arXiv subjects

M. Khodas

Publications and source records attributed to M. Khodas.

45 records · Page 3Linked to original sources

arXiv2007

Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions

We evaluate the spectral function of interacting fermions in one dimension. Contrary to the Tomonaga-Luttinger model, our treatment accounts for the nonlinearity of the free fermion spectrum. In a striking departure from the Luttinger liquid theory, the spectrum nonlinearity restores the main feature of the Fermi liquid: a Lorentzian peak in the spectral function on the particle mass-shell. At the same time, the spectral function displays a power-law singularity on the hole mass-shell, similar to that in the Luttinger liquid.

cond-mat.mes-hall↗

arXiv2007

Dynamics of excitations in a one-dimensional Bose liquid

We show that the dynamic structure factor of a one-dimensional Bose liquid has a power-law singularity defining the main mode of collective excitations. Using the Lieb-Liniger model, we evaluate the corresponding exponent as a function of the wave vector and the interaction strength.

cond-mat.stat-mech↗

arXiv2006

Dynamic response of one-dimensional interacting fermions

We evaluate the dynamic structure factor $S(q,ω)$ 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 $S(q,ω)$. The sharp peak $S\propto qδ(ω-uq)$, characteristic for the Tomonaga-Luttinger model, broadens up; $S(q,ω)$ for a fixed $q$ becomes finite at arbitrarily large $ω$. The main spectral weight, however, is confined to a narrow frequency interval of the width $δω\sim q^2/m$. 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 $q$.

cond-mat.mes-hall↗

arXiv2005

Chiral spin resonance and spin-Hall conductivity in the presence of the electron-electron interactions

We discuss the electron spin resonance in two-dimensional electron gas at zero external magnetic field. This spin-resonance is due to the transitions between the electron states, which are split by the spin-orbit (SO) interaction, and is termed as the chiral spin resonance (CSR). It can be excited by the in-plane component of the electric field of microwave radiation. We show that there exists an inherent relationship between the spin-Hall conductivity and the CSR in a system with the SO interaction. Since in the presence of the SO interaction spin is not conserved, the electron-electron interaction renormalizes the spin-Hall conductivity as well as the frequency of the CSR. The effects of the electron interaction in systems with the SO interaction are analyzed both phenomenologically and microscopically.

cond-mat.str-el↗

arXiv2005

Diffuse emission in the presence of inhomogeneous spin-orbit interaction for the purpose of spin filtration

A lateral interface connecting two regions with different strengths of the Bychkov-Rashba spin-orbit interaction can be used as a spin polarizer of electrons in two dimensional semiconductor heterostructures. [Khodas \emph{et al.}, Phys. Rev. Lett. \textbf{92}, 086602 (2004)]. In this paper we consider the case when one of the two regions is ballistic, while the other one is diffusive. We generalize the technique developed for the solution of the problem of the diffuse emission to the case of the spin dependent scattering at the interface, and determine the distribution of electrons emitted from the diffusive region. It is shown that the diffuse emission is an effective way to get electrons propagating at small angles to the interface that are most appropriate for the spin filtration and a subsequent spin manipulation. Finally, a scheme is proposed of a spin filter device, see Fig. 9, that creates two almost fully spin-polarized beams of electrons.

cond-mat.mes-hall↗

arXiv2004

Spin polarization of electrons by non-magnetic heterostructures : basics of spin-optics

We propose to use the lateral interface between two regions with different strengths of the spin-orbit interaction(s) to spin-polarize the electrons in gated two dimensional semiconductor heterostructures. For a beam with a non zero angle of incidence the transmitted electrons will split into two spin polarization components propagating at different angles. We analyze the refraction at such an interface and outline the basic schemes for filtration and control of the electron spin.

cond-mat.mes-hall↗

arXiv2004

Hall Coefficient in an Interacting Electron Gas

The Hall conductivity in a weak homogeneous magnetic field, $ω_{c}τ\ll 1$, is calculated. We have shown that to leading order in $1/ε_{F}τ$ the Hall coefficient $R_{H}$ is not renormalized by the electron-electron interaction. Our result explains the experimentally observed stability of the Hall coefficient in a dilute electron gas not too close to the metal-insulator transition. We avoid the currently used procedure that introduces an artificial spatial modulation of the magnetic field. The problem of the Hall effect is reformulated in a way such that the magnetic flux associated with the scattering process becomes the central element of the calculation.

cond-mat.str-el↗

arXiv2000

Relaxation to the Invariant Density for Kicked Rotor

The relaxation rates to the invariant density in the chaotic phase space component of the kicked rotor (standard map) are calculated analytically for a large stochasticity parameter, $K$. These rates are the logarithms of the poles of the matrix elements of the resolvent, $ \hat{R}(z)=(z-\hat{U})^{-1} $, of the classical evolution operator $\hat{U} $. The resolvent poles are located inside the unit circle. For hyperbolic systems this is a rigorous result, but little is known about mixed systems such as the kicked rotor. In this work, the leading relaxation rates of the kicked rotor are calculated in presence of noise, to the leading order in $1/\sqrt{K}$. Then the limit of vanishing noise is taken and the relaxation rates are found to be finite, corresponding to poles lying inside the unit circle. It is found that the slow relaxation rates, in essence, correspond to diffusion modes in the momentum direction. Faster relaxation modes intermix the motion in the momentum and the angle space. The slowest relaxation rate of distributions in the angle space is calculated analytically by studying the dynamics of inhomogeneities projected down to this space. The analytical results are verified by numerical simulations.

chao-dyn↗

arXiv1999

Relaxation and Diffusion for the Kicked Rotor

The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase space densities in the chaotic component is calculated in presence of noise, and the limit of vanishing noise is taken is taken in the end of calculation. The relaxation rates (related to the Ruelle resonances) to the invariant equilibrium density are calculated analytically within an approximation that improves with increasing stochasticity. The results are tested numerically. The global picture of relaxation to the equilibrium density in the chaotic component when the system is bounded and of diffusive behavior when it is unbounded is presented.

chao-dyn↗