297 research outputs found
Density perturbations in warm inflation and COBE normalization
Starting from a gauge invariant treatment of perturbations an analytical
expression for the spectrum of long wavelength density perturbations in warm
inflation is derived. The adiabatic and entropy modes are exhibited explicitly.
As an application of the analytical results, we determined the observational
constraint for the dissipation term compatible with COBE observation of the
cosmic microwave radiation anisotropy for some specific models. In view of the
results the feasibility of warm inflation is discussed.Comment: 11 pages, no figure
Correlations and Pairing Between Zeros and Critical Points of Gaussian Random Polynomials
We study the asymptotics of correlations and nearest neighbor spacings
between zeros and holomorphic critical points of , a degree N Hermitian
Gaussian random polynomial in the sense of Shiffman and Zeldtich, as N goes to
infinity. By holomorphic critical point we mean a solution to the equation
Our principal result is an explicit asymptotic formula
for the local scaling limit of \E{Z_{p_N}\wedge C_{p_N}}, the expected joint
intensity of zeros and critical points, around any point on the Riemann sphere.
Here and are the currents of integration (i.e. counting
measures) over the zeros and critical points of , respectively. We prove
that correlations between zeros and critical points are short range, decaying
like e^{-N\abs{z-w}^2}. With \abs{z-w} on the order of however,
\E{Z_{p_N}\wedge C_{p_N}}(z,w) is sharply peaked near causing zeros
and critical points to appear in rigid pairs. We compute tight bounds on the
expected distance and angular dependence between a critical point and its
paired zero.Comment: 35 pages, 3 figures. Some typos corrected and Introduction revise
Peer-group and price influence students drinking along with planned behaviour
This article is available open access through the publisher’s website at the link below. Copyright @ 2008 The Authors.Aims: To examine the theory of planned behaviour (TPB), as a framework for explaining binge drinking among young adults. Methods: One hundred and seventy-eight students in a cross-sectional design study completed self-report questionnaires examining attitudes to drinking, intention to drink and drinking behaviour in university. Binge drinking was defined for females (and males) as consuming ‘four (males—five) or more pints of beer/glasses of wine/measures of spirits’ in a single session. Results: Drinking alcohol was common; 39.6% of males and 35.9% of females reported binge drinking. The TPB explained 7% of the variance in intention to drink. Overall, 43% of the variance in intention, 83% of the variance in total weekly consumption and 44% of the variance in binge drinking was explained. The frequency of drinking and the drinking behaviour of friends significantly predicted intention to drink and binge drinking, respectively. Binge drinkers were influenced by peers and social-situational factors. Pressure to drink was greater for males; undergraduates were influenced by the size of the drinking group, ‘special offer’ prices, and the availability of alcohol. Conclusions: The TPB appeared to be a weak predictor of student drinking but this may be a result of how constructs were measured. With friends’ drinking behaviour emerging as a significant predictor of alcohol consumption, interventions seeking to reduce excessive drinking should target the role of peers and the university environment in which drinking occurs
On the notion of phase in mechanics
The notion of phase plays an esential role in both classical and quantum
mechanics.But what is a phase? We show that if we define the notion of phase in
phase (!) space one can very easily and naturally recover the Heisenberg-Weyl
formalism; this is achieved using the properties of the Poincare-Cartan
invariant, and without making any quantum assumption
Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation
A generalized approach to the quantization of a large class of maps on a
torus, i.e. quantization via the von Neumann Equation, is described and a
number of issues related to the quantization of model systems are discussed.
The approach yields well behaved mixed quantum states for tori for which the
corresponding Schrodinger equation has no solutions, as well as an extended
spectrum for tori where the Schrodinger equation can be solved.
Quantum-classical correspondence is demonstrated for the class of mappings
considered, with the Wigner-Weyl density going to the correct
classical limit. An application to the cat map yields, in a direct manner,
nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the
correspondence limit.Comment: 36 pages, RevTex preprint forma
QUANTIZATION OF A CLASS OF PIECEWISE AFFINE TRANSFORMATIONS ON THE TORUS
We present a unified framework for the quantization of a family of discrete
dynamical systems of varying degrees of "chaoticity". The systems to be
quantized are piecewise affine maps on the two-torus, viewed as phase space,
and include the automorphisms, translations and skew translations. We then
treat some discontinuous transformations such as the Baker map and the
sawtooth-like maps. Our approach extends some ideas from geometric quantization
and it is both conceptually and calculationally simple.Comment: no. 28 pages in AMSTE
Spectral statistics in chaotic systems with a point interaction
We consider quantum systems with a chaotic classical limit that are perturbed
by a point-like scatterer. The spectral form factor K(tau) for these systems is
evaluated semiclassically in terms of periodic and diffractive orbits. It is
shown for order tau^2 and tau^3 that off-diagonal contributions to the form
factor which involve diffractive orbits cancel exactly the diagonal
contributions from diffractive orbits, implying that the perturbation by the
scatterer does not change the spectral statistic. We further show that
parametric spectral statistics for these systems are universal for small
changes of the strength of the scatterer.Comment: LaTeX, 21 pages, 7 figures, small corrections, new references adde
Non-Abelian Geometrical Phase for General Three-Dimensional Quantum Systems
Adiabatic geometric phases are studied for arbitrary quantum systems
with a three-dimensional Hilbert space. Necessary and sufficient conditions for
the occurrence of the non-Abelian geometrical phases are obtained without
actually solving the full eigenvalue problem for the instantaneous Hamiltonian.
The parameter space of such systems which has the structure of \xC P^2 is
explicitly constructed. The results of this article are applicable for
arbitrary multipole interaction Hamiltonians and their linear combinations for spin systems. In particular it
is shown that the nuclear quadrupole Hamiltonian does actually
lead to non-Abelian geometric phases for . This system, being bosonic, is
time-reversal-invariant. Therefore it cannot support Abelian adiabatic
geometrical phases.Comment: Plain LaTeX, 17 page
Quantization of multidimensional cat maps
In this work we study cat maps with many degrees of freedom. Classical cat
maps are classified using the Cayley parametrization of symplectic matrices and
the closely associated center and chord generating functions. Particular
attention is dedicated to loxodromic behavior, which is a new feature of
two-dimensional maps. The maps are then quantized using a recently developed
Weyl representation on the torus and the general condition on the Floquet
angles is derived for a particular map to be quantizable. The semiclassical
approximation is exact, regardless of the dimensionality or of the nature of
the fixed points.Comment: 33 pages, latex, 6 figures, Submitted to Nonlinearit
Phase Splitting for Periodic Lie Systems
In the context of the Floquet theory, using a variation of parameter
argument, we show that the logarithm of the monodromy of a real periodic Lie
system with appropriate properties admits a splitting into two parts, called
dynamic and geometric phases. The dynamic phase is intrinsic and linked to the
Hamiltonian of a periodic linear Euler system on the co-algebra. The geometric
phase is represented as a surface integral of the symplectic form of a
co-adjoint orbit.Comment: (v1) 15 pages. (v2) 16 pages. Some typos corrected. References and
further comments added. Final version to appear in J. Phys. A
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