Hysteresis in one-dimensional reaction-diffusion systems

We introduce a simple nonequilibrium model for a driven diffusive system with nonconservative reaction kinetics which exhibits ergodicity breaking and hysteresis in one dimension. These phenomena can be understood through a description of the dominant stochastic many-body dynamics in terms of an equilibrium single-particle problem, viz. the random motion of a shock in an effective potential. This picture also leads to the exact phase diagram of the system and suggests a new generic mechanism for "freezing by heating".Comment: 4 Pages, 5 figure

Condensation in the zero range process: stationary and dynamical properties

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.Comment: 22 pages, 4 figures, to appear in J. Stat. Phys.; improvement of presentation and content of Theorem 2, added reference

Coupled NASTRAN/boundary element formulation for acoustic scattering

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells

Superradiance-like Electron Transport through a Quantum Dot

We theoretically show that intriguing features of coherent many-body physics can be observed in electron transport through a quantum dot (QD). We first derive a master equation based framework for electron transport in the Coulomb-blockade regime which includes hyperfine (HF) interaction with the nuclear spin ensemble in the QD. This general tool is then used to study the leakage current through a single QD in a transport setting. We find that, for an initially polarized nuclear system, the proposed setup leads to a strong current peak, in close analogy with superradiant emission of photons from atomic ensembles. This effect could be observed with realistic experimental parameters and would provide clear evidence of coherent HF dynamics of nuclear spin ensembles in QDs.Comment: 21 pages, 10 figure

Hybrid Architecture for Engineering Magnonic Quantum Networks

We show theoretically that a network of superconducting loops and magnetic particles can be used to implement magnonic crystals with tunable magnonic band structures. In our approach, the loops mediate interactions between the particles and allow magnetic excitations to tunnel over long distances. As a result, different arrangements of loops and particles allow one to engineer the band structure for the magnonic excitations. Furthermore, we show how magnons in such crystals can serve as a quantum bus for long-distance magnetic coupling of spin qubits. The qubits are coupled to the magnets in the network by their local magnetic-dipole interaction and provide an integrated way to measure the state of the magnonic quantum network.Comment: Manuscript: 4 pages, 3 figures. Supplemental Material: 9 pages, 4 figures. V2: Published version in PRA: 14 pages + 8 figures. Substantial rearrangement of the content of the previous versio

Nuclear Spin Dynamics in Double Quantum Dots: Multi-Stability, Dynamical Polarization, Criticality and Entanglement

We theoretically study the nuclear spin dynamics driven by electron transport and hyperfine interaction in an electrically-defined double quantum dot (DQD) in the Pauli-blockade regime. We derive a master-equation-based framework and show that the coupled electron-nuclear system displays an instability towards the buildup of large nuclear spin polarization gradients in the two quantum dots. In the presence of such inhomogeneous magnetic fields, a quantum interference effect in the collective hyperfine coupling results in sizable nuclear spin entanglement between the two quantum dots in the steady state of the evolution. We investigate this effect using analytical and numerical techniques, and demonstrate its robustness under various types of imperfections.Comment: 35 pages, 19 figures. This article provides the full analysis of a scheme proposed in Phys. Rev. Lett. 111, 246802 (2013). v2: version as publishe

Boundary-induced bulk phase transition and violation of Fick's law in two-component single-file diffusion with open boundaries

We study two-component single-file diffusion inside a narrow channel that at its ends is open and connected with particle reservoirs. Using a two-species version of the symmetric simple exclusion process as a model, we propose a hydrodynamic description of the coarse-grained dynamics with a self-diffusion coefficient that is inversely proportional to the length of the channel. The theory predicts an unexpected nonequilibrium phase transition for the bulk particle density as the external total density gradient between the reservoirs is varied. The individual particle currents do not in general satisfy Fick's first law. These results are confirmed by extensive dynamical Monte-Carlo simulations for equal diffusivities of the two components.Comment: 12 pages, 3 figure

Wigner crystals in two-dimensional transition-metal dichalcogenides: Spin physics and readout

Wigner crystals are prime candidates for the realization of regular electron lattices under minimal requirements on external control and electronics. However, several technical challenges have prevented their detailed experimental investigation and applications to date. We propose an implementation of two-dimensional electron lattices for quantum simulation of Ising spin systems based on self-assembled Wigner crystals in transition-metal dichalcogenides. We show that these semiconductors allow for minimally invasive all-optical detection schemes of charge ordering and total spin. For incident light with optimally chosen beam parameters and polarization, we predict a strong dependence of the transmitted and reflected signals on the underlying lattice periodicity, thus revealing the charge order inherent in Wigner crystals. At the same time, the selection rules in transition-metal dichalcogenides provide direct access to the spin degree of freedom via Faraday rotation measurements.Comment: 15 pages, 12 figure