In recent experiments on conductance of one-dimensional (1D) channels in ultra-clean samples, a diverse set of plateaus were found at fractions of the quantum of conductance in zero magnetic field. We consider a discrete model of strongly interacting electrons in a clean 1D system where the current between weak tunneling contacts is carried by fractionally charged solutions. While in the spinless case conductance remains unaffected by the interaction, as is typical for the strongly interacting clean 1D systems, we demonstrate that in the spinful case the peak conductance takes fractional values that depend on the filling factor of the 1D channel.

We consider how the absence of thermalization affects the classical Coulomb blockade regime in quantum dots. By solving the quantum kinetic equation in the experimentally accessible regime when the dot has two relevant occupation states, we calculate the current-voltage characteristics for arbitrary coupling to the leads. If the couplings are strongly asymmetric, the Coulomb staircase is practically reduced to the first step, which is independent of the charging energy, when the Fermi energy is comparatively small, while the standard thermalized results are recovered in the opposite case. When the couplings are of the same order, the absence of thermalization has a new, striking signature-a robust additional peak in the differential conductance.

We investigate the Coulomb blockade in quantum dots asymmetrically coupled to the leads for an arbitrary voltage bias focusing on the regime where electrons do not thermalise during their dwell time in the dot. By solving the quantum kinetic equation, we show that the current-voltage characteristics are crucially dependent on the ratio of the Fermi energy to charging energy on the dot. In the standard regime when the Fermi energy is large, there is a Coulomb staircase which is practically the same as in the thermalised regime. In the opposite case of the large charging energy, we identify a new regime in which only one step is left in the staircase, and we anticipate experimental confirmation of this finding.

We investigate nonequilibrium transport properties of a quantum dot in the Coulomb blockade regime under the condition of negligible inelastic scattering during the dwelling time of the electrons in the dot. Using the quantum kinetic equation we show that the absence of thermalization leads to a double step in the distribution function of electrons on the dot, provided that it is symmetrically coupled to the leads. This drastically changes nonlinear transport through the dot resulting in an additional (compared to the thermalized case) jump in the conductance at voltages close to the charging energy, which could serve as an experimental manifestation of the absence of thermalization.

In order to observe many-body localisation in electronic systems, decoupling from the lattice phonons is required, which is possible only in out-of-equilibrium systems. We show that such an electron-phonon decoupling may happen in suspended films and it manifests itself via a bistability in the electron temperature. By studying the electron-phonon cooling rate in disordered, suspended films with two-dimensional phonons, we derive the conditions needed for such a bistability, which can be observed experimentally through hysteretic jumps of several orders of magnitude in the nonlinear current-voltage characteristics. We demonstrate that such a regime is achievable in systems with an Arrhenius form of the equilibrium conductivity, while practically unreachable in materials with Mott or Efros-Shklovskii hopping.

Quantum correlations between parts of a composite system most clearly reveal themselves through entanglement. Designing, maintaining, and controlling entangled systems is very demanding, which raises the stakes for understanding the efficacy of entanglement-free, yet quantum, correlations, exemplified by quantum discord. Discord is defined via conditional mutual entropies of parts of a composite system, and its direct measurement is hardly possible even via full tomographic characterization of the system state. Here we design a simple protocol to detect quantum discord and characterize a discorded state in an unentangled bipartite system. Our protocol is based on an electronic setup and relies on a characteristic of discord that can be extracted from repeated direct measurements of current correlations between subsystems. The proposed protocol opens a way of extending experimental studies of discord to many-body condensed matter systems.

Quantum correlations between parts of a composite system most clearly reveal themselves through entanglement. Designing, maintaining, and controlling entangled systems is very demanding, which raises the stakes for understanding the efficacy of entanglement-free, yet quantum correlations, exemplified by quantum discord. Discord is defined via conditional mutual entropies of parts of a composite system and its direct measurement is hardly possible even via full tomographic characterization of the system state. Here we design a simple protocol to detect and quantify quantum discord in an unentangled bipartite system. Our protocol relies on a characteristic of discord that can be extracted from repeated direct measurements of certain correlations between subsystems of the bipartite system. The proposed protocol opens a way of extending experimental studies of discord to electronic systems, but can also be implemented in quantum-optical systems.

