84 research outputs found
Boundary effects in the stepwise structure of the Lyapunov spectra for quasi-one-dimensional systems
Boundary effects in the stepwise structure of the Lyapunov spectra and the
corresponding wavelike structure of the Lyapunov vectors are discussed
numerically in quasi-one-dimensional systems consisting of many hard-disks.
Four kinds of boundary conditions constructed by combinations of periodic
boundary conditions and hard-wall boundary conditions are considered, and lead
to different stepwise structures of the Lyapunov spectra in each case. We show
that a spatial wavelike structure with a time-oscillation appears in the
spatial part of the Lyapunov vectors divided by momenta in some steps of the
Lyapunov spectra, while a rather stationary wavelike structure appears in the
purely spatial part of the Lyapunov vectors corresponding to the other steps.
Using these two kinds of wavelike structure we categorize the sequence and the
kinds of steps of the Lyapunov spectra in the four different boundary condition
cases.Comment: 33 pages, 25 figures including 10 color figures. Manuscript including
the figures of better quality is available from
http://newt.phys.unsw.edu.au/~gary/step.pd
Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems
We introduce a definition of a "localization width" whose logarithm is given
by the entropy of the distribution of particle component amplitudes in the
Lyapunov vector. Different types of localization widths are observed, for
example, a minimum localization width where the components of only two
particles are dominant. We can distinguish a delocalization associated with a
random distribution of particle contributions, a delocalization associated with
a uniform distribution and a delocalization associated with a wave-like
structure in the Lyapunov vector. Using the localization width we show that in
quasi-one-dimensional systems of many hard disks there are two kinds of
dependence of the localization width on the Lyapunov exponent index for the
larger exponents: one is exponential, and the other is linear. Differences, due
to these kinds of localizations also appear in the shapes of the localized
peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the
spatial and momentum parts of the Lyapunov vectors. We show that the Krylov
relation for the largest Lyapunov exponent as a
function of the density is satisfied (apart from a factor) in the same
density region as the linear dependence of the localization widths is observed.
It is also shown that there are asymmetries in the spatial and momentum parts
of the Lyapunov vectors, as well as in their and -components.Comment: 41 pages, 21 figures, Manuscript including the figures of better
quality is available from http://www.phys.unsw.edu.au/~gary/Research.htm
Equilibrium and dynamical properties of two dimensional self-gravitating systems
A system of N classical particles in a 2D periodic cell interacting via
long-range attractive potential is studied. For low energy density a
collapsed phase is identified, while in the high energy limit the particles are
homogeneously distributed. A phase transition from the collapsed to the
homogeneous state occurs at critical energy U_c. A theoretical analysis within
the canonical ensemble identifies such a transition as first order. But
microcanonical simulations reveal a negative specific heat regime near .
The dynamical behaviour of the system is affected by this transition : below
U_c anomalous diffusion is observed, while for U > U_c the motion of the
particles is almost ballistic. In the collapsed phase, finite -effects act
like a noise source of variance O(1/N), that restores normal diffusion on a
time scale diverging with N. As a consequence, the asymptotic diffusion
coefficient will also diverge algebraically with N and superdiffusion will be
observable at any time in the limit N \to \infty. A Lyapunov analysis reveals
that for U > U_c the maximal exponent \lambda decreases proportionally to
N^{-1/3} and vanishes in the mean-field limit. For sufficiently small energy,
in spite of a clear non ergodicity of the system, a common scaling law \lambda
\propto U^{1/2} is observed for any initial conditions.Comment: 17 pages, Revtex - 15 PS Figs - Subimitted to Physical Review E - Two
column version with included figures : less paper waste
Levinson's theorem and scattering phase shift contributions to the partition function of interacting gases in two dimensions
We consider scattering state contributions to the partition function of a
two-dimensional (2D) plasma in addition to the bound-state sum. A partition
function continuity requirement is used to provide a statistical mechanical
heuristic proof of Levinson's theorem in two dimensions. We show that a proper
account of scattering eliminates singularities in thermodynamic properties of
the nonideal 2D gas caused by the emergence of additional bound states as the
strength of an attractive potential is increased. The bound-state contribution
to the partition function of the 2D gas, with a weak short-range attraction
between its particles, is found to vanish logarithmically as the binding energy
decreases. A consistent treatment of bound and scattering states in a screened
Coulomb potential allowed us to calculate the quantum-mechanical second virial
coefficient of the dilute 2D electron-hole plasma and to establish the
difference between the nearly ideal electron-hole gas in GaAs and the strongly
correlated exciton/free-carrier plasma in wide-gap semiconductors such as ZnSe
or GaN.Comment: 10 pages, 3 figures; new version corrects some minor typo
Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems
The master equation approach to Lyapunov spectra for many-particle systems is
applied to non-equilibrium thermostatted systems to discuss the conjugate
pairing rule. We consider iso-kinetic thermostatted systems with a shear flow
sustained by an external restriction, in which particle interactions are
expressed as a Gaussian white randomness. Positive Lyapunov exponents are
calculated by using the Fokker-Planck equation to describe the tangent vector
dynamics. We introduce another Fokker-Planck equation to describe the
time-reversed tangent vector dynamics, which allows us to calculate the
negative Lyapunov exponents. Using the Lyapunov exponents provided by these two
Fokker-Planck equations we show the conjugate pairing rule is satisfied for
thermostatted systems with a shear flow in the thermodynamic limit. We also
give an explicit form to connect the Lyapunov exponents with the
time-correlation of the interaction matrix in a thermostatted system with a
color field.Comment: 10 page
Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations
The interest of quadratic algebras for position-dependent mass Schr\"odinger
equations is highlighted by constructing spectrum generating algebras for a
class of d-dimensional radial harmonic oscillators with and a
specific mass choice depending on some positive parameter . Via some
minor changes, the one-dimensional oscillator on the line with the same kind of
mass is included in this class. The existence of a single unitary irreducible
representation belonging to the positive-discrete series type for and
of two of them for d=1 is proved. The transition to the constant-mass limit
is studied and deformed su(1,1) generators are constructed.
