4,724 research outputs found
Generalized retarded integral inequalities
We prove some new retarded integral inequalities. The results generalize
those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].Comment: Changes suggested by the referee don
On how to Produce Entangled States Violating Bell's Inequalities in Quantum Theory
Feynman's path integrals provide a hidden variable description of quantum
mechanics (and quantum field theories). The time evolution kernel is unitary in
Minkowski time, but generically it becomes real and non-negative in Euclidean
time. It follows that the entangled state correlations, that violate Bell's
inequalities in Minkowski time, obey the inequalities in Euclidean time. This
observation emphasises the link between violation of Bell's inequalities in
quantum mechanics and unitarity of the theory. Search for an evolution kernel
that cannot be conveniently made non-negative leads to effective interactions
that violate time reversal invariance. Interactions giving rise to geometric
phases in the effective description of the theory, such as the anomalous
Wess-Zumino interactions, have this feature. I infer that they must be present
in any set-up that produces entangled states violating Bell's inequalities.
Such interactions would be a crucial ingredient in a quantum computer.Comment: 8 pages, two column revtex, arguments elaborated and strengthened,
submitted to Physical Review
On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation
AbstractIn this paper, we investigate some new nonlinear retarded integral inequalities of Gronwall–Bellman–Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear retarded differential and integral equations. An application is also presented to illustrate the usefulness of some of our results in estimation of solution of certain retarded nonlinear differential equations with the initial conditions
Spectral sum rules for conformal field theories in arbitrary dimensions
We derive spectral sum rules in the shear channel for conformal field
theories at finite temperature in general dimensions. The sum rules
result from the OPE of the stress tensor at high frequency as well as the
hydrodynamic behaviour of the theory at low frequencies. The sum rule states
that a weighted integral of the spectral density over frequencies is
proportional to the energy density of the theory. We show that the
proportionality constant can be written in terms the Hofman-Maldacena variables
which determine the three point function of the stress tensor. For
theories which admit a two derivative gravity dual this proportionality
constant is given by . We then use causality constraints and
obtain bounds on the sum rule which are valid in any conformal field theory.
Finally we demonstrate that the high frequency behaviour of the spectral
function in the vector and the tensor channel are also determined by the
Hofman-Maldacena variables.Comment: Corrected typos, JHEP versio
On certain new Gronwall-ou-iang type integral inequalities in two variables and their applications
Some new Gronwall-Ou-Iang type integral inequalities in twoindependent variables are established. These integral inequalitiescan be applied as tools to the study of certain class of integraland differential equations. Some applications to a terminal valueproblem are also indicated. Copyright © 2005 Hindawi Publishing Corporation.published_or_final_versio
Some new nonlinear retarded sum-difference inequalities with applications
The main objective of this paper is to establish some new retarded nonlinear sum-difference inequalities with two independent variables, which provide explicit bounds on unknown functions. These inequalities given here can be used as handy tools in the study of boundary value problems in partial difference equations. © 2011 Wang et al; licensee Springer.published_or_final_versio
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