2,982,536 research outputs found
A Strategy for a Vanishing Cosmological Constant in the Presence of Scale Invariance Breaking
Recent work has shown that complex quantum field theory emerges as a
statistical mechanical approximation to an underlying noncommutative operator
dynamics based on a total trace action. In this dynamics, scale invariance of
the trace action becomes the statement , with the operator stress energy tensor, and with the trace over the
underlying Hilbert space. We show that this condition implies the vanishing of
the cosmological constant and vacuum energy in the emergent quantum field
theory. However, since the scale invariance condition does not require the
operator to vanish, the spontaneous breakdown of scale
invariance is still permitted.Comment: Second award in the Gravity Research Foundation Essay Competition for
1997; to appear in General Relativity and Gravitation. Plain Tex, no figure
Efficient Simulation of Quantum State Reduction
The energy-based stochastic extension of the Schrodinger equation is a rather
special nonlinear stochastic differential equation on Hilbert space, involving
a single free parameter, that has been shown to be very useful for modelling
the phenomenon of quantum state reduction. Here we construct a general closed
form solution to this equation, for any given initial condition, in terms of a
random variable representing the terminal value of the energy and an
independent Brownian motion. The solution is essentially algebraic in
character, involving no integration, and is thus suitable as a basis for
efficient simulation studies of state reduction in complex systems.Comment: 4 pages, No Figur
The identification of physical close galaxy pairs
A classification scheme for close pairs of galaxies is proposed. The scheme
is motivated by the fact that the majority of apparent close pairs are in fact
wide pairs in three-dimensional space. This is demonstrated by means of
numerical simulations of random samples of binary galaxies and the scrutiny of
the resulting projected and spatial separation distributions.
Observational strategies for classifying close pairs according to the scheme
are suggested. As a result, physical (i.e., bound and spatially) close pairs
are identified.Comment: 16 pages, 5 figures, accepted for publication in The Astronomical
Journal, added text corrections on proof
Geometry of Quantum Principal Bundles I
A theory of principal bundles possessing quantum structure groups and
classical base manifolds is presented. Structural analysis of such quantum
principal bundles is performed. A differential calculus is constructed,
combining differential forms on the base manifold with an appropriate
differential calculus on the structure quantum group. Relations between the
calculus on the group and the calculus on the bundle are investigated. A
concept of (pseudo)tensoriality is formulated. The formalism of connections is
developed. In particular, operators of horizontal projection, covariant
derivative and curvature are constructed and analyzed. Generalizations of the
first structure equation and of the Bianchi identity are found. Illustrative
examples are presented.Comment: 64 pages, AMS-LaTeX, To appear in CM
Bounds on Decoherence and Error
When a confined system interacts with its walls (treated quantum
mechanically), there is an intertwining of degrees of freedom. We show that
this need not lead to entanglement, hence decoherence. It will generally lead
to error. The wave function optimization required to avoid decoherence is also
examined.Comment: 10 pages, plain TeX, no figure
Optical activity of noncentrosymmetric metals
We describe the phenomenon of optical activity of noncentrosymmetric metals
in their normal and superconducting states. The found conductivity tensor
contains the linear in wave vector off diagonal part responsible for the
natural optical activity. Its value is expressed through the ratio of light
frequency to the band splitting due to the spin-orbit interaction. The Kerr
rotation of polarization of light reflected from the metal surface is
calculated.
In the additional file "Erratum" I've pointed out the sign error in
arXiv:1001.2113 ( PRB v.81, 094525 (2010)) that leads to the wrong statement
about the Kerr effect in light reflection from the surface of media without
space parity.Comment: 9 pages + 2 pages of Erratum. arXiv admin note: text overlap with
arXiv:0903.330
Coherent Waveform Consistency Test for LIGO Burst Candidates
The burst search in LIGO relies on the coincident detection of transient
signals in multiple interferometers. As only minimal assumptions are made about
the event waveform or duration, the analysis pipeline requires loose
coincidence in time, frequency and amplitude. Confidence in the resulting
events and their waveform consistency is established through a time-domain
coherent analysis: the r-statistic test.
This paper presents a performance study of the r-statistic test for triple
coincidence events in the second LIGO Science Run (S2), with emphasis on its
ability to suppress the background false rate and its efficiency at detecting
simulated bursts of different waveforms close to the S2 sensitivity curve.Comment: 11 pages, 9 figures. Submitted to the Proceedings of the 8th
Gravitational Wave Data Analysis Workshop, in Classic and Quantum Gravit
Schulman Replies
This is a reply to a comment of Casati, Chirikov and Zhirov (PRL 85, 896
(2000)) on PRL 83, 5419 (1999).
The suitability of the particlar two-time boundary value problem used in the
earlier PRL is argued
On the Euler angles for SU(N)
In this paper we reconsider the problem of the Euler parametrization for the
unitary groups. After constructing the generic group element in terms of
generalized angles, we compute the invariant measure on SU(N) and then we
determine the full range of the parameters, using both topological and
geometrical methods. In particular, we show that the given parametrization
realizes the group as a fibration of U(N) over the complex projective
space . This justifies the interpretation of the parameters as
generalized Euler angles.Comment: 16 pages, references adde
- …