Coulomb drag by small momentum transfer between quantum wires

Parametric study for optimal performance of Coulomb-coupled quantum dots

We study the optimal output power and efficiency of the three-terminal quantum heat engine with Coulomb-coupled quantum-dots (CCQD). It has been well known that in the weak coupling regime, two kinds of dominant transport mechanisms are sequential tunneling and cotunneling processes in CCQD. What process becomes dominant, which can be controlled by several parameters such as temperature difference, bias voltage, Coulomb interaction and tunneling parameters, is one of the key problems to determine the performance of the heat engine. We show the parametric dependence of the output power and coefficient and find the optimal performance of this CCQD heat engine through genetic algorithm.

Viscous Dissipation in One-Dimensional Quantum Liquids

We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zero-temperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. Our consideration is applicable to all single-component Galilean-invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.

Kinetics of mobile impurities and correlation functions in one-dimensional superfluids at finite temperature

We examine the hydrodynamic approach to dynamical correlations in one-dimensional superfluids near integrability and calculate the characteristic time scale, τ, beyond which this approach is valid. For time scales shorter than τ, hydrodynamics fails, and we develop an approach based on kinetics of fermionic quasiparticles described as mobile impurities. New universal results for the dynamical structure factor relevant to experiments in ultracold atomic gases are obtained.

One-dimensional fermions with neither Luttinger-liquid nor Fermi-liquid behavior

It is well known that, generically, one-dimensional interacting fermions cannot be described in terms of a Fermi liquid. Instead, they present a different phenomenology, that of a Tomonaga-Luttinger liquid: the Landau quasiparticles are ill defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine tuning of the interaction between fermions can stabilize a peculiar state of one-dimensional matter, which is dissimilar to both Tomonaga-Luttinger and Fermi liquids. We propose to call this state a quasi-Fermi liquid. Technically speaking, such a liquid exists only when the fermion interaction is irrelevant (in the renormalization group sense). The quasi-Fermi liquid exhibits the properties of both a Tomonaga-Luttinger liquid and a Fermi liquid. Similar to a Tomonaga-Luttinger liquid, no finite-momentum quasiparticles are supported by the quasi-Fermi liquid; on the other hand, its fermion occupation number demonstrates a finite discontinuity at the Fermi energy, which is a hallmark feature of a Fermi liquid. A possible realization of the quasi-Fermi liquid with the help of cold atoms in an optical trap is discussed.

Decay of fermionic quasiparticles in one-dimensional quantum liquids

The low-energy properties of one-dimensional quantum liquids are commonly described in terms of the Tomonaga-Luttinger liquid theory, in which the elementary excitations are free bosons. To this approximation, the theory can be alternatively recast in terms of free fermions. In both approaches, small perturbations give rise to finite lifetimes of excitations. We evaluate the decay rate of fermionic excitations and show that it scales as the eighth power of energy, in contrast to the much faster decay of bosonic excitations. Our results can be tested experimentally by measuring the broadening of power-law features in the density structure factor or spectral functions.

Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid

We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with a linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is strong, and the excitation spectrum is nonlinear. Although at low energies the nonlinearity is weak, it regularizes the divergence in the decay rate. We develop a theoretical description of the approach of the system to thermal equilibrium. The typical relaxation rate scales as the fifth power of temperature.

Equilibration of a one-dimensional Wigner crystal

Equilibration of a one-dimensional system of interacting electrons requires processes that change the numbers of left- and right-moving particles. At low temperatures such processes are strongly suppressed, resulting in slow relaxation towards equilibrium. We study this phenomenon in the case of spinless electrons with strong long-range repulsion, when the electrons form a one-dimensional Wigner crystal. We find the relaxation rate by accounting for the umklapp scattering of phonons in the crystal. For the integrable model of particles with inverse-square repulsion, the relaxation rate vanishes.

Phenomenology of one-dimensional quantum liquids beyond the low-energy limit

We consider the zero temperature behavior of dynamic response functions of 1D systems near edges of support in the momentum-energy plane (k,omega). The description of the singularities of dynamic response functions near an edge epsilon(k) is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function epsilon(k). This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of epsilon(k) and Luttinger liquid parameters for any k. For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.

