arXiv subjects

W. Wonneberger

Publications and source records attributed to W. Wonneberger.

11 recordsLinked to original sources

arXiv2006

Dynamic response of interacting one-dimensional fermions in the harmonic atom trap: Phase response and the inhomogeneous mobility

The problem of the Kohn mode in bosonized theories of one-dimensional interacting fermions in the harmonic trap is investigated and a suitable modification of the interaction is proposed which preserves the Kohn mode. The modified theory is used to calculate exactly the inhomogeneous linear mobility at position z in response to a spatial force pulse at another position. It is found the inhomogeneous particle mobility exhibits resonances not only at the trap frequency but also at multiples of a new renormalized collective mode frequency which depends on the strength of the interaction. In contrast, the local response obtained by averaging over the pulse position remains that of the non-interacting system.

quant-ph↗

arXiv2004

Treatment of backscattering in a gas of interacting fermions confined to a one-dimensional harmonic atom trap

An asymptotically exact many body theory for spin polarized interacting fermions in a one-dimensional harmonic atom trap is developed using the bosonization method and including backward scattering. In contrast to the Luttinger model, backscattering in the trap generates one-particle potentials which must be diagonalized simultaneously with the two-body interactions. Inclusion of backscattering becomes necessary because backscattering is the dominant interaction process between confined identical one-dimensional fermions. The bosonization method is applied to the calculation of one-particle matrix elements at zero temperature. A detailed discussion of the validity of the results from bosonization is given, including a comparison with direct numerical diagonalization in fermionic Hilbert space. A model for the interaction coefficients is developed along the lines of the Luttinger model with only one coupling constant $K$. With these results, particle densities, the Wigner function, and the central pair correlation function are calculated and displayed for large fermion numbers. It is shown how interactions modify these quantities. The anomalous dimension of the pair correlation function in the center of the trap is also discussed and found to be in accord with the Luttinger model.

cond-mat.mes-hall↗

arXiv2004

Phase theory and critical exponents for the Tomonaga-Luttinger model with harmonic confinement

A phase operator formulation for a recent model of interacting one-dimensional fermions in a harmonic trap is developed. The resulting theory is similar to the corresponding approach for the Luttinger model with open boundary conditions (OBC). However, in place of the spatial coordinate $z$, a dimensionless variable $u$ defined on the unit circle appears as argument of the phase fields and $u$ is non-linearly related to $z$. Furthermore, form factors appear which reflect the harmonic trap geometry. The theory is applied to calculate one-particle correlation functions. In a properly defined thermodynamic limit, bulk and boundary critical exponents are calculated for the static two-point correlation function and the dynamic local correlation function. The local spectral density is also considered. The critical exponents found are in agreement with those known for OBC with the exception of the boundary scaling exponent $Δ_\perp$.

cond-mat.str-el↗

arXiv2003

Coupling constants for a degenerate Fermi gas confined to a quasi one-dimensional harmonic trap

A theory for the coupling constants between spin polarized degenerate fermionic atoms is developed for the case of atoms confined to a quasi one-dimensional harmonic trap. Exploiting the presence of the Fermi edge and the large number of fermions it is shown that the resulting effective one-dimensional interaction can be parameterized by three sets of interaction coefficients, two for forward scattering and one for backward scattering. In the case of identical fermions, backscattering dominates because the contact part of the effective one-dimensional interaction must be subtracted. Analytic expressions for the interaction coefficients for the effective contact interaction, which is relevant for the inter-component interactions, and for the "p-wave" interaction appearing in next order, are given. As an example, we calculate and discuss in detail the effective coupling constants for the marginally long ranged dipole--dipole interaction.

cond-mat.mes-hall↗

arXiv2003

Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap

Using an asymptotic phase representation of the particle density operator $\hatρ(z)$ in the one-dimensional harmonic trap, the part $δ\hatρ_F(z)$ which describes the Friedel oscillations is extracted. The expectation value $<δ\hatρ_F(z)>$ with respect to the interacting ground state requires the calculation of the mean square average of a properly defined phase operator. This calculation is performed analytically for the Tomonaga-Luttinger model with harmonic confinement. It is found that the envelope of the Friedel oscillations at zero temperature decays with the boundary exponent $ν= (K+1)/2$ away from the classical boundaries. This value differs from that known for open boundary conditions or strong pinning impurities. The soft boundary in the present case thus modifies the decay of Friedel oscillations. The case of two components is also discussed.

