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We construct multi-mode viscous hydrodynamics for one dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In a four-mode regime, all modes are ballistic and acquire KPZ-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to $\omega^{-1/3}$ scaling of its real part. In a three-mode regime, the system is in the universality class of classical viscous fluid[9,24]. Self-interaction of the sound modes results in KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to $\omega^{-1/3}$ scaling of heat conductivity., Comment: 6+13 pages

We study thermal conductivity for one-dimensional electronic fluid. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than bosonic Umklapp time, the momentum of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to $T / i\omega$. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by L{\'e}vy flights of low-momentum bosons that lead to a fractional scaling, $\omega^{-\frac{1}{3}}$ and $L^{1/3}$, of heat conductivity with the frequency $\omega$ and system size $L$ respectively., Comment: 14 pages (including Appendix), 4 figures, v2: references added, typos corrected

Dirac materials have unique transport properties, partly due to the presence of surface states. A new type of Dirac materials, protected by non-symmorphic symmetries was recently proposed by Young and Kane [1]. By breaking of time reversal or inversion symmetry one can split the Dirac cones into Weyl nodes. The later are characterized by local Chern numbers, that makes them two-dimensional analogs of Weyl semimetals. We find that the formation of the Weyl nodes is accompanied by an emergence of one-dimensional surface states, similar to Fermi arcs in Weyl semimetals and edge states in two-dimensional graphene. We explore these states for a quasi-one-dimensional non-symmorphic ribbon. The type and strength of applied deformation control the location and Weyl nodes and their composition. This determines the properties of emerging edge states. The sensitivity of these edge states to the external deformations makes non-symmorphic materials potentially useful as a new type of electromechanical sensors., Comment: 9 pages, 8 figures

The interplay between topology and interactions on the edge of a two dimensional topological insulator with time reversal symmetry is studied. We consider a simple non-interacting system of three helical channels with an inherent $\mathbb{Z}_{2}$ topological protection, and hence a zero-temperature conductance of $G=e^2/h$. We show that when interactions are added to the model, the ground state exhibits two different phases as function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the non-interacting topological phase is spontaneously broken. In this phase, there is zero conductance $G=0$ at zero-temperature. The other phase displays enhanced topological properties, with the neutral sector described by a massive version of $\mathbb{Z}_{3}$ parafermions. In this phase, the system at low energies displays an emergent $\mathbb{Z}_3$ symmetry, which is not present in the lattice model, and has a topologically protected zero-temperature conductance of $G=3e^2/h$. This state is an example of a dynamically enhanced symmetry protected topological state., Comment: Extended discussion on disorder, one figure and references added

We study the effect of inelastic processes on the magneto-transport of a quasi-one dimensional Weyl semi-metal, using a modified Boltzmann-Langevin approach. The magnetic field drives a crossover to a ballistic regime in which the propagation along the wire is dominated by the chiral anomaly, and the role of fluctuations inside the sample is exponentially suppressed. We show that inelastic collisions modify the parametric dependence of the current fluctuations on the magnetic field. By measuring shot noise as a function of a magnetic field, for different applied voltage, one can estimate the electron-electron inelastic length $l_{\rm ee}$., Comment: 7 pages, 1 figure

We discuss two one-dimensional model systems -- the first is a single channel quantum wire with Ising anisotropy, while the second is two coupled helical edge states. We show that the two models are governed by the same low energy effective field theory, and interactions drive both systems to exhibit phases which are metallic, but with all single particle excitations gapped. We show that such states may be either topological or trivial; in the former case, the system demonstrates gapless end states, and insensitivity to disorder., Comment: 8 pages, 8 figures

We study wave propagation in interacting Bose liquid, where the short range part of the interaction between atoms is of a hard core type, and its long range part scales with a distance as a power law. The cases of Coulomb, dipole-dipole and Van der Waals interaction are considered. We employ a hydrodynamic approach, based on the exact solution of Lieb-Liniger model, and study the evolution of a density pulse instantly released from a potential trap. We analyze semi-classical Euler and continuity equations and construct the corresponding Riemann invariants. We supplement our analysis with numerical calculations and discuss experimental applications for ultacold atom experiments., Comment: 10 pages, 8 figures

We study quantum manipulation based on four Majorana bound states in X-junction geometry. The parameter space of this setup is bigger than of the previously studied Y-junction and is described by SO(4) symmetry group. In order for quantum computation to be dephasing free, two Majorana states have to stay degenerate at all times. We find a condition necessary for that and compute the Berry's phase, $2\alpha$, accumulated during the manipulation. We construct simple protocols for the variety of values of $\alpha$, including $\pi/8$ needed for the purposes of quantum computation. Although the manipulations in general X-junction geometry are not topologically protected, they may prove to be a feasible compromise for aims of quantum computation., Comment: 6 pages, 4 figures

