fi{}0.02, in agreement with several previous numerical calculations. The spin-wave velocity at criticality is determined by an analysis of the excitation spectrum series: the result, \ensuremath{\Elzxh}c/${\mathit{J}}_{1}$a=1.89\ifmmode\pm\else\textpm\fi{}0.02, is very precise and consistent with other estimates based on numerical calculations at finite temperature. The critical spin-wave dispersion at general wave vectors is shown to deviate significantly from a uniformly renormalized mean-field spectrum. \textcopyright{} 1996 The American Physical Society.

Series expansions for excited states of quantum lattice models

We show that by means of connected-graph expansions one can effectively generate exact high-order series expansions which are informative of low-lying excited states for quantum many-body systems defined on a lattice. In particular, the Fourier series coefficients of elementary excitation spectra are directly obtained. The numerical calculations involved are straightforward extensions of those which have already been used to calculate series expansions for ground-state correlations and T = 0 susceptibilities in a wide variety of models.

Microscopic origins of superfluidity in confined geometries

LIQUID helium provides a convenient model system in which to study the effects of disorder on strongly interacting media such as superfluids1,2 and superconductors3. Confinement of liquid helium in porous glasses profoundly affects its behaviour, even to the extent of changing the universality class of the normal-to-superfluid phase transition1,4,5. Although the effects of disorder on macroscopic fluid properties (such as the superfluid fraction) have been studied extensively6–11, the microscopic processes underlying these effects have received much less attention. For example, little is known theoretically12 or experimentally13,14about the effects of disorder on the spectrum of elementary superfluid excitations, which reflects the dynamics of the system on a microscopic scale. Here we report inelastic neutron scattering measurements of the collective excitation spectrum for 4He confined in porous aerogel glass. Near the superfluid transition temperature, the behaviour of the superfluid phase is governed by rotons (elementary excitations that are often compared to microscopic vortex rings), which we find to exhibit an increased effective mass and a decreased lifetime in the disordered system, relative to the unconfined supefluid. No theoretical predictions for these changes exist, and their origin is unclear; nevertheless, the disorder-induced changes in the microscopic collective excitation spectrum account fully for the observed changes in macroscopic fluid behaviour.

Variational density matrix approach to the temperature-dependent elementary excitation spectrum of two-dimensional liquid4He

Using the variational density matrix method, we obtain a temperature-dependent elementary excitation spectrum for two-dimensional liquid4He. For more precise results, we use a Jastrow-Feenberg-type trial wave function and include the contribution of elementary diagrams within the hypernetted chain approximation. The behavior of the excitation spectrum as a function of the temperature and density in two dimensions is similar to that of the bulk system, but has a smaller roton minimum. The roton minimum of the excitation spectrum decreases with increasing temperature and increases with increasing density at low densities but decreases at large densities. The results agree well with Monte Carlo calculations and are closer than pevious theories to experimental measurements of4He film adsorbed on substrates.

Strong-coupling theory for the thermodynamics of spin-1 planar magnetic chains.

Earlier work on the $T=0$ dynamics of spin-1 chains with a strong easy-plane anisotropy is extended to include thermodynamics. Thus we carry out a systematic strong-coupling expansion to obtain analytical approximations for the spectrum of elementary excitations, the specific heat, and the magnetic susceptibility. Comparison with numerical data for the specific heat available in some important special cases indicates that our result is accurate for practically the entire temperature range. Similarly our calculation of the magnetic susceptibility reproduces to leading order a result obtained earlier through a molecular-field approximation and provides a definite improvement by including the two-loop correction. These theoretical predictions are directly relevant for a number of magnetic materials of current experimental interest.

Temperature variation of the elementary excitation spectrum of two- and three-dimensional liquid 4He

Adopting the separability assumption in conjunction with the hypernetted-chain approximation and the minimum principle of Helmholtz free energy based on the trial density matrix expressed in terms of Jastrow-type wave functions, a set of coupled Euler-Lagrange equations are obtained for the radial distribution function, structure function, excitation spectrum and occupation number of a quantum fluid at finite temperatures. Numerical solutions of these functions are determined through a generalization of the linearized variational calculation method. The behavior of these functions as the temperature and density is varied in two dimensions is similar to three-dimensional experimental data.

Modulation-doped quantum-well wires: Elementary excitation spectra.

Modulation-doped quantum-well wires: Elementary excitation spectra.

Bose condensation and superfluidity of excitons in a high magnetic field.