cond-mat.str-el↗

arXiv2001

Two-component Fermi gas in a one-dimensional harmonic trap

A many body theory for a two-component system of spin polarized interacting fermions in a one-dimensional harmonic trap is developed. The model considers two different states of the same fermionic species and treats the dominant interactions between the two using the bosonization method for forward scattering. Asymptotically exact results for the one-particle matrix elements at zero temperature are given. Using them, occupation probabilities of oscillator states are discussed. Particle and momentum densities are calculated and displayed. It is demonstrated how interactions modify all these quantities. An asymptotic connection with Luttinger liquids is suggested. The relation of the coupling constant of the theory to the dipole-dipole interaction is also discussed.

quant-ph↗

arXiv2001

Luttinger model approach to interacting one-dimensional fermions in a harmonic trap

A model of interacting one--dimensional fermions confined to a harmonic trap is proposed. The model is treated analytically to all orders of the coupling constant by a method analogous to that used for the Luttinger model. As a first application, the particle density is evaluated and the behavior of Friedel oscillations under the influence of interactions is studied. It is found that attractive interactions tend to suppress the Friedel oscillations while strong repulsive interactions enhance the Friedel oscillations significantly. The momentum distribution function and the relation of the model interaction to realistic pair interactions are also discussed.

quant-ph↗

arXiv2000

Non-Interacting Fermions in a One-Dimensional Harmonic Atom Trap: Exact One-Particle Properties at Zero Temperature

One-particle properties of non-interacting Fermions in a one-dimensional harmonic trap and at zero temperature are studied. Exact expressions and asymptotic results for large Fermion number N are given for the particle density distribution n_0(z,N). For large N and near the classical boundary at the Fermi energy the density displays increasing fluctuations. A simple scaling of these tails of the density distribution with respect to N is established. The Fourier transform of the density distribution is calculated exactly. It displays a small but characteristic hump near 2 k_F with k_F being a properly defined Fermi wave number. This is due to Friedel oscillations which are identified and discussed. These quantum effects are missing in the semi-classical approximation. Momentum distributions are also evaluated and discussed. As an example of a time-dependent one-particle problem we calculate exactly the evolution of the particle density when the trap is suddenly switched off and find a simple scaling behaviour in agreement with recent general results.

quant-ph↗

arXiv1999

AC-Conductivity of Pinned Charge Density Wave Fluctuations in Quasi One-Dimensional Conductors

Quasi one-dimensional conductors which undergo a Peierls transition to a charge density wave state at a temperature T_P show a region of one-dimensional fluctuations above T_P. The Ginzburg-Landau-Langevin theory for the frequency dependent collective conductivity from conductive fluctuations into the charge density wave state is developed. By inclusion of a phase breaking term the effect of local pinning due to random impurities is simulated. It is found that the spectral weight of unpinned fluctuations is partly redistributed into a pinned mode around a pinning frequency in the far infrared region. In addition, selection rule breaking by the imputities makes the fluctuating amplitude mode visible in the optical response.

cond-mat↗

arXiv1999

Local Impurity Phase Pinning and Pinning Force in Charge Density Waves

Starting from the static Fukuyama-Lee-Rice equation for a three-dimensional incommensurate charge density wave (CDW) in quasi one-dimensional conductors a solvable model for local phase pinning by impurities is defined and studied. We find that average CDW energy and average pinning force show critical behaviour with respect to the pinning parameter $h$. Specifically the pinning force exhibits a threshold at $h=1$ with exponent $β=2$. Our model examplifies a general concept of local impurity pinning in which the force exerted by the impurity on the periodic CDW structure becomes multivalued and metastable states appear beyond a threshold. It is found that local impurity pinning becomes less effective at low temperatures and may eventually cease completely. These results are independent of spatial dimensionality as expected for local impurity pinning. Comparison with Larkin's model is also made.

cond-mat.str-el↗

arXiv1997

Surface Phason-Polaritons in Charge Density Wave Films

The coupled non-radiative excitations of the electromagnetic field and phasons in films with a quasi one-dimensional charge density wave (CDW) are evaluated for P--polarization and CDW conducting axis inside the film. The prominent features are two surface phason-polariton branches extending from the CDW pinning frequency to the frequency of the longitudinal optical phason. These surface phason-polariton states are confined to a finite band of longitudinal wave numbers. Besides surface polaritons, infinite series of guided wave modes are found which extend to large wave numbers. These differences to usual phonon-polaritons are caused by the extreme anisotropy of the electric CDW reponse. This new class of surface polaritons is expected to be found in the submillimeter frequency range.

cond-mat↗