Non-trivial classical backgrounds with vanishing quantum corrections

Vacuum polarization and particle production effects in classical electromagnetic and gravitational backgrounds can be studied by the effective lagrangian method. Background field configurations for which the effective lagrangian is zero are special in the sense that the lowest order quantum corrections vanishes for such configurations. We propose here the conjecture that there will be neither particle production nor vacuum polarization in classical field configurations for which all the scalar invariants are zero. We verify this conjecture, by explicitly evaluating the effective lagrangian, for non-trivial electromagnetic and gravitational backgrounds with vanishing scalar invariants. The implications of this result are discussed.Comment: 20 pages, Revtex, Accepted for publication in Physical Review

The eightfold way to dissipation

We provide a complete characterization of hydrodynamic transport consistent with the second law of thermodynamics at arbitrary orders in the gradient expansion. A key ingredient in facilitating this analysis is the notion of adiabatic hydrodynamics, which enables isolation of the genuinely dissipative parts of transport. We demonstrate that most transport is adiabatic. Furthermore, of the dissipative part, only terms at the leading order in gradient expansion are constrained to be sign-definite by the second law (as has been derived before).Comment: 5 pages, 1 figure. v2: minor clarifications. v3: minor changes. title in published version differ

Schwinger-Keldysh formalism II: Thermal equivariant cohomology

Causally ordered correlation functions of local operators in near-thermal quantum systems computed using the Schwinger-Keldysh formalism obey a set of Ward identities. These can be understood rather simply as the consequence of a topological (BRST) algebra, called the universal Schwinger-Keldysh superalgebra, as explained in our companion paper arXiv:1610.01940. In the present paper we provide a mathematical discussion of this topological algebra. In particular, we argue that the structures can be understood in the language of extended equivariant cohomology. To keep the discussion self-contained, we provide a basic review of the algebraic construction of equivariant cohomology and explain how it can be understood in familiar terms as a superspace gauge algebra. We demonstrate how the Schwinger-Keldysh construction can be succinctly encoded in terms a thermal equivariant cohomology algebra which naturally acts on the operator (super)-algebra of the quantum system. The main rationale behind this exploration is to extract symmetry statements which are robust under renormalization group flow and can hence be used to understand low-energy effective field theory of near-thermal physics. To illustrate the general principles, we focus on Langevin dynamics of a Brownian particle, rephrasing some known results in terms of thermal equivariant cohomology. As described elsewhere, the general framework enables construction of effective actions for dissipative hydrodynamics and could potentially illumine our understanding of black holes.Comment: 72 pages; v2: fixed typos. v3: minor clarifications and improvements to non-equilbirum work relations discussion. v4: typos fixed. published versio

Exact Geosedics and Shortest Paths on Polyhedral Surface

We present two algorithms for computing distances along a non-convex polyhedral surface. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimalgeodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.National Institute for Biomedical Imaging and Bioengineering (R01 EB001550

Thermal out-of-time-order correlators, KMS relations, and spectral functions

We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuation-dissipation type relations implied by the KMS condition. These end up relating correlation functions with different time ordering and thus should naturally be viewed in the larger context of out-of-time-ordered (OTO) observables. In particular, eschewing the standard formulation of KMS relations where thermal periodicity is combined with time-reversal to stay within the purview of Schwinger-Keldysh functional integrals, we show that there is a natural way to phrase them directly in terms of OTO correlators. We use these observations to construct a natural causal basis for thermal n-point functions in terms of fully nested commutators. We provide several general results which can be inferred from cyclic orbits of permutations, and exemplify the abstract results using a quantum oscillator as an explicit example.Comment: 36 pages + appendices. v2: minor changes + refs added. v3: minor changes, published versio