Conductance of fully equilibrated quantum wires

We study the conductance of a quantum wire in the presence of weak electron-electron scattering. In a sufficiently long wire the scattering leads to full equilibration of the electron distribution function in the frame moving with the electric current. At nonzero temperature this equilibrium distribution differs from the one supplied by the leads. As a result the contact resistance increases, and the quantized conductance of the wire acquires a quadratic in temperature correction. The magnitude of the correction is found by analysis of the conservation laws of the system and does not depend on the details of the interaction mechanism responsible for equilibration.

Resistivity of inhomogeneous quantum wires

We study the effect of electron-electron interactions on the transport in an inhomogeneous quantum wire. We show that contrary to the well-known Luttinger liquid result, nonuniform interactions contribute substantially to the resistance of the wire. In the regime of weakly interacting electrons and moderately low temperatures we find a linear in T resistivity induced by the interactions. We then use the bosonization technique to generalize this result to the case of arbitrarily strong interactions.

Temperature dependence of coulomb drag between finite-length quantum wires

We evaluate the Coulomb drag current in two finite-length Tomonaga-Luttinger-liquid wires coupled by an electrostatic backscattering interaction. The drag current in one wire shows oscillations as a function of the bias voltage applied to the other wire, reflecting interferences of the plasmon standing waves in the interacting wires. In agreement with this picture, the amplitude of the current oscillations is reduced with increasing temperature. This is a clear signature of non-Fermi-liquid physics because for coupled Fermi liquids the drag resistance is always expected to increase as the temperature is raised.

Generation of spin current by Coulomb drag

Coulomb drag between two quantum wires is exponentially sensitive to the mismatch of their electronic densities. The application of a magnetic field can compensate this mismatch for electrons of opposite spin directions in different wires. The resulting enhanced momentum transfer leads to the conversion of the charge current in the active wire to the spin current in the passive wire.

Dynamic structure factor of the Calogero-Sutherland model

We evaluate the dynamic structure factor S(q, omega) of a one-dimensional quantum Hamiltonian with the inverse-square interaction (Calogero-Sutherland model). For a fixed small q, the structure factor differs from zero in a finite interval of frequencies of the width deltaomega proportional to q2/m. At the borders of this interval S(q, omega) exhibits power-law singularities with exponents depending on the interaction strength. The singularities are similar in origin to the well-known Fermi-edge singularity in the x-ray absorption spectra of metals.

Dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain

The longitudinal spin structure factor for the XXZ-chain at small wave vector q is obtained using Bethe ansatz, field theory methods, and the density matrix renormalization group. It consists of a peak with a peculiar, non-Lorentzian shape and a high-frequency tail. We show that the width of the peak is proportional to q2 for finite magnetic field compared to q3 for a zero field. For the tail we derive an analytic formula without any adjustable parameters and demonstrate that the integrability of the model directly affects the line shape.

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.

Pseudospin ferromagnetism in double-quantum-wire systems

We propose that a pseudospin ferromagnetic (i.e., interwire coherent) state can exist in a system of two parallel wires of finite width in the presence of a perpendicular magnetic field. This novel quantum many-body state appears when the interwire distance decreases below a certain critical value which depends on the magnetic field. We determine the phase boundary of the ferromagnetic phase by analyzing the softening of the spin-mode velocity using the bosonization approach. We also discuss the signatures of this state in tunneling and Coulomb drag experiments.

Phonon-induced resistivity of electron liquids in quantum wires

We study the resistivity of a quantum wire caused by backscattering of electrons by acoustic phonons. In the presence of Coulomb interactions, backscattering is strongly enhanced at low temperatures due to Luttinger liquid effects. Information about the strength of the interactions can be obtained from a measurement of the temperature dependence of the resistivity.

Green's function for magnetically incoherent interacting electrons in one dimension

Using a path integral approach and bosonization, we calculate the low-energy asymptotics of the one particle Green's function for a "magnetically incoherent" one dimensional strongly interacting electron gas at temperatures much greater than the typical exchange energy but much lower than the Fermi energy. The Green's function exhibits features reminiscent of spin-charge separation, with exponential spatial decay and scaling behavior with interaction dependent anomalous exponents inconsistent with any unitary conformal field theory. We compute the tunneling density of states at low energies and find that it is a power law in energy with exponent 1/(4g)-1, where g is the Luttinger interaction parameter in the charge sector. The underlying physics is made transparent by the simplicity of the approach. Our results generalize those of Cheianov and Zvonarev [Phys. Rev. Lett. 92, 176401 (2004)]].