Boson Dispersion Research Articles

Aspects of the gauge boson-gaugino mixing in a supersymmetric scenario with Lorentz-symmetry violation

We write down an $\mathcal{N}=1$ supersymmetric extension for non-Abelian gauge theories in ($1+3$) dimensions with a Lorentz- and $CPT$-violating term of the Carroll-Field-Jackiw type. By including effects of the background (supersymmetric) fermion bilinears that accompany Lorentz-symmetry violation in a Carroll-Field-Jackiw scenario, we investigate both the gauge boson and gaugino dispersion relations in order to compute their respective masses in terms of the background structures. Such results open up a potential path towards a possible mechanism for gaugino-gauge boson conversion, an analog of the Primakoff effect, induced here not by an external magnetic field, but instead by the (Majorana) fermionic sector of the supersymmetry multiplet in the backstage of the Lorentz-symmetry violation.

Basis invariant description of chemical equilibrium with implications for a recent axionic leptogenesis model

We provide a systematic treatment of chemical equilibrium in the presence of a specific type of time dependent background. The type of time dependent background we consider appears, for example, in recently proposed axion/Majoron leptogenesis models [1,2]. In describing the chemical equilibrium we use quantities which are invariant under redefinition of fermion phases (we refer to this redefinition as a change of basis for short), and therefore it is a basis invariant treatment. The change of the anomaly terms due to the change of the path integral measure [3,4] under a basis change is taken into account. We find it is useful to go back and forth between different bases, and there are insights which can be more easily obtained in one basis rather than another. A toy model is provided to illustrate the ideas. For the axion leptogenesis model [1], our result suggests that at $T > 10^{13}$ GeV , when sphaleron processes decouple, and $\Gamma_{B+L} << H < \Gamma_L$ (where $H$ is the Hubble parameter at temperature $T$ and $\Gamma_L$ is the $\Delta L = 2$ lepton number violating interaction rate), the amount of $B-L$ created is controlled by the smallness of the sphaleron interaction rate, $\Gamma_{B+L}$. Therefore it is not as efficient as described. In addition, we notice an interesting modification of gauge boson dispersion relations at subleading order.

Bosons and Magnons in Ordered Magnets

In earlier experimental studies we have shown that in accordance with the principles of renormalization group theory the spin dynamics of ordered magnets is controlled by a boson guiding eld instead by exchange interactions between nearest magnetic neighbors. In particular, thermal decrease of the magnetic order parameter is given by the heat capacity of the boson eld. The typical signature of boson dynamics is that the critical power functions either at T = Tc or at T = 0 hold up to a considerable distance from critical temperature. The critical power functions of the atomistic models hold asymptotically at T = Tc or at T = 0 only. In contrast to the atomistic magnons eld bosons cannot directly be observed using inelastic neutron scattering. However, for some classes of magnets the eld bosons seem to have magnetic moment and thus are able to interact directly with magnons. This interaction, although weak in principle, leads to surprisingly strong functional modi cations in the magnon dispersions at small q-values. In particular, the magnon excitation gap seems to be due to the magnon boson interaction. In this communication we want to show that for small q-values the continuous part of the magnon dispersions can be tted over a nite q-range by a power function of wave vector. The power function can be identi ed with the dispersion of the eld bosons. It appears that for low q-values magnon dispersions get attracted by the boson dispersion and assume the dispersion of the bosons. This allows for an experimental evaluation of the boson dispersions from the known magnon dispersions. Exponent values of 1, 1.25, 1.5, and 2 have been identi ed. The boson dispersion relations and the associated power functions of temperature for the heat capacity of the boson elds are now empirically known for all dimensions of the eld and for magnets with integer and half-integer spin quantum number. These are two 2× 3 exponent schemes.

How does color neutrality affect collective modes in color superconductors?

We revisit the issue of color neutrality in effective model descriptions of dense quark matter based on global color symmetry. While the equilibrium thermodynamics of such models is now well understood, we examine the collective modes, focusing on the fluctuations of the order parameter. We point out that the constraint of color neutrality must be carefully generalized in order to obtain physically consistent and well-defined results. Particularly important is that the collective modes associated with order parameter fluctuations couple to charge density fluctuations in the neutral medium. We start by proving explicitly that, in contrast to claims made previously in literature, Nambu-Goldstone bosons of spontaneously broken global color symmetry remain exactly massless even after imposing the color neutrality constraint. As the next step, we make the argument general by using effective field theory. We then employ the high-density approximation to calculate the couplings in the effective Lagrangian and thus the Nambu-Goldstone boson dispersion relations.

Charge-density-wave formation in a half-filled fermion-boson transport model: A projective renormalization approach

We study the metal-insulator transition in a very general two-channel transport model, where charge carriers are coupled to a correlated background medium. The fluctuations of the background were described as bosonic excitations, having the ability to relax. Employing an analytical projector-based renormalization technique, we calculate the ground-state and spectral properties of this fermion-boson model and corroborate recent numerical results, which indicate---in dependence on the `stiffness' of the background medium---a Luttinger-liquid to charge-density-wave transition for the one-dimensional half-filled band case. In particular, we determine the renormalized electron and boson dispersion relations and show that the quantum phase transition is not triggered by a softening of the boson modes. Thus the charge density wave is different in nature from an usual Peierls distorted state.