Advances in cooling and trapping of atoms have enabled unprecedented experimental control of many-body quantum systems. This led to the observation of numerous quantum phenomena, important for fundamental science, indispensable for high-precision simulations of condensed-matter systems and promising for technological applications. However, transport measurements in neutral quantum gases are still in their infancy in contrast to the central role they play in electronics. In these lectures, after reviewing nascent experiments on quantum fermionic transport, I will focus on our theoretical prediction sand the possibility of experimental observations of qualitatively new phenomena in transport of ultracold bosons which do not have a direct counterpart in quantum electronic transport in condensed matter systems. The description of this transport is based on the Luttinger liquid (LL) theory. So in the first part of the lectures I will introduce main concepts of the LL based on the functional bosonisation approach.

We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays in the absence of a magnetic field. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or 'Coulomb-blockade' type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling of repulsive fermions (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire forward scattering interaction.

We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled onedimensional quantum wires packed in twoor three-dimensional arrays. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or “Coulombblockade” type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire interaction. Introduction. – The Luttinger liquid (LL) describes one-dimensional interacting systems with a linear (or linearised) spectrum [1–3]. The interaction strongly enhances the impact of impurities leading to a zerotemperature metal-insulator transition in the presence of either disorder [4] or even a single impurity [5, 6], both being described by the renormalisation group (RG) approach. Progress in the fabrication of low-dimensional nanostructures based on carbon nanotubes [7–10], semiconductor and metallic nanowires [11, 12], self-assembled DNA scaffolds [13, 14], etc., revived the interest to theoretical studies of the LL superstructures. Theoretically, the most challenging bunch of problems in this field is the crossover from the 1D LL behaviour of an individual metallic wire to a 2D or 3D Fermi-liquid (FL) behaviour of ensembles of coupled 1D wires. Such finite systems may support various topological states with gapless modes propagating through the edge wires [15]. It is known that the inter-wire electron tunnelling is a relevant perturbation which results in the transition from the LL to FL phase [16, 17]. Nevertheless, the LL fixed point remains (under proper conditions) stable in a phase of the sliding Luttinger liquid (SLL) [18–23]. In this phase, the canonic phase – density variables (φj , θj) describing bosonised degrees of freedom in each wire j are invariant under the constant shifts. The phase remains stable as long as three distinct inter-wire processes are all RG irrelevant. Namely, these processes are the single-particle inter-wire tunnelling (SP), the particle-hole hopping that may result in a transverse charge density wave (CDW), and the two-particle hopping resulting in a superconducting (SC) state. The SP perturbation becomes irrelevant when a spin gap appears due to an intra-wire large-angle spin-flip scattering relevant for the positive Luttinger parameter, K0 > 0, in a single wire, or for K(q⊥) > 0 in an array (the Luther-Emery regime [17,24,25]). Then the stability of the SLL fixed point would be ensured if the remaining SC and CDW perturbations also become irrelevant [21,22]. In the region where K(q⊥) < 0 the large-angle scattering is irrelevant, the gap does not appear and we deal with a spinful LL unless an in-plane magnetic field is applied [23]. Then the system becomes effectively spinless, but the SP processes are not necessarily irrelevant. Then all three p-1 ar X iv :1 71 1. 01 63 9v 1 [ co nd -m at .s tr -e l] 5 N ov 2 01 7

Igor V. Yurkevich, 2, 3, 4 Alexey Galda, 5 Oleg M. Yevtushenko, 3 and Igor V. Lerner 3 Nonlinearity and Complexity Research Group, Aston University, Birmingham B4 7ET, United Kingdom School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom The Abdus Salam International Centre for Theoretical Physics, P.O. Box 586, 34100 Trieste, Italy Institut für Nanotechnologie, Karlsruhe Institute of Technology, D-76021 Karlsruhe, Germany Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA Arnold Sommerfeld Center and Center for Nano-Science, Ludwig Maximilians University, Munich, DE-80333, Germany

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We investigate the stability of conducting and insulating phases in multichannel Luttinger liquids with respect to embedding a single impurity. We devise a general approach for finding critical exponents of the conductance in the limits of both weak and strong scattering. In contrast to the one-channel Luttinger liquid, the system state in certain parametric regions depends on the scattering strength which results in the emergence of a bistability. Focusing on the two-channel liquid, the method developed here enables us to provide a generic analysis of phase boundaries governed by the most relevant (i.e., not necessarily single-particle) scattering mechanism. The present approach is applicable to channels of different nature as in fermion-boson mixtures, or to identical ones as on the opposite edges of a topological insulator. We show that interaction per se cannot provide protection in the particular case of topological insulators realized in narrow Hall bars.

