100 research outputs found
Symmetries of microcanonical entropy surfaces
Symmetry properties of the microcanonical entropy surface as a function of
the energy and the order parameter are deduced from the invariance group of the
Hamiltonian of the physical system. The consequences of these symmetries for
the microcanonical order parameter in the high energy and in the low energy
phases are investigated. In particular the breaking of the symmetry of the
microcanonical entropy in the low energy regime is considered. The general
statements are corroborated by investigations of various examples of classical
spin systems.Comment: 15 pages, 5 figures include
Microcanonical entropy for small magnetisations
Physical quantities obtained from the microcanonical entropy surfaces of
classical spin systems show typical features of phase transitions already in
finite systems. It is demonstrated that the singular behaviour of the
microcanonically defined order parameter and susceptibility can be understood
from a Taylor expansion of the entropy surface. The general form of the
expansion is determined from the symmetry properties of the microcanonical
entropy function with respect to the order parameter. The general findings are
investigated for the four-state vector Potts model as an example of a classical
spin system.Comment: 15 pages, 7 figure
Theory of Distinct Crystal Structures of Polymerized Fullerides AC60, A=K, Rb, Cs: the Specific Role of Alkalis
The polymer phases of AC60 form distinct crystal structures characterized by
the mutual orientations of the (C60-)n chains. We show that the direct electric
quadrupole interaction between chains always favors the orthorhombic structure
Pmnn with alternating chain orientations. However the specific quadrupolar
polarizability of the alkali metal ions leads to an indirect interchain
coupling which favors the monoclinic structure I2/m with equal chain
orientations. The competition between direct and indirect interactions explains
the structural difference between KC60 and RbC60, CsC60.Comment: 4 pages, 2 figures, 1 tabl
Finite-size behaviour of the microcanonical specific heat
For models which exhibit a continuous phase transition in the thermodynamic
limit a numerical study of small systems reveals a non-monotonic behaviour of
the microcanonical specific heat as a function of the system size. This is in
contrast to a treatment in the canonical ensemble where the maximum of the
specific heat increases monotonically with the size of the system. A
phenomenological theory is developed which permits to describe this peculiar
behaviour of the microcanonical specific heat and allows in principle the
determination of microcanonical critical exponents.Comment: 15 pages, 7 figures, submitted to J. Phys.
Coulombically Interacting Electrons in a One-dimensional Quantum Dot
The spectral properties of up to four interacting electrons confined within a
quasi one--dimensional system of finite length are determined by numerical
diagonalization including the spin degree of freedom. The ground state energy
is investigated as a function of the electron number and of the system length.
The limitations of a description in terms of a capacitance are demonstrated.
The energetically lowest lying excitations are physically explained as
vibrational and tunneling modes. The limits of a dilute, Wigner-type
arrangement of the electrons, and a dense, more homogeneous charge distribution
are discussed.Comment: 10 pages (excl. Figures), Figures added in POSTSCRIPT, LaTe
Inequivalence of ensembles in a system with long range interactions
We study the global phase diagram of the infinite range Blume-Emery-Griffiths
model both in the canonical and in the microcanonical ensembles. The canonical
phase diagram is known to exhibit first order and continuous transition lines
separated by a tricritical point. We find that below the tricritical point,
when the canonical transition is first order, the phase diagrams of the two
ensembles disagree. In this region the microcanonical ensemble exhibits energy
ranges with negative specific heat and temperature jumps at transition
energies. These results can be extended to weakly decaying nonintegrable
interactions.Comment: Revtex, 4 pages with 3 figures, submitted to Phys. Rev. Lett., e-mail
[email protected]
Structural complexity and benthic metabolism: resolving the links between carbon cycling and biodiversity in restored seagrass meadows
Due to large losses of seagrass meadows worldwide, restoration is proposed as a key strategy for increasing coastal resilience and recovery. The emergence of a seagrass meadow is expected to substantially amplify biodiversity and enhance benthic metabolism by increasing primary productivity and respiration. Nevertheless, open questions remain regarding the metabolic balance of aging seagrass meadows and the roles benthic communities within the seagrass ecosystem play in overall metabolism.
To address these questions, we investigated a chronosequence of bare sediments and adjacent Zostera marina meadows of 3 and 7 years since restoration alongside a natural meadow located within a high-temperate marine embayment in Gåsö, Sweden. We combined continuous measurements of O2 fluxes using underwater eddy covariance with dissolved inorganic carbon (DIC) and O2 fluxes from benthic chambers during the productive season (July). Based on the ratio between O2 and DIC, we derived site-specific photosynthetic and respiratory quotients, enabling the conversion of eddy covariance fluxes to DIC. We assessed benthic diversity parameters as potential drivers of metabolic flux variability.
We observed high rates of gross primary productivity (GPP) spanning −18 to −82 mmolDICm-2d-1, which increased progressively with meadow age. Community respiration (CR) mirrored the GPP trend, and all meadows were net heterotrophic (GPP < CR), with net community productivity (NCP) ranging from 16 to 28 mmolDICm-2d-1. While autotrophic biomass did not increase with meadow age, macrophyte diversity did, elucidating potential effects of niche complementarity among macrophytes on community metabolism. These findings provide valuable insights into how community composition and meadow development relate to ecosystem functioning, highlighting potential tradeoffs between carbon uptake and biodiversity.</p
Effective charge-spin models for quantum dots
It is shown that at low densities, quantum dots with few electrons may be
mapped onto effective charge-spin models for the low-energy eigenstates. This
is justified by defining a lattice model based on a many-electron pocket-state
basis in which electrons are localised near their classical ground-state
positions. The equivalence to a single-band Hubbard model is then established
leading to a charge-spin () model which for most geometries reduces to a
spin (Heisenberg) model. The method is refined to include processes which
involve cyclic rotations of a ``ring'' of neighboring electrons. This is
achieved by introducing intermediate lattice points and the importance of ring
processes relative to pair-exchange processes is investigated using high-order
degenerate perturbation theory and the WKB approximation. The energy spectra
are computed from the effective models for specific cases and compared with
exact results and other approximation methods.Comment: RevTex, 24 pages, 7 figures submitted as compressed and PostScript
file
A Method to Study Relaxation of Metastable Phases: Macroscopic Mean-Field Dynamics
We propose two different macroscopic dynamics to describe the decay of
metastable phases in many-particle systems with local interactions. These
dynamics depend on the macroscopic order parameter through the restricted
free energy and are designed to give the correct equilibrium
distribution for . The connection between macroscopic dynamics and the
underlying microscopic dynamic are considered in the context of a projection-
operator formalism. Application to the square-lattice nearest-neighbor Ising
ferromagnet gives good agreement with droplet theory and Monte Carlo
simulations of the underlying microscopic dynamic. This includes quantitative
agreement for the exponential dependence of the lifetime on the inverse of the
applied field , and the observation of distinct field regions in which the
derivative of the lifetime with respect to depends differently on . In
addition, at very low temperatures we observe oscillatory behavior of this
derivative with respect to , due to the discreteness of the lattice and in
agreement with rigorous results. Similarities and differences between this work
and earlier works on finite Ising models in the fixed-magnetization ensemble
are discussed.Comment: 44 pages RevTeX3, 11 uuencoded Postscript figs. in separate file
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