Two interacting particles in a disordered chain IV: Scaling of level curvatures

The curvatures of two-particle energy levels with respect to the enclosed magnetic flux in mesoscopic disordered rings are investigated numerically. We find that the typical value of the curvatures is increased by interactions in the localised regime and decreased in the metallic regime. This confirms a prediction by Akkermans and Pichard (Eur. Phys. J. B 1, 223 (1998)). The interaction-induced changes of the typical curvatures at different energies and disorder strengths exhibit one-parameter scaling with a conductance-like single parameter. This suggests that interactions could influence the conductance of mesoscopic systems similarly. Received 24 August 1998     

Correlations in a non-equilibrium disordered system

Correlations in a one-dimensional model are studied as it evolves between different disordered equilibrium states. The disorder is generated by an external agency (e.g. a heat reservoir) which induces stochastic behaviour. Even though the time scales for the evolution of the system and the intrinsic motion of the constituent particles are distinctly different there is a complicated interplay between the two processes as observed in static and dynamic structure factors.     

Long-range order in a simple model of interacting fermions

We consider a model of spinless fermions on a lattice, interacting through a nearest neighbor repulsion. In the half-filled band case and for dimensionsd 2, we rigorously prove that there is long-range order in some domain of the parameters=(k _B T)^–1 andt/U, wheret is the hopping amplitude of the particles,U the strength of their repulsion, and the inverse temperature. Our technique is based on the usual Peierls argument of classical statistical mechanics but fails for the groundstate. We discuss the specific difficulties introduced by the Fermi statistics.Work supported in part by U.S. NSF grant PHY 90-19433-A02.     

Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements

For N interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the “sites”. The hopping terms are induced by the interaction. When the one body states are localized, we numerically find that the set of directly connected “sites” is multifractal. For the case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize the Golden rule decay of the non interacting states and the enhancement factor of the localization length. Received: 17 April 1998 / Accepted: 14 May 1998     

Two interacting particles in a disordered chain III: Dynamical aspects of the interplay disorder-interaction

The interplay between the quantum interferences responsible for one particle localization over a length L₁, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over a length L ₂ > L ₁ , is illustrated by a study of the motion of two particles put close to each other at the initial time. Localization is reached in two steps. First, before the time t₁ necessary to propagate over L₁, the interaction slows down the ballistic motion. On the contrary, after t₁ the interaction favors a very slow delocalization, characterized by a spreading of the center of mass, until L₂ is reached. This slow motion is related to the absence of quantum chaos in this one dimensional model, the interaction being only able to induce weaker chaos with critical spectral statistics. Under appropriate initial conditions, the motion remains invariant under the duality transformation mapping the behavior at small U onto the behavior at large U. Received 24 August 1998     

Shell structure and pairing for interacting fermions in a trap

The shell structures for weakly interacting fermions in harmonic oscillator traps at zero temperature undergo several transitions depending on the number of particles in the trap and their interaction strength. Calculations of the one and two-particle spectra give the pairing gaps, and the many particle state is constructed by the seniority scheme. For sufficiently few particles, N less than or similar to 10(4), the pairing field exceeds the mean-field splitting of single particle levels at the Fermi surface and the greater number of almost degenerate states due to the SU(3) symmetry in the harmonic oscillator shell lead to supergaps. Deformation and rotation are also discussed.     

Thermodynamics of interacting fermions in atomic traps

We calculate the entropy in a trapped, resonantly interacting Fermi gas as a function of temperature for a wide range of magnetic fields between the BCS and Bose-Einstein condensation end points. This provides a basis for the important technique of adiabatic sweep thermometry and serves to characterize quantitatively the evolution and nature of the excitations of the gas. The results are then used to calibrate the temperature in several ground breaking experiments on (6)Li and (40)K.     

Influence of heat bath on the heat conductivity in disordered anharmonic chain

We study heat conduction in a one-dimensional disordered anharmonic chain with arbitrary heat bath by using extended Ford, Kac and Mazur (FKM) formulation, which satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat conductivity κ is obtained, from which the asymptotic system-size (N) dependence is extracted. It shows κ∼N^α. As a special case we give the expression that κ∼N^1/2 for free boundaries, and κ∼ N^-1/2 for fixed boundaries, from which we can get the conclusion that the momentum conservation is a key factor of the anomalous heat conduction. Comparing with different ∇T, the heat conductivity shows large difference between the linear system and the nonlinear system.     

