1,125 research outputs found
Causal sets and conservation laws in tests of Lorentz symmetry
Many of the most important astrophysical tests of Lorentz symmetry also
assume that energy-momentum of the observed particles is exactly conserved. In
the causal set approach to quantum gravity a particular kind of Lorentz
symmetry holds but energy-momentum conservation may be violated. We show that
incorrectly assuming exact conservation can give rise to a spurious signal of
Lorentz symmetry violation for a causal set. However, the size of this spurious
signal is much smaller than can be currently detected and hence astrophysical
Lorentz symmetry tests as currently performed are safe from causal set induced
violations of energy-momentum conservation.Comment: 8 pages, matches version published in PR
The Discrete Fundamental Group of the Associahedron, and the Exchange Module
The associahedron is an object that has been well studied and has numerous
applications, particularly in the theory of operads, the study of non-crossing
partitions, lattice theory and more recently in the study of cluster algebras.
We approach the associahedron from the point of view of discrete homotopy
theory. We study the abelianization of the discrete fundamental group, and show
that it is free abelian of rank . We also find a combinatorial
description for a basis of this rank. We also introduce the exchange module of
the type cluster algebra, used to model the relations in the cluster
algebra. We use the discrete fundamental group to the study of exchange module,
and show that it is also free abelian of rank .Comment: 16 pages, 4 figure
The depletion in Bose Einstein condensates using Quantum Field Theory in curved space
Using methods developed in Quantum Field Theory in curved space we can
estimate the effects of the inhomogeneities and of a non vanishing velocity on
the depletion of a Bose Einstein condensate within the hydrodynamical
approximation.Comment: 4 pages, no figure. Discussion extended and references adde
Regularization of fluctuations near the sonic horizon due to the quantum potential and its influence on the Hawking radiation
We consider dynamics of fluctuations in transonically accelerating
Bose-Einstein condensates and luminous liquids (coherent light propagating in a
Kerr nonlinear medium) using the hydrodynamic approach. It is known that
neglecting the quantum potential (QP) leads to a singular behavior of quantum
and classical fluctuations in the vicinity of the Mach (sonic) horizon, which
in turn gives rise to the Hawking radiation. The neglect of QP is well founded
at not too small distances from the horizon, where is the
healing length. Taking the QP into account we show that a second characteristic
length exists, such that the linear fluctuation modes become
regularized for . At the modes keep their singular
behavior, which however is influenced by the QP. As a result we find a
deviation of the high frequency tail of the spectrum of Hawking radiation from
Planck's black body radiation distribution. Similar results hold for the wave
propagation in Kerr nonlinear media where the length and exist due
to the nonlinearity.Comment: 23 pages, 2 figure
About Locality and the Relativity Principle Beyond Special Relativity
Locality of interactions is an essential ingredient of Special Relativity.
Recently, a new framework under the name of relative locality
\cite{AmelinoCamelia:2011bm} has been proposed as a way to consider Planckian
modifications of the relativistic dynamics of particles. We note in this paper
that the loss of absolute locality is a general feature of theories beyond
Special Relativity with an implementation of a relativity principle. We give an
explicit construction of such an implementation and compare it both with the
previously mentioned framework of relative locality and the so-called Doubly
Special Relativity theories.Comment: 10 pages, no figure
Social heuristics and social roles: Intuition favors altruism for women but not for men
Are humans intuitively altruistic, or does altruism require self-control? A theory of social heuristics, whereby intuitive responses favor typically successful behaviors, suggests that the answer may depend on who you are. In particular, evidence suggests that women are expected to behave altruistically, and are punished for failing to be altruistic, to a much greater extent than men. Thus, women (but not men) may internalize altruism as their intuitive response. Indeed, a meta-analysis of 13 new experiments and 9 experiments from other groups found that promoting intuition increased giving in a Dictator Game among women, but not among men (Study 1). Furthermore, this effect was shown to be moderated by explicit sex role identification (Study 2, N=1,831): the more women described themselves using traditionally masculine attributes (e.g., dominance, independence) relative to traditionally feminine attributes (e.g., warmth, tenderness), the more deliberation reduced their altruism. Our findings shed light on the connection between gender and altruism, and highlight the importance of social heuristics in human prosociality
Noether Current, Horizon Virasoro Algebra and Entropy
We provide a simple and straightforward procedure for defining a Virasoro
algebra based on the diffeomorphisms near a null surface in a spacetime and
obtain the entropy density of the null surface from its central charge. We use
the off-shell Noether current corresponding to the diffeomorphism invariance of
a gravitational Lagrangian and define the Virasoro algebra
from its variation. This allows us to identify the central charge and the zero
mode eigenvalue using which we obtain the entropy density of the Killing
horizon. Our approach works for all Lanczos-Lovelock models and reproduces the
correct Wald entropy. The entire analysis is done off-shell without using the
field equations and allows us to define an entropy density for any null surface
which acts as a local Rindler horizon for a particular class of observers.Comment: V2: to appear in Phys. Rev.
Analogue Cosmological Particle Creation: Quantum Correlations in Expanding Bose Einstein Condensates
We investigate the structure of quantum correlations in an expanding Bose
Einstein Condensate (BEC) through the analogue gravity framework. We consider
both a 3+1 isotropically expanding BEC as well as the experimentally relevant
case of an elongated, effectively 1+1 dimensional, expanding condensate. In
this case we include the effects of inhomogeneities in the condensate, a
feature rarely included in the analogue gravity literature. In both cases we
link the BEC expansion to a simple model for an expanding spacetime and then
study the correlation structure numerically and analytically (in suitable
approximations). We also discuss the expected strength of such correlation
patterns and experimentally feasible BEC systems in which these effects might
be detected in the near future.Comment: Reference adde
Superradiant scattering from a hydrodynamic vortex
We show that sound waves scattered from a hydrodynamic vortex may be
amplified. Such superradiant scattering follows from the physical analogy
between spinning black holes and hydrodynamic vortices. However a sonic horizon
analogous to the black hole event horizon does not exist unless the vortex
possesses a central drain, which is challenging to produce experimentally. In
the astrophysical domain, superradiance can occur even in the absence of an
event horizon: we show that in the hydrodynamic analogue, a drain is not
required and a vortex scatters sound superradiantly. Possible experimental
realization in dilute gas Bose-Einstein condensates is discussed.Comment: 10 pages, 1 figur
Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity
I show that the principle of equipartition, applied to area elements of a
surface which are in equilibrium at the local Davies-Unruh temperature, allows
one to determine the surface number density of the microscopic spacetime
degrees of freedom in any diffeomorphism invariant theory of gravity. The
entropy associated with these degrees of freedom matches with the Wald entropy
for the theory. This result also allows one to attribute an entropy density to
the spacetime in a natural manner. The field equations of the theory can then
be obtained by extremising this entropy. Moreover, when the microscopic degrees
of freedom are in local thermal equilibrium, the spacetime entropy of a bulk
region resides on its boundary.Comment: v1: 20 pages; no figures. v2: Sec 4 added; 23 page
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