We consider two coupled time reversal invariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the low energy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges. We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is non-zero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intra-edge interaction is stronger than the inter-edge interaction, the state is characterised as a spin-nematic phase. However in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spin-density wave forms, with emergent topological properties. Firstly, the gap protects the conducting phase against localization by weak nonmagnetic impurities; and secondly the protected phase hosts localized zero modes on ends of the edge that may be created by sufficiently strong non-magnetic impurities., Comment: 9 pages, 6 figures

We study the heat conductivity in Anderson insulators in the presence of power-law interaction. Particle-hole excitations built on localized electron states are viewed as two-level systems randomly distributed in space and energy and coupled due to electron-electron interaction. A small fraction of these states form resonant pairs that in turn build a complex network allowing for energy propagation. We identify the character of energy transport through this network and evaluate the thermal conductivity. For physically relevant cases of 2D and 3D spin systems with $1/r^3$ dipole-dipole interaction (originating from the conventional $1/r$ Coulomb interaction between electrons), the found thermal conductivity $\kappa$ scales with temperature as $\kappa\propto T^3 $ and $\kappa\propto T^{4/3}$, respectively. Our results may be of relevance also to other realizations of random spin Hamiltonians with long-range interactions., Comment: 22 pages, 7 figures, extended and revised version published in Phys. Rev. B

Zero-dimensional dissipative action possesses non-trivial minima known as Korshunov instantons. They have been known so far only for imaginary time representation that is limited to equilibrium systems. In this work we reconstruct and generalise Korshunov instantons using real-time Keldysh approach. This allows us to formulate the dissipative action theory for generic non-equilibrium conditions. Possible applications of the theory to transport in strongly biased quantum dots are discussed.., Comment: 6 pages, 2 figures

We use a novel technique to experimentally explore transport properties through a single metallic nanoparticle with variable coupling to electric leads. For strong dot-lead coupling the conductance is an oscillatory function of the gate voltage with periodicity determined by the charging energy, as expected. For weaker coupling we observe the appearance of additional multi-periodic oscillations of the conductance with the gate voltage. These harmonics correspond to a change of the charge on the dot by a fraction of an electron. This notion is supported by theoretical calculations based on dissipative action theory. Within this framework the multiple periodicity of the conductance oscillations arises due to non-pertubative instanton solutions., Comment: 4 pages, 5 figures

Anderson's localization on the edge of two dimensional time reversal (TR) topological insulator (TI) is studied. For the non-interacting case the topological protection acts accordingly to the $\mathbb{Z}_2$ classification, leading to conducting and insulating phases for odd and even fillings respectively. In the presence of repulsive interaction the phase diagram is notably changed. We show that for sufficiently strong values of the interaction the zero temperature fixed point of the TI is conducting, including the case of even fillings. We compute the boundaries of the conducting phase for various fillings and types of disorder., Comment: 6 pages, 4 figures, discussion about multiparticle processes added. Published version

The sliding Luttinger liquids (LL) approach is applied to study fractional topological insulators (FTI). We show that FTI is the low energy fixed point of the theory for realistic spin-orbit and electron-electron interaction. We find that the topological phase pertains in the presence of interaction that breaks the spin invariance and its boundaries are even extended by those terms. Finally we show that one dimensional chiral anomaly in the LL leads to the emergence of topological Chern-Simons terms in the effective gauge theory of the FTI state., Comment: 15 pages, 6 figures. Changes in style. Supplementary material expanded. Added references

We explore the weak-strong-coupling Bose-Fermi duality in a model of a single-channel integer or fractional quantum Hall edge state with a finite-range interaction. The system is described by a chiral Luttinger liquid with non-linear dispersion of bosonic and fermonic excitations. We use the bosonization, a unitary transformation, and a refermionization to map the system onto that of weakly interacting fermions at low temperature $T$ or weakly interacting bosons at high $T$. We calculate the equilibration rate which is found to scale with temperature as $T^5$ and $T^{14}$ in the high-temperature ("bosonic") and the low-temperature ("fermonic") regimes, respectively. The relaxation rate of a hot particle with the momentum $k$ in the fermonic regime scales as $k^7T^7$., Comment: 9 pages, 2 figures

We explore the life time of excitations in a dispersive Luttinger liquid. We perform a bosonization supplemented by a sequence of unitary transformations that allows us to treat the problem in terms of weakly interacting quasiparticles. The relaxation described by the resulting Hamiltonian is analyzed by bosonic and (after a refermionization) by fermionic perturbation theory. We show that the the fermionic and bosonic formulations of the problem exhibit a remarkable strong-weak-coupling duality. Specifically, the fermionic theory is characterized by a dimensionless coupling constant $\lambda= m^*l^2T$ and the bosonic theory by $\lambda^{-1}$, where $1/m^*$ and $l$ characterize the curvature of the fermionic and bosonic spectra, respectively, and $T$ is the temperature., Comment: 15 page, 2 Figures; manuscript unchanged; misprint in metadata corrected