Schwinger-Keldysh superspace in quantum mechanics

We examine, in a quantum mechanical setting, the Hilbert space representation of the BRST symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals in coarse-grained systems with dissipation, or in open quantum systems. Operationally, this entails uplifting the standard Schwinger-Keldysh two-copy formalism into superspace by appending BRST ghost degrees of freedom. These statements were previously argued at the level of the correlation functions. We provide herein a complementary perspective by working out the Hilbert space structure explicitly. Our analysis clarifies two crucial issues not evident in earlier works: firstly, certain background ghost insertions necessary to reproduce the correct Schwinger-Keldysh correlators arise naturally. Secondly, the Schwinger-Keldysh difference operators are systematically dressed by the ghost bilinears, which turn out to be necessary to give rise to a consistent operator algebra. We also elaborate on the structure of the final state (which is BRST closed) and the future boundary condition of the ghost fields.Comment: 30 page

Performance Comparison of Symmetric and Offset Reflector Antennas Adaptively Illuminated by Novel Triple Mode Feedhorn

Parabolic symmetric and offset reflector antennas adaptively illuminated using a novel triple-mode feedhorn (TE11+TM01+TE21) with different mode combinations and impedance and radiation performances are presented. The combination of the radiating modes in a feedhorn with proper amplitude and fixed phase values helps in electronically pointing the main beam of the radiating patterns such as that obtained in a beam-steering antenna with limited beam-scan range. This type of radiation performance virtually creates a displaced phase center location for the feedhorn, which, consequently, adaptively illuminates the reflector antenna surface. Impedance-matching bandwidths are preserved for both reflector antennas similar to the case of feedhorn alone. The copolarization gain and peak cross-polarization levels are far better with the offset reflector antenna than the symmetric reflector antenna. Such reflector antennas find applications in ground moving target indicator (GMTI) and space based radars. The investigation results are solely computed using FEKO full-wave analysis tool

Holographic thermal correlators: A tale of Fuchsian ODEs and integration contours

We analyze real-time thermal correlation functions of conserved currents in holographic field theories using the grSK geometry, which provides a contour prescription for their evaluation. We demonstrate its efficacy, arguing that there are situations involving components of conserved currents, or derivative interactions, where such a prescription is, in fact, essential. To this end, we first undertake a careful analysis of the linearized wave equations in AdS black hole backgrounds and identify the ramification points of the solutions as a function of (complexified) frequency and momentum. All the equations we study are Fuchsian with only regular singular points that for the most part are associated with the geometric features of the background. Special features, e.g., the appearance of apparent singular points at the horizon, whence outgoing solutions end up being analytic, arise at higher codimension loci in parameter space. Using the grSK geometry, we demonstrate that these apparent singularities do not correspond to any interesting physical features in higher-point functions. We also argue that the Schwinger-Keldysh collapse and KMS conditions, implemented by the grSK geometry, continue to hold even in the presence of such singularities. For charged black holes above a critical charge, the energy density operator does not possess an exponentially growing mode, associated with `pole-skipping' (from one such apparent singularity). Our analysis suggests that the connection between the scrambling physics of black holes and energy transport has, at best, a limited domain of validity.Comment: 35 pages plus appendice

PHARMACEUTICAL PREPARATION OF HINGULLOTHA PARADA

In Ayurveda Classics Rasaushadhi are prepare from Ashtasanskarita Parada because of its Rasayana guna and therapeutic properties, but it require great patience, time, skill and money hence a way has been given in the literature i.e. Hingulatha parada can be used in place of Astha sunskarita parada. Present study done with the aim of pharmaceutical Standardization of Extraction of Hingullotha Parada & study for usefulness of Hingullotha parada instead of Ashtasanskarita Parada in Ayurveda formulations.In the present study Extraction of Hingullotha Parada done three times then last three Sanskaras were done for Gunavardhana. After extraction of Hingullotha Parada % of yield was 42.61 % that is less it may be because of instrumental error.In Ashtasanskara of Parada last three Sanskar Bodhana, Niyamana & Deepan are having Gunavardhana property. Deepan sanskar improve Boobhuksha (bonding capacity) of Parada. After go through the classics it can be conclude that Hingullotha parada can be use instead of Astasanskarit Parada. And last three Sanskara can be doing for Gunavardhana (improving the Rasayana & Rogashamana property of Parada)