In a high magnetic field, such that the distance between the Landau levels exceeds the binding energy of an exciton, an exciton gas in a semiconductor is capable of forming the Bose-Einstein condensate as well as a superfluid state even at a relatively high temperature. We consider the problem of excitonic interaction in a semiconductor in its multielectron formulation, starting from the second-quantization representation of the Hamiltonian of interacting electrons and holes in a high magnetic field. The expressions for the ground-state energy, the chemical potential, and the spectrum of elementary excitations of the system are obtained in a linear approximation in the concentration of excitons. It is shown that a system of excitons in a high magnetic field is similar to a weakly nonideal Bose gas. The existence and the stability of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field are established at a high density of excitons. The results obtained show that the excitation spectrum vanishes linearly, with a slope equal to a macroscopic speed of sound which depends on the direction of the magnetic field. Thus this spectrum satisfies the Landau criterion for superfluidity. The possible observable effects of the Bose condensate and the superfluidity of excitons in a high magnetic field are also discussed. It is shown that Bose condensation leads to unusual optical properties of a semiconductor, e.g., anomalous absorption of light, and to another mechanism of light amplification.

Thermal conductivity and first viscosity via temperature-dependent elementary excitation spectra in thin and bulk liquid 4He

The coefficients of thermal conductivity (ϰ) and first viscosity (η) in thin and bulk liquid 4He are evaluated explicitly as a function of temperature via the zero-temperature and temperature-dependent two- and three-dimensional elementary excitation spectra that are microscopic only in the long-wavelength limit. The coefficients ϰ( T) and η( T) obtained from the temperature-dependent spectrum have slightly larger values than those of the zero-temperature spectrum through the whole range of temperatures, while as the temperature approaches absolute zero, the coefficients ϰ( T) and η( T) coincide with each other in both spectra. Below about 0.8 K, both coefficients increase exponentially with decreasing temperature. At temperatures below about 0.3 K, ϰ( T) in the thin and bulk cases have T -5 and T -6 dependences, respectively, whereas η ph( T) has a T -1 dependence in both dimensions with extra temperature-dependent terms, which originate from three-phonon processes for both excitation spectra.

Elementary excitation spectrum for the multichannel Kondo model at finite temperatures.

Spectral density for the elementary excitation of the multichannel Kondo model is investigated at finite temperatures with the use of the Bethe-ansatz method. Our formulation is based on the method of Yang and Yang developed in one-dimensional interacting boson systems. In the orbital singlet case, the narrow peak structure develops in the low-energy region as the temperature is decreased, whereas in the underscreened case, the excitation spectrum exhibits a divergence property at zero excitation energy, irrespective of the temperature. In the overscreened case, in which the non-Fermi-liquid fixed point is stable in the ground state, the peak structure develops in the low-energy region and the weight at zero excitation energy increases as the temperature is decreased. We discuss characteristic properties of the excitation spectrum in connection with bulk properties.

Square-lattice frustrated Heisenberg antiferromagnet of spin 1/2 in a strong magnetic field.

The properties of the two-dimensional antiferromagnet of spin 1/2 on a square lattice with nearest- and next-nearest-neighbors interactions in a strong magnetic field close to saturation are studied in terms of the equivalent Bose-gas problem. A phase with a gap in the elementary excitations spectrum, short-range-ordered ground state, and a corresponding plateau in the magnetization curve is shown to exist in the interval of fields between the first and second critical fields ${\mathit{h}}_{0}$h${\mathit{h}}_{01}$. Its existence is closely related to the two-particle attraction in the vicinity of the wave vector ${\mathbf{p}}_{0\mathit{u}}$=(\ensuremath{\pi},\ensuremath{\pi}). In the interval between the second and third critical fields ${\mathit{h}}_{01}$h${\mathit{h}}_{\mathit{c}\mathit{f}}$ the system behaves as a quasi-one-dimensional magnetic phase with long-range order in the ground state and a gapless mode. The magnetization depends on field linearly, with logarithmic corrections.

Raman-scattering spectra of elementary electronic excitations in coupled double-quantum-well structures.

Using the time-dependent local-density approximation (TDLDA) within a self-consistent-linear response theory, we calculate the elementary excitation energies and the associated inelastic light-scattering spectra of a strongly coupled two-component plasma in a double-quantum-well system with electron occupation of symmetric and antisymmetric subbands. We find, consistent with the results of a recent experimental Raman-scattering study, that the intersubband spin-density excitations tend to merge with the single-particle excitations (i.e., the excitonic shift decreases monotonically) as the Fermi energy increases beyond the symmetric-antisymmetric energy gap ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{SAS}}$. However, our TDLDA calculation does not show the abrupt suppression of the excitonic shift seen experimentally at a finite value of the subband occupancy parameter \ensuremath{\eta}==${\mathrm{\ensuremath{\Delta}}}_{\mathrm{SAS}}$/${\mathit{E}}_{\mathit{F}}$.