arXiv subjects

D. B. Gutman

Publications and source records attributed to D. B. Gutman.

At least 37 records · Page 2Linked to original sources

arXiv2012

Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion

We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time the density profile develops strong oscillations with a period much larger than the Fermi wave length. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation.

cond-mat.str-el↗

arXiv2012

Luttinger liquids with multiple Fermi edges: Generalized Fisher-Hartwig conjecture and numerical analysis of Toeplitz determinants

It has been shown that solutions of a number of many-body problems out of equilibrium can be expressed in terms of Toeplitz determinants with Fisher-Hartwig (FH) singularities. In the present paper, such Toeplitz determinants are studied numerically. Results of our numerical calculations fully agree with the FH conjecture in an extended form that includes a summation over all FH representations (corresponding to different branches of the logarithms). As specific applications, we consider problems of Fermi edge singularity and tunneling spectroscopy of Luttinger liquid with multiple-step energy distribution functions, including the case of population inversion. In the energy representation, a sum over FH branches produces power-law singularities at multiple edges.

cond-mat.str-el↗

arXiv2011

Cold bosons in the Landauer setup

We consider one dimensional potential trap that connects two reservoirs containing cold Bose atoms. The thermal current and single-particle bosonic Green functions are calculated under non-equilibrium conditions. The bosonic statistics leads to Luttinger liquid state with non-linear spectrum of collective modes. This results in suppression of thermal current at low temperatures and affects the single-particle Green functions.

cond-mat.quant-gas↗

arXiv2011

Many-particle correlations in non-equilibrium Luttinger liquid

We develop an operator-based approach to the problem of Luttinger liquid conductor in a non-equilibrium stationary state. We show that the coherent-state many-body fermionic density matrix as well as all fermionic correlation functions out of equilibrium are given by one-dimensional functional determinants of the Fredholm type. Thus, the model constitutes a remarkable example of a many-body problem where all the correlation functions can be evaluated exactly. On the basis of the general formalism we investigate four-point correlation functions of the fermions coming out of the Luttinger liquid wire. Obtained correlations in the fermionic distribution functions represent the combined effect of interaction and non-equilibrium conditions.

cond-mat.mes-hall↗

arXiv2010

Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants

Non-equilibrium bosonization technique facilitates the solution of a number of important many-body problems out of equilibrium, including the Fermi-edge singularity, the tunneling spectroscopy and full counting statistics of interacting fermions forming a Luttinger liquid. We generalize the method to non-equilibrium hard-core bosons (Tonks-Girardeau gas) and establish interrelations between all these problems. The results can be expressed in terms of Fredholm determinants of Toeplitz type. We analyze the long time asymptotics of such determinants, using Szegő and Fisher-Hartwig theorems. Our analysis yields dephasing rates as well as power-law scaling behavior, with exponents depending not only on the interaction strength but also on the non-equilibrium state of the system.

cond-mat.mes-hall↗

arXiv2010

Full counting statistics of Luttinger liquid conductor

Non-equilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the full counting statistics of the transmitted charge is derived. It is given by Fredholm determinant of the counting operator with a time dependent scattering phase. The result has a form of counting statistics of non-interacting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the non-interacting leads.

cond-mat.str-el↗

arXiv2009

Bosonization of one dimensional fermions out of equilibrium

Bosonization technique for one-dimensional fermions out of equilibrium is developed in the framework of the Keldysh action formalism. We first demonstrate how this approach is implemented for free fermions and for the problem of non-equilibrium Fermi edge singularity. We then employ the technique to study an interacting quantum wire attached to two electrodes with arbitrary energy distributions. The non-equilibrium electron Green functions, which can be measured via tunneling spectroscopy technique and carry the information about energy distribution, zero-bias anomaly, and dephasing, are expressed in terms of functional determinants of single-particle "counting" operators. The corresponding time-dependent scattering phase is found to be intrinsically related to "fractionalization" of electron-hole excitations in the tunneling process and at boundaries with leads. Results are generalized to the case of spinful particles as well to Green functions at different spatial points (relevant to the problem of dephasing in Luttinger liquid interferometers). For double-step distributions, the dephasing rates are oscillatory functions of the interaction strength.

cond-mat.mes-hall↗

arXiv2009

Graphite in the bi-layer regime: in-plane transport

An interplay between the increase in the number of carriers and the decrease in the scattering time is expected to result in a saturation of the in-plane resistivity, $ρ_{ab}$, in graphite above room temperature. Contrary to this expectation, we observe a pronounced increase in $ρ_{ab}$ in the interval between 300 and 900 K. We provide a theory of this effect based on intervalley scattering of charge carriers by high-frequency, graphene-like optical phonons.

