Quantum Reciprocity Conjecture for the Non-Equilibrium Steady State

By considering the lack of history dependence in the non-equilibrium steady state of a quantum system we are led to conjecture that in such a system, there is a set of quantum mechanical observables whose retarded response functions are insensitive to the arrow of time, and which consequently satisfy a quantum analog of the Onsager reciprocity relations. Systems which satisfy this conjecture can be described by an effective Free energy functional. We demonstrate that the conjecture holds in a resonant level model of a multi-lead quantum dot.Comment: References revised to take account of related work on Onsager reciprocity in mesoscopics by Christen, and in hydrodynamics by Mclennan, Dufty and Rub

Perturbative behaviour of a vortex in a trapped Bose-Einstein condensate

We derive a set of equations that describe the shape and behaviour of a single perturbed vortex line in a Bose-Einstein condensate. Through the use of a matched asymptotic expansion and a unique coordinate transform a relation for a vortex's velocity, anywhere along the line, is found in terms of the trapping, rotation, and distortion of the line at that location. This relation is then used to find a set of differential equations that give the line's specific shape and motion. This work corrects a previous similar derivation by Anatoly A. Svidzinsky and Alexander L. Fetter [Phys. Rev. A \textbf{62}, 063617 (2000)], and enables a comparison with recent numerical results.Comment: 12 pages with 3 figure

Offside goals and induced breaches of contract

An analysis of Global Resources Group Ltd v Mackay which explores the possibility of building links between the offside goals rule and nominate delict of inducing breach of contract

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review

The shape and erosion of pebbles

The shapes of flat pebbles may be characterized in terms of the statistical distribution of curvatures measured along their contours. We illustrate this new method for clay pebbles eroded in a controlled laboratory apparatus, and also for naturally-occurring rip-up clasts formed and eroded in the Mont St.-Michel bay. We find that the curvature distribution allows finer discrimination than traditional measures of aspect ratios. Furthermore, it connects to the microscopic action of erosion processes that are typically faster at protruding regions of high curvature. We discuss in detail how the curvature may be reliable deduced from digital photographs.Comment: 10 pages, 11 figure

Stochastic time-dependent current-density functional theory: a functional theory of open quantum systems

The dynamics of a many-body system coupled to an external environment represents a fundamentally important problem. To this class of open quantum systems pertains the study of energy transport and dissipation, dephasing, quantum measurement and quantum information theory, phase transitions driven by dissipative effects, etc. Here, we discuss in detail an extension of time-dependent current-density-functional theory (TDCDFT), we named stochastic TDCDFT [Phys. Rev. Lett. {\bf 98}, 226403 (2007)], that allows the description of such problems from a microscopic point of view. We discuss the assumptions of the theory, its relation to a density matrix formalism, and the limitations of the latter in the present context. In addition, we describe a numerically convenient way to solve the corresponding equations of motion, and apply this theory to the dynamics of a 1D gas of excited bosons confined in a harmonic potential and in contact with an external bath.Comment: 17 pages, 7 figures, RevTex4; few typos corrected, a figure modifie

Herschel observations of EXtra-Ordinary Sources (HEXOS): Methanol as a probe of physical conditions in Orion KL

We have examined methanol emission from Orion KL withthe Herschel/HIFI instrument, and detected two methanol bands centered at 524 GHz and 1061 GHz. The 524 GHz methanol band (observed in HIFI band 1a) is dominated by the isolated ΔJ = 0, K = −4 → −3, v_t = 0 Q branch, and includes 25 E-type and 2 A-type transitions. The 1061 GHz methanol band (observed in HIFI band 4b) is dominated by the ΔJ = 0, K = 7 → 6, v_t = 0 Q branch transitions which are mostly blended. We have used the isolated E-type v_t = 0 methanol transitions to explore the physical conditions in the molecular gas. With HIFI’s high velocity resolution, the methanol emission contributed by different spatial components along the line of sight toward Orion KL (hot core, low velocity flow, and compact ridge) can be distinguished and studied separately. The isolated transitions detected in these bands cover a broad energy range (upper state energy ranging from 80 K to 900 K), which provides a unique probe of the thermal structure in each spatial component. The observations further show that the compact ridge is externally heated. These observations demonstrate the power of methanol lines as probes of the physical conditions in warm regions in close proximity to young stars

Herschel observations of ortho- and para-oxidaniumyl (H_2O^+) in spiral arm clouds toward Sagittarius B2(M)

H_2O^+ has been observed in its ortho- and para- states toward the massive star forming core Sgr B2(M), located close to the Galactic center. The observations show absorption in all spiral arm clouds between the Sun and Sgr B2. The average o/p ratio of H_2O^+ in most velocity intervals is 4.8, which corresponds to a nuclear spin temperature of 21 K. The relationship of this spin temperature to the formation temperature and current physical temperature of the gas hosting H_2O^+ is discussed, but no firm conclusion is reached. In the velocity interval 0–60 km s^(−1), an ortho/para ratio of below unity is found, but if this is due to an artifact of contamination by other species or real is not clear