These operators are finally used to generate all the bound-state wavefunctions
by an algebraic procedure.Comment: 21 pages, no figure, 2 misprints corrected; published versio
A general scheme for the effective-mass Schrodinger equation and the generation of the associated potentials
A systematic procedure to study one-dimensional Schr\"odinger equation with a
position-dependent effective mass (PDEM) in the kinetic energy operator is
explored. The conventional free-particle problem reveals a new and interesting
situation in that, in the presence of a mass background, formation of bound
states is signalled. We also discuss coordinate-transformed, constant-mass
Schr\"odinger equation, its matching with the PDEM form and the consequent
decoupling of the ambiguity parameters. This provides a unified approach to
many exact results known in the literature, as well as to a lot of new ones.Comment: 16 pages + 1 figure; minor changes + new "free-particle" problem;
version published in Mod. Phys. Lett.
Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR
Substantial experimental and theoretical efforts worldwide are devoted to
explore the phase diagram of strongly interacting matter. At LHC and top RHIC
energies, QCD matter is studied at very high temperatures and nearly vanishing
net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was
created at experiments at RHIC and LHC. The transition from the QGP back to the
hadron gas is found to be a smooth cross over. For larger net-baryon densities
and lower temperatures, it is expected that the QCD phase diagram exhibits a
rich structure, such as a first-order phase transition between hadronic and
partonic matter which terminates in a critical point, or exotic phases like
quarkyonic matter. The discovery of these landmarks would be a breakthrough in
our understanding of the strong interaction and is therefore in the focus of
various high-energy heavy-ion research programs. The Compressed Baryonic Matter
(CBM) experiment at FAIR will play a unique role in the exploration of the QCD
phase diagram in the region of high net-baryon densities, because it is
designed to run at unprecedented interaction rates. High-rate operation is the
key prerequisite for high-precision measurements of multi-differential
observables and of rare diagnostic probes which are sensitive to the dense
phase of the nuclear fireball. The goal of the CBM experiment at SIS100
(sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD
matter: the phase structure at large baryon-chemical potentials (mu_B > 500
MeV), effects of chiral symmetry, and the equation-of-state at high density as
it is expected to occur in the core of neutron stars. In this article, we
review the motivation for and the physics programme of CBM, including
activities before the start of data taking in 2022, in the context of the
worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal
The effect of angular momentum conservation in the phase transitions of collapsing systems
The effect of angular momentum conservation in microcanonical thermodynamics
is considered. This is relevant in gravitating systems, where angular momentum
is conserved and the collapsing nature of the forces makes the microcanonical
ensemble the proper statistical description of the physical processes. The
microcanonical distribution function with non-vanishing angular momentum is
obtained as a function of the coordinates of the particles. As an example, a
simple model of gravitating particles, introduced by Thirring long ago, is
worked out. The phase diagram contains three phases: for low values of the
angular momentum the system behaves as the original model, showing a
complete collapse at low energies and an entropy with a convex intruder. For
intermediate values of the collapse at low energies is not complete and the
entropy still has a convex intruder. For large there is neither collapse
nor anomalies in the thermodynamical quantities. A short discussion of the
extension of these results to more realistic situations is exposed.Comment: Latex, 21 pages, 5 figures. Corrected misprints in some equations and
a few clarifying remarks adde
Distribution maps of vegetation alliances in Europe
Aim
The first comprehensive checklist of European phytosociological alliances, orders and classes (EuroVegChecklist) was published by Mucina et al. (2016, Applied Vegetation Science, 19 (Suppl. 1), 3–264). However, this checklist did not contain detailed information on the distribution of individual vegetation types. Here we provide the first maps of all alliances in Europe.
Location
Europe, Greenland, Canary Islands, Madeira, Azores, Cyprus and the Caucasus countries.
Methods
We collected data on the occurrence of phytosociological alliances in European countries and regions from literature and vegetation-plot databases. We interpreted and complemented these data using the expert knowledge of an international team of vegetation scientists and matched all the previously reported alliance names and concepts with those of the EuroVegChecklist. We then mapped the occurrence of the EuroVegChecklist alliances in 82 territorial units corresponding to countries, large islands, archipelagos and peninsulas. We subdivided the mainland parts of large or biogeographically heterogeneous countries based on the European biogeographical regions. Specialized alliances of coastal habitats were mapped only for the coastal section of each territorial unit.
Results
Distribution maps were prepared for 1,105 alliances of vascular-plant dominated vegetation reported in the EuroVegChecklist. For each territorial unit, three levels of occurrence probability were plotted on the maps: (a) verified occurrence; (b) uncertain occurrence; and (c) absence. The maps of individual alliances were complemented by summary maps of the number of alliances and the alliance–area relationship. Distribution data are also provided in a spreadsheet.
Conclusions
The new map series represents the first attempt to characterize the distribution of all vegetation types at the alliance level across Europe. There are still many knowledge gaps, partly due to a lack of data for some regions and partly due to uncertainties in the definition of some alliances. The maps presented here provide a basis for future research aimed at filling these gaps
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