cond-mat.mtrl-sci↗

arXiv2009

Bosonization out of equilibrium

We develop a bosonization technique for one-dimensional fermions out of equilibrium. The approach is used to study a quantum wire attached to two electrodes with arbitrary energy distributions. The non-equilibrium electron Green function is expressed in terms of functional determinants of a single-particle``counting'' operator with a time-dependent scattering phase. The result reveals an intrinsic relation of dephasing and energy redistribution in Luttinger-liquids to ``fractionalization'' of electron-hole excitations in the tunneling process and at boundaries with leads.

cond-mat.mes-hall↗

arXiv2009

Tunneling spectroscopy of Luttinger-liquid structures far from equilibrium

We develop a theory of tunneling spectroscopy of interacting electrons in a non-equilibrium quantum wire coupled to reservoirs. The problem is modelled as an out-of-equilibrium Luttinger liquid with spatially dependent interaction. The interaction leads to the renormalization of the tunneling density of states, as well as to the redistribution of electrons over energies. Energy relaxation is controlled by plasmon scattering at the boundaries between regions with different interaction strength, and affects the distribution function of electrons in the wire as well as that of electrons emitted from the interacting regions into non-interacting electrodes.

cond-mat.mes-hall↗

arXiv2008

Non-equilibrium Luttinger liquid: Zero-bias anomaly and dephasing

A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left- and right-movers, yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.

cond-mat.mes-hall↗

arXiv2007

Boson-assisted tunneling in layered metals

A theory for boson-assisted tunneling via randomly distributed resonant states in a layered metals is developed. As particular examples, we consider the electron-phonon interaction and the interaction between localized and conduction electrons. The theory is applied to explain a non-monotonic variation of the out-plane resistivity with temperature observed in quasi-two-dimensional metals.

cond-mat.str-el↗

arXiv2007

Zero bias anomaly out of equilibrium

The non-equilibrium zero bias anomaly (ZBA) in the tunneling density of states of a diffusive metallic film is studied. An effective action describing virtual fluctuations out-of-equilibrium is derived. The singular behavior of the equilibrium ZBA is smoothed out by real processes of inelastic scattering.

cond-mat.mes-hall↗

arXiv2007

Anomalous c-axis transport in layered metals

Transport in metals with strongly anisotropic single-particle spectrum is studied. Coherent band transport in all directions, described by the standard Boltzmann equation, is shown to withstand both elastic and inelastic scattering as long as $E_Fτ\gg 1$. A model of phonon-assisted tunneling via resonant states located in between the layers is suggested to explain a non-monotonic temperature dependence of the c-axis resistivity observed in experiments.

cond-mat.str-el↗

arXiv2006

Modulation theory of quantum tunneling into a Calogero-Sutherland fluid

Quantum hydrodynamics of interacting electrons with a parabolic single particle spectrum is studied using the Calogero-Sutherland model. The effective action and modulation equations, describing evolution of periodic excitations in the fluid, are derived. Applications to the problem of a single electron tunneling into the FQHE edge state are discussed.

cond-mat.mes-hall↗

arXiv2006

Green's Function of Anyons in Calogero Model and Quantum Hydrodynamics

We find that correlation functions at one dimension are crucially affected by the curvature of the bare single particle spectrum. Parabolic curvature leads to two closely related phenomena: the Green's function exhibits oscillation (as a function of the coordinate), while the polarization operator acquires support in part of the frequency-momentum plane. We calculated the Green's function using the WKB approximation for collective variables theory \cite{JevickiSakita}. Within this approach, the single particle Green's function is related to a quantum soliton \cite{Polychronakos}. The finite support of the polarization operator is due to periodic density waves.

cond-mat.mes-hall↗

arXiv2004

Kinetic theory of fluctuations in conducting systems

We propose an effective field theory describing the time dependent fluctuations of electrons in conducting systems, generalizing the well known kinetic theory of fluctuations. On several examples, we show its equivalence, (when quantum corrections are neglected) to a microscopic quantum mechanical non-linear $σ$-model theory. We apply then the theory to analyze the effects of strong electron-electron and electron-phonon scattering on the statistics of current fluctuations. We find that if the electron-electron scattering length is much shorter than the transport mean free path the higher cumulants of current are parametrically enhanced.

cond-mat.mes-hall↗

arXiv2002

High cumulants of current fluctuations out of equilibrium

We consider high order current cumulants in disordered systems out of equilibrium. They are interesting and reveal information which is not easily exposed by the traditional shot noise. Despite the fact that the dynamics of the electrons is classical, the standard kinetic theory of fluctuations needs to be modified to account for those cumulants. We perform a quantum-mechanical calculation using the Keldysh technique and analyze its relation to the quasi classical Boltzmann-Langevin scheme. We also consider the effect of inelastic scattering. Strong electron-phonon scattering renders the current fluctuations Gaussian, completely suppressing the $n>2$ cumulants. Under strong electron-electron scattering the current fluctuations remain non-Gaussian.

cond-mat.mes-hall↗