Ground state properties and excitation spectra of non-Galilean invariant interacting Bose systems

We study the ground state properties and the excitation spectrum of bosons which, in addition to a short-range repulsive two body potential, interact through the exchange of some dispersionless bosonic modes. The latter induces a time dependent (retarded) boson-boson interaction which is attractive in the static limit. Moreover the coupling with dispersionless modes introduces a reference frame for the moving boson system and hence breaks the Galilean invariance of this system. The ground state of such a system is depleted {\it linearly} in the boson density due to the zero point fluctuations driven by the retarded part of the interaction. Both quasiparticle (microscopic) and compressional (macroscopic) sound velocities of the system are studied. The microscopic sound velocity is calculated up the second order in the effective two body interaction in a perturbative treatment, similar to that of Beliaev for the dilute weakly interacting Bose gas. The hydrodynamic equations are used to obtain the macroscopic sound velocity. We show that these velocities are identical within our perturbative approach. We present analytical results for them in terms of two dimensional parameters -- an effective interaction strength and an adiabaticity parameter -- which characterize the system. We find that due the presence of several competing effects, which determine the speed of the sound of the system, three qualitatively different regimes can be in principle realized in the parameter space and discuss them on physical grounds.Comment: 6 pages, 2 figures, to appear in Phys. Rev.

X-ray edge problem of graphene

The X-ray edge problem of graphene with the Dirac fermion spectrum is studied. At half-filling the linear density of states suppresses the singular response of the Fermi liquid, while away from half-filling the singular features of the Fermi liquid reappear. The crossover behavior as a function of the Fermi energy is examined in detail. The exponent of the power-law absorption rate depends both on the intra- and inter-valley scattering, and it changes as a function of the Fermi energy, which may be tested experimentally.Comment: 7 pages, 1 figur

Excitation spectrum in a cylindrical Bose-Einstein gas

Whole excitation spectrum is calculated within the Popov approximation of the Bogoliubov theory for a cylindrical symmetric Bose-Einstein gas trapped radially by a harmonic potential. The full dispersion relation and its temperature dependence of the zero sound mode propagating along the axial direction are evaluated in a self-consistent manner. The sound velocity is shown to depend not only on the peak density, but also on the axial area density. Recent sound velocity experiment on Na atom gas is discussed in light of the present theory.Comment: 4 pages, 5 eps figure

Superfluidity of bosons on a deformable lattice

We study the superfluid properties of a system of interacting bosons on a lattice which, moreover, are coupled to the vibrational modes of this lattice, treated here in terms of Einstein phonon model. The ground state corresponds to two correlated condensates: that of the bosons and that of the phonons. Two competing effects determine the common collective soundwave-like mode with sound velocity $v$, arising from gauge symmetry breaking: i) The sound velocity $v_0$ (corresponding to a weakly interacting Bose system on a rigid lattice) in the lowest order approximation is reduced due to reduction of the repulsive boson-boson interaction, arising from the attractive part of phonon mediated interaction in the static limit. ii) the second order correction to the sound velocity is enhanced as compared to the one of bosons on a rigid lattice when the the boson-phonon interaction is switched on due to the retarded nature of phonon mediated interaction. The overall effect is that the sound velocity is practically unaffected by the coupling with phonons, indicating the robustness of the superfluid state. The induction of a coherent state in the phonon system, driven by the condensation of the bosons could be of experimental significance, permitting spectroscopic detections of superfluid properties of the bosons. Our results are based on an extension of the Beliaev - Popov formalism for a weakly interacting Bose gas on a rigid lattice to that on a deformable lattice with which it interacts.Comment: 12 pages, 14 figures, to appear in Phys. Rev.

