45,114 research outputs found
Non-universality of chaotic classical dynamics : implications for quantum chaos
It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal agreement between their quantum spectral statistics and random matrix theory. It is argued that no such universality exists. Two statistical properties of long period orbits are considered. The distribution of the phase-space density of periodic orbits of fixed length is shown to have a log-normal distribution. Also, a correlation function of periodic-orbit actions is discussed, which has a semiclassical correspondence to the quantum spectral two-point correlation function. It is shown that bifurcations are a mechanism for creating correlations of periodic-orbit actions. They lead to a result which is non-universal, and which in general may not be an analytic function of the action difference
Semiclassical trace formulae using coherent states
We derive semiclassical trace formulae including Gutzwiller's trace formula
using coherent states. This formulation has several advantages over the usual
coordinate-space formulation. Using a coherent-state basis makes it immediately
obvious that classical periodic orbits make separate contributions to the trace
of the quantum-mechanical time evolution operator. In addition, our approach is
manifestly canonically invariant at all stages, and leads to the simplest
possible derivation of Gutzwiller's formula.Comment: 19 pages, 1 figur
Twelve tips to teaching (legal and ethical aspects of) research ethics/responsible conduct of research
Teaching research ethics is a requirement within modern health science, nursing and medical curricula. We have drawn on our experience of designing, developing and integrating the teaching of research ethics in a new, fully integrated medical school curriculum, delivered using Problem Based Learning and the recent literature relating to the teaching of research ethics to produce the following 12 Top Tips designed to encourage readers to seek opportunities to embed this teaching within a variety of curricula
Precise asymptotics for a variable-range hopping model
For a system of localised electron states the DC conductivity vanishes at
zero temperature, but localised electrons can conduct at finite temperature.
Mott gave a theory for the low-temperature conductivity in terms of a
variable-range hopping model, which is hard to analyse. Here we give precise
asymptotic results for a modified variable-range hopping model proposed by S.
Alexander [Phys. Rev. B 26, 2956 (1982)].Comment: 7 pages, 2 figure
Psychosocial and material pathways in the relation between income and health: a response to Lynch et al
Summary points: Economic and social circumstances affect health through the physiological effects of their emotional and social meanings and the direct effects of material circumstances. Material conditions do not adequately explain health inequalities in rich countries. The relation between smaller inequalities in income and better population health reflects increased psychosocial wellbeing. In rich countries wellbeing is more closely related to relative income than absolute income. Social dominance, inequality, autonomy, and the quality of social relations have an impact on psychosocial wellbeing and are among the most powerful explanations for the pattern of population health in rich countries
Ergodic and non-ergodic clustering of inertial particles
We compute the fractal dimension of clusters of inertial particles in mixing
flows at finite values of Kubo (Ku) and Stokes (St) numbers, by a new series
expansion in Ku. At small St, the theory includes clustering by Maxey's
non-ergodic 'centrifuge' effect. In the limit of St to infinity and Ku to zero
(so that Ku^2 St remains finite) it explains clustering in terms of ergodic
'multiplicative amplification'. In this limit, the theory is consistent with
the asymptotic perturbation series in [Duncan et al., Phys. Rev. Lett. 95
(2005) 240602]. The new theory allows to analyse how the two clustering
mechanisms compete at finite values of St and Ku. For particles suspended in
two-dimensional random Gaussian incompressible flows, the theory yields
excellent results for Ku < 0.2 for arbitrary values of St; the ergodic
mechanism is found to contribute significantly unless St is very small. For
higher values of Ku the new series is likely to require resummation. But
numerical simulations show that for Ku ~ St ~ 1 too, ergodic 'multiplicative
amplification' makes a substantial contribution to the observed clustering.Comment: 4 pages, 2 figure
The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems
The autocorrelation function of the force acting on a slow classical system,
resulting from interaction with a fast quantum system is calculated following
Berry-Robbins and Jarzynski within the leading order correction to the
adiabatic approximation. The time integral of the autocorrelation function is
proportional to the rate of dissipation. The fast quantum system is assumed to
be chaotic in the classical limit for each configuration of the slow system. An
analytic formula is obtained for the finite time integral of the correlation
function, in the framework of random matrix theory (RMT), for a specific
dependence on the adiabatically varying parameter. Extension to a wider class
of RMT models is discussed. For the Gaussian unitary and symplectic ensembles
for long times the time integral of the correlation function vanishes or falls
off as a Gaussian with a characteristic time that is proportional to the
Heisenberg time, depending on the details of the model. The fall off is
inversely proportional to time for the Gaussian orthogonal ensemble. The
correlation function is found to be dominated by the nearest neighbor level
spacings. It was calculated for a variety of nearest neighbor level spacing
distributions, including ones that do not originate from RMT ensembles. The
various approximate formulas obtained are tested numerically in RMT. The
results shed light on the quantum to classical crossover for chaotic systems.
The implications on the possibility to experimentally observe deterministic
friction are discussed.Comment: 26 pages, including 6 figure
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