Goldstone bosons in presence of charge density

We investigate spontaneous symmetry breaking in Lorentz-noninvariant theories. Our general discussion includes relativistic systems at finite density as well as intrinsically nonrelativistic systems. The main result of the paper is a direct proof that nonzero density of a non-Abelian charge in the ground state implies the existence of a Goldstone boson with nonlinear (typically, quadratic) dispersion law. We show that the Goldstone boson dispersion relation may in general be extracted from the current transition amplitude and demonstrate on examples from recent literature, how the calculation of the dispersion relation is utilized by this method. After then, we use the general results to analyze the nonrelativistic degenerate Fermi gas of four fermion species. Because of its internal SU(4) symmetry, this system provides an analog to relativistic two-color quantum chromodynamics with two quark flavors. In the end, we extend our results to pseudo-Goldstone bosons of an explicitly broken symmetry.

Effects of boson dispersion in fermion-boson coupled systems

We study the nonlinear feedback in a fermion-boson system using an extension of dynamical mean-field theory and the quantum Monte Carlo method. In the perturbative regimes (weak-coupling and atomic limits) the effective interaction among fermions increases as the width of the boson dispersion increases. In the strong-coupling regime away from the antiadiabatic limit, the effective interaction decreases as we increase the width of the boson dispersion. This behavior is closely related to complete softening of the boson field. We elucidate the parameters that control this nonperturbative region where fluctuations of the dispersive bosons enhance the delocalization of fermions.

Lattice and spin polarons in two dimensions

A variational approach is employed to compute the wave function of a single polaron for a two-dimensional Holstein Hamiltonian with arbitrary forms of linear particle–boson interactions and boson dispersion relations. The Toyozawa ansatz is utilized, and generalizations to multiple polarons are outlined. Applications are made to model superradiance in pseudoisocyanine bromide J-aggregates, and to calculate quasiparticle dispersion of an itinerant hole in a two-dimensional antiferromagnet.

Two-Dimensional Boson–Fermion Model

We studied the influence of the electron–boson interaction (hybridization) on the bosonic spectrum in the case of a two dimensional (2D) electronic system. The boson dispersion is affected by this interaction and we showed that for a constant density of states the wavevector dependence is quadratic for qvF/4T ≪ 1, and the imaginary part is small for qvF/4T ≫ 1. However, the 2D electronic system presents a van Hove density of states, and we considered this energy dependence in the calculation of the bosonic energy spectrum. The real part becomes logarithmic dependent on the wavevector and the imaginary part can be neglected if qvF ∼ EF or 2 Ec ∼ z, for qvF/4T ≫ 1.

SO(5) invariance and effective field theory for high-Tcsuperconductors

We set up the effective field theories which describe the SO(5)-invariant picture of the high-${T}_{c}$ cuprates in various regimes. We use these to get quantitative conclusions concerning the size of SO(5) breaking effects. We consider two applications in detail: (i) the thermodynamic free energy, which describes the phase diagram and critical behavior, and (ii) the Lagrangian governing the interactions of the pseudo-Goldstone bosons with each other and with the electron quasiparticles deep within the ordered phases. We use these effective theories to obtain predictions for the critical behavior near the possible bicritical point and the pseudo-Goldstone boson dispersion relations, as well as some preliminary results concerning their contribution to response functions. We systematically identify which predictions are independent of the microscopic details of the underlying electron dynamics, and which depend on more model-dependent assumptions.

Solution of the local polaron model with a boson continuum

We study the zero-temperature Green function for the local polaron model that describes the interaction of an electron in an empty band with a boson continuum; the coupling takes place at one site in the lattice. To this end, we propose a new exact approach which consists in two steps: first, the problem is reduced to the solution of an infinite linear algebraic system of recursion equations by the method of excitation amplitudes; then, a systematic expansion of the solution is generated by Feenberg's formalism. Previously, the problem had been solved exactly in the narrow-band limit; otherwise, the solution was achieved for one or a few boson modes. Here we consider a boson continuum and obtain an infinite expansion of the self-energy in terms of the dressed Green function. In this case, the recursive, continued-fraction technique is equivalent to self-consistent perturbation theory. The results are illustrated by selected numerical examples, and show that the satellites are much more sensitive to the boson dispersion than the main line.

Biexcitonic nonlinearity in GaAs/GaxAl1-xAs quantum wells and quantum-well wires.

The recently reported high excitonic and biexcitonic binding energies in GaAs/${\mathrm{Ga}}_{\mathrm{x}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum wells and quantum-well wires suggest the possibility of strong optical nonlinearities around the biexcitonic resonance. We calculate in a simple boson model both absorption and dispersion spectra in GaAs around this resonance for various intensities comparing bulk, quantum-well, and quantum-well-wire structures. An assessment of inhomogeneous line broadening due to a Gaussian distribution of quantum-well-wire radii is also presented.