We study the phase transition between conducting and insulating states taking place in disordered multichannel Luttinger liquids with interchannel interactions. We derive renormalization-group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii-Kosterlitz-Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interaction results in a variety of phases, expected to be observable at intermediate temperatures where the interaction and disorder are relevant but weak hybridization and the charge-density-wave interaction may be ignored.

We study the behavior of ultracold bosonic gases in the critical region above the Bose-Einstein condensation in the presence of an artificial magnetic field, B-art. We show that the condensate fluctuations above the critical temperature T-c cause the fluctuational susceptibility, chi(fl), of a uniform gas to have a stronger power-law divergence than in an analogous superconducting system. Measuring such a divergence opens new ways of exploring critical properties of ultracold gases and an opportunity for an accurate determination of T-c. We describe a method of measuring chi(fl) which requires a constant gradient in B-art and suggest a way of creating such a field in experiment.

The Hong-Ou-Mandel (HOM) effect is widely regarded as the quintessential quantum interference phenomenon in optics. In this work we examine how nonlinearity can smear statistical photon bunching in the HOM interferometer. We model both the nonlinearity and a balanced beam splitter with a single two-level system and calculate a finite probability of anti-bunching arising in this geometry. We thus argue that the presence of such nonlinearity would reduce the visibility in the standard HOM setup, offering some explanation for the diminution of the HOM visibility observed in many experiments. We use the same model to show that the nonlinearity affects a resonant two-photon propagation through a two-level impurity in a waveguide due to a "weak photon blockade" caused by the impossibility of double-occupancy and argue that this effect might be stronger for multi-photon propagation.

We study a flow of ultracold bosonic atoms through a one-dimensional channel that connects two macroscopic three-dimensional reservoirs of Bose-condensed atoms via weak links implemented as potential barriers between each of the reservoirs and the channel. We consider reservoirs at equal chemical potentials so that a superflow of the quasicondensate through the channel is driven purely by a phase difference 2Φ imprinted between the reservoirs. We find that the superflow never has the standard Josephson form ∼sin2Φ. Instead, the superflow discontinuously flips direction at 2Φ=±π and has metastable branches. We show that these features are robust and not smeared by fluctuations or phase slips. We describe a possible experimental setup for observing these phenomena.

We study the quantum corrections to the polarizability of isolated metallic mesoscopic systems using the loop expansion in diffusive propagators. We show that the difference between connected (grand-canonical ensemble) and isolated (canonical ensemble) systems appears only in subleading terms of the expansion, and can be neglected if the frequency of the external field, omega, is of the order of (or even slightly smaller than) the mean level spacing, Delta. If omega << Delta, the two-loop correction becomes important. We calculate it by systematically evaluating the ballistic parts (the Hikami boxes) of the corresponding diagrams and exploiting electroneutrality. Our theory allows one to take into account a finite dephasing rate, gamma, generated by electron interactions, and it is complementary to the nonperturbative results obtained from a combination of random matrix theory (RMT) and the sigma-model, valid at gamma -> 0. Remarkably, we find that the two-loop result for isolated systems with moderately weak dephasing, gamma similar to Delta, is similar to the result of the RMT+ sigma-model even in the limit omega -> 0. For smaller gamma, we discuss the possibility to interpolate between the perturbative and the nonperturbative results. We compare our results for the temperature dependence of the polarizability of isolated rings to the experimental data of Deblock et al. [Phys. Rev. Lett. 84, 5379 (2000); Phys. Rev. B 65, 075301 (2002)], and we argue that the elusive 0D regime of dephasing might have manifested itself in the observed magneto-oscillations. Besides, we thoroughly discuss possible future measurements of the polarizability, which could aim to reveal the existence of 0D dephasing and the role of the Pauli blocking at small temperatures.

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analysing network failures caused by hardware faults or overload. There network reaction was modelled as rerouting of traffic away from failed or congested elements. Here we model network reaction to congestion on much shorter time scales when the input traffic rate through congested routes is reduced. As an example we consider the Internet where local mismatch between demand and capacity results in traffic losses. We describe the onset of congestion as a phase transition characterised by strong, albeit relatively short-lived, fluctuations of losses caused by noise in input traffic and exacerbated by the heterogeneous nature of the network manifested in a power-law load distribution. The fluctuations may result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible.