2,423 research outputs found
Adjointness Relations as a Criterion for Choosing an Inner Product
This is a contribution to the forthcoming book "Canonical Gravity: {}From
Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's
criterion for choosing an inner product in the quantisation of constrained
systems is discussed. An erroneous claim in a previous paper is corrected and a
cautionary example is presented.Comment: 6 pages, MPA-AR-94-
Fundamental Limits on the Speed of Evolution of Quantum States
This paper reports on some new inequalities of
Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution
between two orthogonal pure states. The clear determinant of the qualitative
behavior of this time scale is the statistics of the energy spectrum. An
often-overlooked correspondence between the real-time behavior of a quantum
system and the statistical mechanics of a transformed (imaginary-time)
thermodynamic system appears promising as a source of qualitative insights into
the quantum dynamics.Comment: 6 pages, 1 eps figur
Effects of two dimensional plasmons on the tunneling density of states
We show that gapless plasmons lead to a universal
correction to the tunneling
density of states of a clean two dimensional Coulomb interacting electron gas.
We also discuss a counterpart of this effect in the "composite fermion metal"
which forms in the presence of a quantizing perpendicular magnetic field
corresponding to the half-filled Landau level. We argue that the latter
phenomenon might be relevant for deviations from a simple scaling observed by
A.Chang et al in the tunneling characteristics of Quantum Hall liquids.Comment: 12 pages, Latex, NORDITA repor
Hudson's Theorem for finite-dimensional quantum systems
We show that, on a Hilbert space of odd dimension, the only pure states to
possess a non-negative Wigner function are stabilizer states. The Clifford
group is identified as the set of unitary operations which preserve positivity.
The result can be seen as a discrete version of Hudson's Theorem. Hudson
established that for continuous variable systems, the Wigner function of a pure
state has no negative values if and only if the state is Gaussian. Turning to
mixed states, it might be surmised that only convex combinations of stabilizer
states give rise to non-negative Wigner distributions. We refute this
conjecture by means of a counter-example. Further, we give an axiomatic
characterization which completely fixes the definition of the Wigner function
and compare two approaches to stabilizer states for Hilbert spaces of
prime-power dimensions. In the course of the discussion, we derive explicit
formulas for the number of stabilizer codes defined on such systems.Comment: 17 pages, 3 figures; References updated. Title changed to match
published version. See also quant-ph/070200
Late-time oscillatory behaviour for self-gravitating scalar fields
This paper investigates the late-time behaviour of certain cosmological
models where oscillations play an essential role. Rigorous results are proved
on the asymptotics of homogeneous and isotropic spacetimes with a linear
massive scalar field as source. Various generalizations are obtained for
nonlinear massive scalar fields, -essence models and gravity. The
effect of adding ordinary matter is discussed as is the case of nonlinear
scalar fields whose potential has a degenerate zero.Comment: 17 pages, additional reference
Algebras generated by two bounded holomorphic functions
We study the closure in the Hardy space or the disk algebra of algebras
generated by two bounded functions, of which one is a finite Blaschke product.
We give necessary and sufficient conditions for density or finite codimension
of such algebras. The conditions are expressed in terms of the inner part of a
function which is explicitly derived from each pair of generators. Our results
are based on identifying z-invariant subspaces included in the closure of the
algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some
points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu
The Possibility of Reconciling Quantum Mechanics with Classical Probability Theory
We describe a scheme for constructing quantum mechanics in which a quantum
system is considered as a collection of open classical subsystems. This allows
using the formal classical logic and classical probability theory in quantum
mechanics. Our approach nevertheless allows completely reproducing the standard
mathematical formalism of quantum mechanics and identifying its applicability
limits. We especially attend to the quantum state reduction problem.Comment: Latex, 14 pages, 1 figur
Theory of microwave-induced oscillations in the magnetoconductivity of a 2D electron gas
We develop a theory of magnetooscillations in the photoconductivity of a
two-dimensional electron gas observed in recent experiments. The effect is
governed by a change of the electron distribution function induced by the
microwave radiation. We analyze a nonlinearity with respect to both the dc
field and the microwave power, as well as the temperature dependence determined
by the inelastic relaxation rate.Comment: Extended version of cond-mat/0310668. 12 pages, 4 figures. V2:
published version (minor changes, Fig. 4 corrected, references added
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