Search

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 and 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 theory. So in the first part of the lectures I will introduce main concepts of the Luttinger liquid based on the functional bosonisation approach. [ABSTRACT FROM AUTHOR]

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analyzing network failures caused by hardware faults or overload, where the network reaction was modeled as rerouting of traffic away from failed or congested elements. Here we model another type of the network reaction to congestion —a sharp reduction of the input traffic rate through congested routes which occurs on much shorter time scales. We consider the onset of congestion in the Internet where local mismatch between demand and capacity results in traffic losses and show that it can be described as a phase transition characterized by strong non-Gaussian loss fluctuations at a mesoscopic time scale. The fluctuations, caused by noise in input traffic, are exacerbated by the heterogeneous nature of the network manifested in a scale-free load distribution. They 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. [ABSTRACT FROM AUTHOR]

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 ∼sin 2Φ. 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. [ABSTRACT FROM AUTHOR]

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, ω, is of the order of (or even slightly smaller than) the mean level spacing, Δ. If ω ⪡ Δ, 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, γ, generated by electron interactions, and it is complementary to the nonperturbative results obtained from a combination of random matrix theory (RMT) and the α-model, valid at γ → 0. Remarkably, we find that the two-loop result for isolated systems with moderately weak dephasing, γ ∼ Δ, is similar to the result of the RMT + σ-model even in the limit ω → 0. For smaller γ, 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. [ABSTRACT FROM AUTHOR]

We study Johnson-Nyquist noise in macroscopically inhomogeneous disordered metals and give a microscopic derivation of the correlation function of the scalar electric potentials in real space. Starting from the interacting Hamiltonian for electrons in a metal and the random phase approximation, we find a relation between the correlation function of the electric potentials and the density fluctuations, which is valid for arbitrary geometry and dimensionality. We show that the potential fluctuations are proportional to the solution of the diffusion equation, taken at zero frequency. As an example, we consider networks of quasi-one-dimensional disordered wires and give an explicit expression for the correlation function in a ring attached via arms to absorbing leads. We use this result in order to develop a theory of dephasing by electronic noise in multiply-connected systems. [ABSTRACT FROM AUTHOR]

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.

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 propose a method of measuring the electron temperature T_{e} in mesoscopic conductors and demonstrate experimentally its applicability to micron-size graphene devices in the linear-response regime (T_{e} approximately T, the bath temperature). The method can be especially useful in case of overheating, T_{e}>T. It is based on analysis of the correlation function of mesoscopic conductance fluctuations. Although the fluctuation amplitude strongly depends on the details of electron scattering in graphene, we show that T_{e} extracted from the correlation function is insensitive to these details.

We introduce a continuum model describing data losses in a single node of a packet-switched network (like the Internet) which preserves the discrete nature of the data loss process. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that such a model exhibits strong fluctuations in the loss rate at the critical point and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process. The continuum model allows for rather general incoming data packet distributions and can be naturally generalized to consider the buffer server idleness statistics.

We suggest to use "fluctuation spectroscopy" as a method to detect granularity in a disordered metal close to a superconducting transition. We show that with lowering temperature T the resistance R(T) of a system of relatively large grains initially grows due to the fluctuation suppression of the one-electron tunneling but decreases with further lowering T due to the coherent charge transfer of the fluctuation Cooper pairs. Under certain conditions, such a maximum in R(T) turns out to be sensitive to weak magnetic fields due to a novel Maki-Thompson-type mechanism.

We suggest a model for data losses in a single node (memory buffer) of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that for a finite-capacity buffer at the critical point the loss rate exhibits strong fluctuations and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process.