We study the problem of evolution of a density pulse of one-dimensional interacting fermions with a non-linear single-particle spectrum. We show that, despite non-Fermi-liquid nature of the problem, non-equilibrium phenomena can be described in terms of a kinetic equation for certain quasiparticles related to the original fermions by a non-linear transformation which decouples the left- and right-moving excitations. Employing this approach, we investigate the kinetics of the phase space distribution of the quasiparticles and thus determine the time evolution of the density pulse. This allows us to explore a crossover from the essentially free-fermion evolution for weak or short-range interaction to hydrodynamics emerging in the case of sufficiently strong, long-range interaction., Comment: 4+ pages, supplementary materials are attached as appendix

We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants ${\rm det}(1+\hat{A}\hat{B})$, where $A(\epsilon)$ and $B(t)$ have multiple discontinuities in energy and time spaces. Such determinants are a generalization of Toeplitz determinants with Fisher-Hartwig singularities. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish non-equilibrium power-law singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing correlations between left- and right-moving fermions that have left the interaction region., Comment: 4 pages + Supplemental material as appendix

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., Comment: 20 pages, 13 figures

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., Comment: 14 page, 33 figures

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., Comment: 10 pages, 6 figures

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., Comment: 23 pages,7 figures

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 Szeg\H{o} 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., Comment: 13 pages, 3 figures

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., Comment: 5 pages, 2 figures

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., Comment: 24 pages, 9 figures

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., Comment: 5 pages, 4 figures

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, $\rho_{ab}$, in graphite above room temperature. Contrary to this expectation, we observe a pronounced increase in $\rho_{ab}$ 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., Comment: 5 pages, 2 fig

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., Comment: 11 pages, 4 figures

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., Comment: 5 pages, 2 figures

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., Comment: 14 pages, 5 figures

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., Comment: 4 pages

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 $E_F\tau\gg 1$. 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., Comment: 5 pages 2 figures

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.

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.

We present a vector field method for obtaining the spatial organization of 3D patterns of gene expression based on gradients and lines of force obtained by numerical integration. The convergence of these lines of force in local maxima are centers of gene expression, providing a natural and powerful framework to characterize the organization and dynamics of biological structures. We apply this novel methodology to analyze the expression pattern of the Enhanced Green Fluorescent Protein (EGFP) driven by the promoter of light chain myosin II during zebrafish heart formation., Comment: 9 pages, 2 figures, The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.org

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 $\sigma$-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., Comment: 6 pages, 2 figures

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., Comment: 15 pages, Latex, 3fig (eps). To be published in "Quantum Noise", edited by Yu. V. Nazarov and Ya. M. Blanter (Kluwer)

We consider the possibility of measuring non-equilibrium properties of the current correlation functions at high temperatures (and small bias). Through the example of the third cumulant of the current (${\cal{S}}_3$) we demonstrate that odd order correlation functions represent non-equilibrium physics even at small external bias and high temperatures. We calculate ${\cal{S}}_3=y(eV/T) e^2 I$ for a quasi-one-dimensional diffusive constriction. We calculate the scaling function $y$ in two regimes: when the scattering processes are purely elastic and when the inelastic electron-electron scattering is strong. In both cases we find that $y$ interpolates between two constants. In the low (high) temperature limit $y$ is strongly (weakly) enhanced (suppressed) by the electron-electron scattering., Comment: 11 pages 4 fig. submitted to Phys. Rev. B

We study current correlation functions in a diffusive junction out of equilibrium. We calculate corrections to the electric current and to the zero frequency shot noise due to electron-electron interactions. Contrary to the equilibrium situation (where the corrections to the current and to the current noise are related through the fluctuation-dissipation theorem (FDT)), these two quantities behave differently: the correction to the electron current are governed by the largest of temperature and applied voltage, while the correction to the shot noise is always governed by the temperature. PACS Nos. 71.10.Ay, 71.23.An, 73.50.Td

We employ a non-linear sigma model defined on a Keldysh contour to study the current and the current noise in a diffusive micro-bridge in the presence of electron-electron interactions. Out of equilibrium the fluctuation-dissipation theorem (FDT) does not apply, hence these two quantities are not simply interrelated. For a two-dimensional electron gas (2DEG) we obtain logarithmic singularities in the low frequency limit. PACS Nos. 71.10.Ay, 71.23.An, 73.50.Td, Comment: Submitted to the proceedings of 36 Renconters de Moriond "Electronic correlations: from meso- to nano-physics". One figure added

For a short-correlated Gaussian velocity field the problem of a passive scalar with the imposed constant gradient is considered. It is shown that the scaling of three-point correlation function is anomalous. In the limit of large dimension of space $d$ anomalous exponent is calculated., Comment: 3 pages, RevTeX 3.0