423 research outputs found
Relating Green's Functions in Axial and Lorentz Gauges using Finite Field-Dependent BRS Transformations
We use finite field-dependent BRS transformations (FFBRS) to connect the
Green functions in a set of two otherwise unrelated gauge choices. We choose
the Lorentz and the axial gauges as examples. We show how the Green functions
in axial gauge can be written as a series in terms of those in Lorentz gauges.
Our method also applies to operator Green's functions. We show that this
process involves another set of related FFBRS transfomations that is derivable
from infinitesimal FBRS. We suggest possible applications.Comment: 20 pages, LaTex, Section 4 expanded, typos corrected; last 2
references modified; (this) revised version to appear in J. Math. Phy
Relating the generating functionals in field/antifield formulation through finite field dependent BRST transformation
We study the field/antifield formulation of pure Yang Mills theory in the
framework of finite field dependent BRST transformation. We show that the
generating functionals corresponding to different solutions of quantum master
equation are connected through the finite field dependent BRST transformations.
We establish this result with the help of several explicit examples.Comment: Revtex4, 18 pages, No figs, Accepted in Eur. Phys. J
Superfield approach to symmetry invariance in QED with complex scalar fields
We show that the Grassmannian independence of the super Lagrangian density,
expressed in terms of the superfields defined on a (4, 2)-dimensional
supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST)
and anti-BRST invariance of the corresoponding four (3 + 1)-dimensional (4D)
Lagrangian density that describes the interaction between the U(1) gauge field
and the charged complex scalar fields. The above 4D field theoretical model is
considered on a (4, 2)-dimensional supermanifold parametrized by the ordinary
four spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of
Grassmannian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0,
\theta \bar\theta + \bar\theta \theta = 0). Geometrically, the (anti-)BRST
invariance is encoded in the translation of the super Lagrangian density along
the Grassmannian directions of the above supermanifold such that the outcome of
this shift operation is zero.Comment: LaTeX file, 14 pages, minor changes in the title and text, version to
appear in ``Pramana - Journal of Physics'
New Light on the Unresolved Problem of Megalithic Habitation Sites in Kerala
This paper is intended to evaluate one of the major research problems in Kerala Archaeology, the absence of a habitation site in the Megalithic (Iron Age Early Historic period) context. Although a number of Megalithic sites have been reported from Kerala, the absence of habitation remains as a lacuna to understand the entire cultural processes of this period. Recent investigations conducted in the eastern fringes of Kerala brought to light habitation evidences associated with burials. This paper discusses problems and misconceptions related to the Megalithic habitation in Kerala on the basis of recent discoveries
PT-symmetry from Lindblad dynamics in a linearized optomechanical system
We analyze a lossy linearized optomechanical system in the red-detuned regime under the rotating wave approximation. This so-called optomechanical state transfer protocol provides effective lossy frequency converter (quantum beam-splitter-like) dynamics where the strength of the coupling between the electromagnetic and mechanical modes is controlled by the optical steady-state amplitude. By restricting to a subspace with no losses, we argue that the transition from mode-hybridization in the strong coupling regime to the damped-dynamics in the weak coupling regime, is a signature of the passive parity-time (PT) symmetry breaking transition in the underlying non-Hermitian quantum dimer. We compare the dynamics generated by the quantum open system (Langevin or Lindblad) approach to that of the PT-symmetric Hamiltonian, to characterize the cases where the two are identical. Additionally, we numerically explore the evolution of separable and correlated number states at zero temperature as well as thermal initial state evolution at room temperature. Our results provide a pathway for realizing non-Hermitian Hamiltonians in optomechanical systems at a quantum level
Numerical approach to the Schrodinger equation in momentum space
The treatment of the time-independent Schrodinger equation in real-space is
an indispensable part of introductory quantum mechanics. In contrast, the
Schrodinger equation in momentum space is an integral equation that is not
readily amenable to an analytical solution and is rarely taught. We present a
numerical approach to the Schrodinger equation in momentum space. After a
suitable discretization process, we obtain the Hamiltonian matrix and
diagonalize it numerically. By considering a few examples, we show that this
approach is ideal for exploring bound-states in a localized potential and
complements the traditional (analytical or numerical) treatment of the
Schrodinger equation in real-space.Comment: 14 pages, 4 figures, several changes and one figure correctio
GYM: A Multiround Distributed Join Algorithm
Multiround algorithms are now commonly used in distributed data processing systems, yet the extent to which algorithms can benefit from running more rounds is not well understood. This paper answers this question for several rounds for the problem of computing the equijoin of n relations. Given any query Q with width w, intersection width iw, input size IN, output size OUT, and a cluster of machines with M=Omega(IN frac{1}{epsilon}) memory available per machine, where epsilon > 1 and w ge 1 are constants, we show that:
1. Q can be computed in O(n) rounds with O(n(INw + OUT)2/M) communication cost with high probability.
Q can be computed in O(log(n)) rounds with O(n(INmax(w, 3iw) + OUT)2/M) communication cost with high probability.
Intersection width is a new notion we introduce for queries and generalized hypertree decompositions (GHDs) of queries that captures how connected the adjacent components of the GHDs are.
We achieve our first result by introducing a distributed and generalized version of Yannakakis\u27s algorithm, called GYM. GYM takes as input any GHD of Q with width w and depth d, and computes Q in O(d + log(n)) rounds and O(n (INw + OUT)2/M) communication cost. We achieve our second result by showing how to construct GHDs of Q with width max(w, 3iw) and depth O(log(n)). We describe another technique to construct GHDs with longer widths and lower depths, demonstrating other tradeoffs one can make between communication and the number of rounds
Bias-voltage induced phase-transition in bilayer quantum Hall ferromagnets
We consider bilayer quantum Hall systems at total filling factor in
presence of a bias voltage which leads to different filling factors
in each layer. We use auxiliary field functional integral approach to study
mean-field solutions and collective excitations around them. We find that at
large layer separation, the collective excitations soften at a finite wave
vector leading to the collapse of quasiparticle gap. Our calculations predict
that as the bias voltage is increased, bilayer systems undergo a phase
transition from a compressible state to a phase-coherent state {\it
with charge imbalance}. We present simple analytical expressions for
bias-dependent renormalized charge imbalance and pseudospin stiffness which are
sensitive to the softening of collective modes.Comment: 12 pages, 5 figures. Minor changes, one reference adde
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