Markovian master equations for quantum thermal machines: local vs global approach

The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches.Comment: Published version. See also the related work by J. Onam Gonzalez et al. arXiv:1707.0922

A History of BlockingQueues

This paper describes a way to formally specify the behaviour of concurrent data structures. When specifying concurrent data structures, the main challenge is to make specifications stable, i.e., to ensure that they cannot be invalidated by other threads. To this end, we propose to use history-based specifications: instead of describing method behaviour in terms of the object's state, we specify it in terms of the object's state history. A history is defined as a list of state updates, which at all points can be related to the actual object's state. We illustrate the approach on the BlockingQueue hierarchy from the java.util.concurrent library. We show how the behaviour of the interface BlockingQueue is specified, leaving a few decisions open to descendant classes. The classes implementing the interface correctly inherit the specifications. As a specification language, we use a combination of JML and permission-based separation logic, including abstract predicates. This results in an abstract, modular and natural way to specify the behaviour of concurrent queues. The specifications can be used to derive high-level properties about queues, for example to show that the order of elements is preserved. Moreover, the approach can be easily adapted to other concurrent data structures.Comment: In Proceedings FLACOS 2012, arXiv:1209.169

Observing Brane Inflation

Linking the slow-roll scenario and the Dirac-Born-Infeld scenario of ultra-relativistic roll (where, thanks to the warp factor, the inflaton moves slowly even with an ultra-relativistic Lorentz factor), we find that the KKLMMT D3/anti-D3 brane inflation is robust, that is, enough e-folds of inflation is quite generic in the parameter space of the model. We show that the intermediate regime of relativistic roll can be quite interesting observationally. Introducing appropriate inflationary parameters, we explore the parameter space and give the constraints and predictions for the cosmological observables in this scenario. Among other properties, this scenario allows the saturation of the present observational bound of either the tensor/scalar ratio r (in the intermediate regime) or the non-Gaussianity f_NL (in the ultra-relativistic regime), but not both.Comment: 31 pages, 12 figures; typo correcte

Fluid dynamics of R-charged black holes

We construct electrically charged AdS_5 black hole solutions whose charge, mass and boost-parameters vary slowly with the space-time coordinates. From the perspective of the dual theory, these are equivalent to hydrodynamic configurations with varying chemical potential, temperature and velocity fields. We compute the boundary theory transport coefficients associated with a derivative expansion of the energy momentum tensor and R-charge current up to second order. In particular, we find a first order transport coefficient associated with the axial component of the current.Comment: 31 pages, v2: published version; added some references, discussion of the charge-current changed, results unchanged, v3: typo in formula (15) changed, v4: added footnote 3 in order to clarify the relation of our results to those of arXiv:0809.259

String Loop Corrections to Kahler Potentials in Orientifolds

We determine one-loop string corrections to Kahler potentials in type IIB orientifold compactifications with either N=1 or N=2 supersymmetry, including D-brane moduli, by evaluating string scattering amplitudes.Comment: 80 pages, 4 figure

Galilean type IIA backgrounds and a map

We obtain non-relativistic AdS4 X CP3 solutions with dynamical exponent 3 in type IIA string theory, both with and without Romans mass. The compactifications to four dimensions are found to describe Proca fields in anti-de Sitter spacetime. This leads us to conclude that the massive and massless IIA theories should be identified in four dimensions and the Romans mass should be identified with the `flux' along CP3 in a definite manner. From supergravity point of view, it is suggestive of some four-dimensional symmetry that rotates Romans mass into the flux along CP3. We also provide M-theory Galilean ABJM background which gives rise to the nonrelativistic type IIA solution.Comment: 10 pages;v2: major revisions, errors on supersymmetry corrected and references added; to be published in MPL

Universal properties of thermal and electrical conductivity of gauge theory plasmas from holography

We propose that for conformal field theories admitting gravity duals, the thermal conductivity is fixed by the central charges in a universal manner. Though we do not have a proof as yet, we have checked our proposal against several examples. This proposal, if correct, allows us to express electrical conductivity in terms of thermodynamical quantities even in the presence of chemical potential.Comment: 13 pages, appendix added, close to journal versio

Generalized geometry, calibrations and supersymmetry in diverse dimensions

We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d, preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor equations, that there is a one-to-one correspondence between background supersymmetry equations in pure-spinor form and D-brane generalized calibrations; this correspondence had been known to hold in the d = 4 case. Assuming the correspondence to hold for all d, we list the calibration forms for all admissible D-branes, as well as the background supersymmetry equations in pure-spinor form. We find a number of general features, including the following: The pattern of codimensions at which each calibration form appears exhibits a (mod 4) periodicity. In all cases one of the pure-spinor equations implies that the internal manifold is generalized Calabi-Yau. Our results are manifestly invariant under generalized mirror symmetry.Comment: 28 pages, 1 tabl

Calabi-Yau Fourfolds with Flux and Supersymmetry Breaking

In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of general N=2 gauged supergravities, in the special case where only translational symmetries are gauged. This allows us to extract supersymmetry-breaking conditions, and interpret them as conditions on the 4-form flux and Calabi-Yau geometry. For N=2 unbroken supersymmetry in three dimensions we recover previously known results, and we find a new condition for breaking supersymmetry from N=2 to N=1, i.e. from four to two supercharges. An example of a Calabi-Yau hypersurface in a toric variety that satisfies this condition is provided.Comment: 26 page