Effects of Disorder in a Dilute Bose Gas

We discuss the effects of a weak random external potential on the properties of the dilute Bose gas at zero temperature. The results recently obtained by Huang and Meng for the depletion of the condensate and of the superfluid density are recovered. Results for the shift of the velocity of sound as well as for its damping due to collisions with the external field are presented. The damping of phonons is calculated also for dense superfluids. (submitted to Phys.Rev.B)Comment: 21 pages, Plain Tex, 2 figures available upon request, preprint UTF 31

Polaronic excitations in CMR manganite films

In the colossal magnetoresistance manganites polarons have been proposed as the charge carrier state which localizes across the metal-insulator transition. The character of the polarons is still under debate. We present an assessment of measurements which identify polarons in the metallic state of La{2/3}Sr{1/3}MnO{3} (LSMO) and La{2/3}Ca{1/3}MnO{3} (LCMO) thin films. We focus on optical spectroscopy in these films which displays a pronounced resonance in the mid-infrared. The temperature dependent resonance has been previously assigned to polaron excitations. These polaronic resonances are qualitatively distinct in LSMO and LCMO and we discuss large and small polaron scenarios which have been proposed so far. There is evidence for a large polaron excitation in LSMO and small polarons in LCMO. These scenarios are examined with respect to further experimental probes, specifically charge carrier mobility (Hall-effect measurements) and high-temperature dc-resistivity.Comment: 16 pages, 10 figure

Infrared Behavior of Interacting Bosons at Zero Temperature

We exploit the symmetries associated with the stability of the superfluid phase to solve the long-standing problem of interacting bosons in the presence of a condensate at zero temperature. Implementation of these symmetries poses strong conditions on the renormalizations that heal the singularities of perturbation theory. The renormalized theory gives: For d>3 the Bogoliubov quasiparticles as an exact result; for 1<d<=3 a nontrivial solution with the exact exponent for the singular longitudinal correlation function, with phonons again as low-lying excitations.Comment: Minor Changes. 4 pages, RevTeX, no figures, uses multicol.sty e-mail: [email protected]

Theoretical study of the dynamic structure factor of superfluid 4He

We study the dynamic structure factor $S(\vec{q},\omega)$ of superfluid 4He at zero temperature in the roton momentum region and beyond using field-theoretical Green's function techniques. We start from the Gavoret-Nozi\`{e}res two-particle propagator and introduce the concept of quasiparticles. We treat the residual (weak) interaction between quasiparticles as being local in coordinate space and weakly energy dependent. Our quasiparticle model explicitly incorporates the Bose-Einstein condensate. A complete formula for the dynamic susceptibility, which is related to $S (\vec{q},\omega)$, is derived. The structure factor is numerically calculated in a self-consistent way in the special case of a momentum independent interaction between quasiparticles. Results are compared with experiment and other theoretical approaches.Comment: 17 pages, 16 figure

Fermi edge singularities in X-ray spectra of strongly correlated fermions

We discuss the problem of the X-ray absorption in a system of interacting fermions and, in particular, those features in the X-ray spectra that can be used to discriminate between conventional Fermi-liquids and novel "strange metals". Focusing on the case of purely forward scattering off the core-hole potential, we account for the relevant interactions in the conduction band by means of the bosonization technique. We find that the X-ray Fermi edge singularities can still be present, although modified, even if the density of states vanishes at the Fermi energy, and that, in general, the relationship between the two appears to be quite subtle.Comment: Latex, 16 pages, Princeton preprin

Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate

We theoretically study the properties of Nambu-Goldstone bosons in an interacting single-component Bose-Einstein condensate (BEC). We first point out that the proofs of Goldstone's theorem by Goldstone, et al. [Phys. Rev. {\bf 127} (1962) 965] may be relevant to distinct massless modes of the BEC: whereas the first proof deals with the poles of the single-particle Green's function $\hat{G}$, the second one concerns those of the two-particle Green's function. Thus, there may be multiple Nambu-Goldstone bosons even in the single-component BEC with broken U(1) symmetry. The second mode turns out to have an infinite lifetime in the long-wavelength limit in agreement with the conventional viewpoint. In contrast, the first mode from $\hat{G}$, i.e., the Bogoliubov mode in the weak-coupling regime, is shown to be a "bubbling" mode fluctuating temporally out of and back into the condensate. The substantial lifetime originates from an "improper" structure of the self-energy inherent in the BEC, which has been overlooked so far and will be elucidated here, and removes various infrared divergences pointed out previously.Comment: 9 pages, 6 gigure