Dynamic response of one-dimensional interacting fermions

We evaluate the dynamic structure factor S(q, omega) of interacting one-dimensional spinless fermions with a nonlinear dispersion relation. The combined effect of the nonlinear dispersion and of the interactions leads to new universal features of S(q, omega). The sharp peak S(q, omega) approximately q(delta(omega -uq), characteristic for the Tomonaga-Luttinger model, broadens up; for a fixed becomes finite at arbitrarily large . The main spectral weight, however, is confined to a narrow frequency interval of the width deltaomega approximately q(2)/m. At the boundaries of this interval the structure factor exhibits power-law singularities with exponents depending on the interaction strength and on the wave number q.     

Charge and spin dynamics of interacting fermions in a one-dimensional harmonic trap

We study an atomic Fermi gas interacting through repulsive contact forces in a one-dimensional harmonic trap. Bethe-ansatz solutions lead to an inhomogeneous Tomonaga-Luttinger model for the low energy excitations. The equations of motion for charge and spin density waves are analyzed both near the trap center and near the trap edges. While the center shows conventional spin-charge separation, the edges cause a giant increase of the separation between these modes.     

Functional bosonization of interacting fermions in arbitrary dimensions

We bosonize the long-wavelength excitations of interacting fermions in arbitrary dimension by directly applying a suitable Hubbard-Stratonowich transformation to the Grassmannian generating functional of the fermionic correlation functions. With this technique we derive a surprisingly simple expression for the singleparticle Greens-function, which is valid for arbitrary interaction strength and can describe Fermi- as well as Luttinger liquids. Our approach sheds further light on the relation between bosonization and the random-phase approximation, and enables us to study screening in a nonperturbative way.     

Theory of rf-spectroscopy of strongly interacting fermions

We show that strong pairing correlations in Fermi gases lead to the appearance of a gaplike structure in the rf spectrum, both in the balanced superfluid and in the normal phase above the Clogston-Chandrasekhar limit. The average rf shift of a unitary gas is proportional to the ratio of the Fermi velocity and the scattering length with the final state. In the strongly imbalanced case, the rf spectrum measures the binding energy of a minority atom to the Fermi sea of majority atoms. Our results provide a qualitative understanding of recent experiments by Schunck et al.     

Ground-state instability in systems of strongly interacting fermions

The stability of a fermion system is analyzed for a model repulsive pair interaction potential. The possibility of different types of restructuring of the Fermi ground state (at sufficiently great coupling constant) is related to the analyticity properties of such potential. In particular, for the screened Coulomb law it is shown that the restructuring cannot be of the Fermi condensation type, known earlier for some exactly solvable models, but instead belongs to the class of topological transitions. A phase diagram constructed for this model in the variables “screening parameter-coupling constant” displays two kinds of topological transitions: a “5/2” kind, similar to the known Lifshitz transitions in metals, and a “2” kind, characteristic for a uniform strongly interacting system. Pis'ma Zh. éksp. Teor. Fiz. 68, No. 12, 893–899 (25 December 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Weak localization in disordered spin-1 chiral fermions

We theoretically investigate the quantum interference theory of magnetotransport of the three-component or spin-1 chiral fermions, which possess two linear Dirac bands and a flat band. For isotropic scalar impurities, the correction of conductivity from the coherent backscatter and non-coherent backscatter contributions cancel out in the intravalley scattering, leading to a weak localization correction to the Drude conductivity from the intervalley scattering. For the anisotropic impurities, the above cancelation is removed, we find the approximative quantum interference conductivity in the weak anisotropy case. The contributions from the chiral anomaly and classical Lorentz force are also discussed. Our work reveals some intriguing and detectable transport signatures of the novel spin-1 chiral fermions.     

Electrical resistivity of dilute,interacting fermions

A first-principles calculation of the initial decay of a current-carrying state is used to infer the electrical resistivity ofinteracting fermions (electrons or holes). This approach is useful when it is impractical to apply the Kubo formalism.     

Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics. Received: 22 May 1998 / Received in final form: 24 August 1998 / Accepted: 4 September 1998     

Scaling behavior of disordered lattice fermions in two dimensions

We propose a lattice model for Dirac fermions which allows us to break the degeneracy of the node structure. In the presence of a random gap we analyze the scaling behavior of the localization length as a function of the system width within a numerical transfer-matrix approach. Depending on the strength of the randomness, there are different scaling regimes for weak, intermediate and strong disorder. These regimes are separated by transitions that are characterized by one-parameter scaling.