3,112 research outputs found
Calculation of the Autocorrelation Function of the Stochastic Single Machine Infinite Bus System
Critical slowing down (CSD) is the phenomenon in which a system recovers more
slowly from small perturbations. CSD, as evidenced by increasing signal
variance and autocorrelation, has been observed in many dynamical systems
approaching a critical transition, and thus can be a useful signal of proximity
to transition. In this paper, we derive autocorrelation functions for the state
variables of a stochastic single machine infinite bus system (SMIB). The
results show that both autocorrelation and variance increase as this system
approaches a saddle-node bifurcation. The autocorrelation functions help to
explain why CSD can be used as an indicator of proximity to criticality in
power systems revealing, for example, how nonlinearity in the SMIB system
causes these signs to appear.Comment: Accepted for publication/presentation in Proc. North American Power
Symposium, 201
Dynamic properties of the spin-1/2 XY chain with three-site interactions
We consider a spin-1/2 XY chain in a transverse (z) field with multi-site
interactions. The additional terms introduced into the Hamiltonian involve
products of spin components related to three adjacent sites. A Jordan-Wigner
transformation leads to a simple bilinear Fermi form for the resulting
Hamiltonian and hence the spin model admits a rigorous analysis. We point out
the close relationships between several variants of the model which were
discussed separately in previous studies. The ground-state phases (ferromagnet
and two kinds of spin liquid) of the model are reflected in the dynamic
structure factors of the spin chains, which are the main focus in this study.
First we consider the zz dynamic structure factor reporting for this quantity a
closed-form expression and analyzing the properties of the two-fermion
(particle-hole) excitation continuum which governs the dynamics of transverse
spin component fluctuations and of some other local operator fluctuations. Then
we examine the xx dynamic structure factor which is governed by many-fermion
excitations, reporting both analytical and numerical results. We discuss some
easily recognized features of the dynamic structure factors which are
signatures for the presence of the three-site interactions.Comment: 28 pages, 10 fugure
Integration of Small Farmers into Value Chains: Evidence from Eastern Europe and Central Asia
The economic breakdown of the early transition process weighed heavily on food supply relationships in the Eastern European and Central Asian (EECA) countries. Small and medium-sized farm suppliers and processors suffered from lack of necessary production inputs whereas processors and retailers faced problems of insufficient quantity and quality of supplies. At the same time, changes in consumer demand as well as the accompanying entry of foreign investors in the retail and processing sectors necessitated significant and lengthy reforms and adjustments in the structure of food commodity chains to overcome these problems. Based on an extensive literature overview and a synthesis of five case studies conducted upon the assignment of Food and Agriculture Organization (FAO) of the United Nations, the current chapter demonstrates how small and medium-sized food processors manage to install effective procurement systems in weak institutional environments of EECA. The chapter also identifies the factors that drive small farmer-processor business linkages and their integration into national and international value chains in order to develop options for support and assistance
The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond
We consider the spin-1/2 antiferromagnetic Heisenberg model on the
two-dimensional square-kagome lattice with almost dispersionless lowest magnon
band. For a general exchange coupling geometry we elaborate low-energy
effective Hamiltonians which emerge at high magnetic fields. The effective
model to describe the low-energy degrees of freedom of the initial frustrated
quantum spin model is the (unfrustrated) square-lattice spin-1/2 model in
a -aligned magnetic field. For the effective model we perform quantum Monte
Carlo simulations to discuss the low-temperature properties of the
square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We
pay special attention to a magnetic-field driven
Berezinskii-Kosterlitz-Thouless phase transition which occurs at low
temperatures.Comment: 6 figure
Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields
We investigate the thermodynamic properties of the frustrated bilayer quantum
Heisenberg antiferromagnet at low temperatures in the vicinity of the
saturation magnetic field. The low-energy degrees of freedom of the spin model
are mapped onto a hard-square gas on a square lattice. We use exact
diagonalization data for finite spin systems to check the validity of such a
description. Using a classical Monte Carlo method we give a quantitative
description of the thermodynamics of the spin model at low temperatures around
the saturation field. The main peculiarity of the considered two-dimensional
Heisenberg antiferromagnet is related to a phase transition of the hard-square
model on the square lattice, which belongs to the two-dimensional Ising model
universality class. It manifests itself in a logarithmic (low-)temperature
singularity of the specific heat of the spin system observed for magnetic
fields just below the saturation field
Quantum phase transitions in the exactly solved spin-1/2 Heisenberg-Ising ladder
Ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with
the Heisenberg intra-rung and Ising inter-rung interactions is examined in
detail. The investigated model is transformed to the quantum Ising chain with
composite spins in an effective transverse and longitudinal field by employing
either the bond-state representation or the unitary transformation. It is shown
that the ground state of the Heisenberg-Ising ladder can be descended from
three exactly solvable models: the quantum Ising chain in a transverse field,
the 'classical' Ising chain in a longitudinal field or the spin-chain model in
a staggered longitudinal-transverse field. The last model serves in evidence of
the staggered bond phase with alternating singlet and triplet bonds on the
rungs of two-leg ladder, which appears at moderate values of the external
magnetic field and consequently leads to a fractional plateau at a half of the
saturation magnetization. The ground-state phase diagram totally consists of
five ordered and one quantum disordered phase, which are separated from each
other either by the lines of discontinuous or continuous quantum phase
transitions. The order parameters are exactly calculated for all five ordered
phases and the quantum disordered phase is characterized through different
short-range spin-spin correlations.Comment: corrected version, figure A1 has been changed, accepted in J. Phys.
A, 19 pages, 7 figure
Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance
We study long-range correlations of equilibrium current densities in a
two-dimensional mesoscopic system with the time reversal invariance broken by a
random or homogeneous magnetic field. Our result is universal, i.e. it does not
depend on the type (random potential or random magnetic field) or correlation
length of disorder. This contradicts recent sigma-model calculations of
Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well
as for the renormalization of the conductivity. We show explicitly that the new
term in the sigma-model derived by TS&E and claimed to lead to delocalization
does not exist. The error in the derivation of TS&E is traced to an incorrect
ultraviolet regularization procedure violating current conservation and gauge
invariance.Comment: 8 pages, 3 figure
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