Finite-temperature conductance of strongly interacting quantum wire with a nuclear spin order

We study the temperature dependence of the electrical conductance of a clean strongly interacting quantum wire in the presence of a helical nuclear spin order. The nuclear spin helix opens a temperature-dependent partial gap in the electron spectrum. Using a bosonization framework we describe the gapped electron modes by sine-Gordon-like kinks. We predict an internal resistivity caused by an Ohmic-like friction these kinks experience via interacting with gapless excitations. As a result, the conductance rises from $G=e^2/h$ at temperatures below the critical temperature when nuclear spins are fully polarized to $G=2e^2/h$ at higher temperatures when the order is destroyed, featuring a relatively wide plateau in the intermediate regime. The theoretical results are compared with the experimental data for GaAs quantum wires obtained recently by Scheller et al. [Phys. Rev. Lett. 112, 066801 (2014)].Comment: 18 pages, 10 figure

Stabilization of the surface CDW order parameter by long-range Coulomb interaction

We study theoretically formation of two-dimensional (2D) charge density wave (CDW) in a system of conducting chains at the surface of an insulator due to interaction of quasi 1D surface electrons with phonons. We show that the unscreened long-range Coloumb interaction between the charges induced by fluctuations of the CDW phase stabilizes the finite order parameter value at finite temperatures, and thus the long-range order (LRO) exists. In the case of screened Coloumb interaction the phase fluctuations suppress the phase transition, but decay of the order parameter is rather slow, it obeys a power-law $\propto r^{-\gamma}$ with small exponent $\gamma

Electronic transport through a contact of a correlated quantum wire with leads of higher dimension

We study theoretically electronic transport through a contact of a quantum wire with 2D or 3D leads and find that if the contact is not smooth and adiabatic then the conduction is strongly suppressed below a threshold voltage $V_T$, while above $V_T$ the dc current $\bar I$ is accompanied by coherent oscillations of frequency $f=\bar I / e$. The effect is related to interelectronic repulsion and interaction of dc current with the Friedel oscillations near a sharp contact. In short conducting channels of length $L < L_0 \simeq \hbar v_F/eV_T$ and at high temperatures $T > T_0 \simeq eV_T/k_B$ the effect is destroyed by fluctuations.Comment: 10 pages, to be published in JETP Letters, vol. 9

A Dynamic Model of Stochastic Innovation Race: Leader-Follower Case

We provide steps towards analysis of rational behaviors of innovators acting on a market of a technological product. The situation when a technological leader competes with a large number of identical followers is in the focus. The process of development of new generations of the product is treated as a Poisson-type cyclic stochastic process. The technology spillovers effect acts as a driving force of the technological progress. We obtain an analytic characterization of optimal leaders R&D and manufacturing investment policies. Numerical simulations and economic interpretations are presented as well

Degeneracy lifting of Majorana bound states due to electron-phonon interactions

We study theoretically how electron-phonon interaction affects the energies and level broadening (inverse lifetime) of Majorana bound states (MBSs) in a clean topological nanowire at low temperatures. At zero temperature, the energy splitting between the right and left MBSs remains exponentially small with increasing nanowire length $L$. At finite temperatures, however, the absorption of thermal phonons leads to the broadening of energy levels of the MBSs that does not decay with system length, and the coherent absorption/emission of phonons at opposite ends of the nanowire results in MBSs energy splitting that decays only as an inverse power-law in $L$. Both effects remain exponential in temperature. In the case of quantized transverse motion of phonons, the presence of Van Hove singularities in the phonon density of states causes additional resonant enhancement of both the energy splitting and the level broadening of the MBSs. This is the most favorable case to observe the phonon-induced energy splitting of MBSs as it becomes much larger than the broadening even if the topological nanowire is much longer than the coherence length. We also calculate the charge and spin associated with the energy splitting of the MBSs induced by phonons. We consider both a spinless low-energy continuum model, which we evaluate analytically, as well as a spinful lattice model for a Rashba nanowire, which we evaluate numerically

The Pontryagin Maximum Principle for Infinite-Horizon Optimal Controls

this paper (motivated by recent works on optimization of long-term economic growth) suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons. We describe an approximation technique involving auxiliary finite-horizon optimal control problems and use it to prove new versions of the Pontryagin maximum principle. A special attention is paid to behavior of the adjoint variables and the Hamiltonian. Typical cases, in which standard transversality conditions hold at infinity, are described. Several significant earlier results are generalized

Lifetime of Majorana qubits in Rashba nanowires with non-uniform chemical potential

We study the lifetime of topological qubits based on Majorana bound states hosted in a one-dimensional Rashba nanowire (NW) with proximity-induced superconductivity and non-uniform chemical potential needed for manipulation and read-out. If nearby gates tune the chemical potential locally so that part of the NW is in the trivial phase, Andreev bound states (ABSs) can emerge which are localized at the interface between topological and trivial phases with energies significantly less than the gap. The emergence of such subgap states strongly decreases the Majorana qubit lifetime at finite temperatures due to local perturbations that can excite the system into these ABSs. Using Keldysh formalism, we study such excitations caused by fluctuating charges in capacitively coupled gates and calculate the corresponding Majorana lifetimes due to thermal noise, which are shown to be much shorter than those in NWs with uniform chemical potential.Comment: 9 pages, 8 figure

Maximum Principle for Infinite-horizon Optimal Control Problems under Weak Regularity Assumptions

The paper deals with first order necessary optimality conditions for a class of infinite-horizon optimal control problems that arise in economic applications. Neither convergence of the integral utility functional nor local boundedness of the optimal control is assumed. Using the classical needle variations technique we develop a normal form version of the Pontryagin maximum principle with an explicitly specified adjoint variable under weak regularity assumptions. The result generalizes some previous results in this direction. An illustrative economical example is presented