2,941 research outputs found
Density functional theory of vortex lattice melting in layered superconductors: a mean-field--substrate approach
We study the melting of the pancake vortex lattice in a layered
superconductor in the limit of vanishing Josephson coupling. Our approach
combines the methodology of a recently proposed mean-field substrate model for
such systems with the classical density functional theory of freezing. We
derive a free-energy functional in terms of a scalar order-parameter profile
and use it to derive a simple formula describing the temperature dependence of
the melting field. Our theoretical predictions are in good agreement with
simulation data. The theoretical framework proposed is thermodynamically
consistent and thus capable of describing the negative magnetization jump
obtained in experiments. Such consistency is demonstrated by showing the
equivalence of our expression for the density discontinuity at the transition
with the corresponding Clausius-Clapeyron relation.Comment: 11 pages, 4 figure
Analysis of Dislocation Mechanism for Melting of Elements: Pressure Dependence
In the framework of melting as a dislocation-mediated phase transition we
derive an equation for the pressure dependence of the melting temperatures of
the elements valid up to pressures of order their ambient bulk moduli. Melting
curves are calculated for Al, Mg, Ni, Pb, the iron group (Fe, Ru, Os), the
chromium group (Cr, Mo, W), the copper group (Cu, Ag, Au), noble gases (Ne, Ar,
Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These calculated
melting curves are in good agreement with existing data. We also discuss the
apparent equivalence of our melting relation and the Lindemann criterion, and
the lack of the rigorous proof of their equivalence. We show that the would-be
mathematical equivalence of both formulas must manifest itself in a new
relation between the Gr\"{u}neisen constant, bulk and shear moduli, and the
pressure derivative of the shear modulus.Comment: 19 pages, LaTeX, 9 eps figure
Instability of insulating states in optical lattices due to collective phonon excitations
The role of collective phonon excitations on the properties of cold atoms in
optical lattices is investigated. These phonon excitations are collective
excitations, whose appearance is caused by intersite atomic interactions
correlating the atoms, and they do not arise without such interactions. These
collective excitations should not be confused with lattice vibrations produced
by an external force. No such a force is assumed. But the considered phonons
are purely self-organized collective excitations, characterizing atomic
oscillations around lattice sites, due to intersite atomic interactions. It is
shown that these excitations can essentially influence the possibility of atoms
to be localized. The states that would be insulating in the absence of phonon
excitations can become delocalized when these excitations are taken into
account. This concerns long-range as well as local atomic interactions. To
characterize the region of stability, the Lindemann criterion is used.Comment: Latex file, 27 pages, 1 figur
Fragility and compressibility at the glass transition
Isothermal compressibilities and Brillouin sound velocities from the
literature allow to separate the compressibility at the glass transition into a
high-frequency vibrational and a low-frequency relaxational part. Their ratio
shows the linear fragility relation discovered by x-ray Brillouin scattering
[1], though the data bend away from the line at higher fragilities. Using the
concept of constrained degrees of freedom, one can show that the vibrational
part follows the fragility-independent Lindemann criterion; the fragility
dependence seems to stem from the relaxational part. The physical meaning of
this finding is discussed. [1] T. Scopigno, G. Ruocco, F. Sette and G. Monaco,
Science 302, 849 (2003)Comment: 4 pages, 2 figures, 2 tables, 33 references. Slightly changed after
refereein
Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory
We demonstrate the accuracy of the hypernetted chain closure and of the
mean-field approximation for the calculation of the fluid-state properties of
systems interacting by means of bounded and positive-definite pair potentials
with oscillating Fourier transforms. Subsequently, we prove the validity of a
bilinear, random-phase density functional for arbitrary inhomogeneous phases of
the same systems. On the basis of this functional, we calculate analytically
the freezing parameters of the latter. We demonstrate explicitly that the
stable crystals feature a lattice constant that is independent of density and
whose value is dictated by the position of the negative minimum of the Fourier
transform of the pair potential. This property is equivalent with the existence
of clusters, whose population scales proportionally to the density. We
establish that regardless of the form of the interaction potential and of the
location on the freezing line, all cluster crystals have a universal Lindemann
ratio L = 0.189 at freezing. We further make an explicit link between the
aforementioned density functional and the harmonic theory of crystals. This
allows us to establish an equivalence between the emergence of clusters and the
existence of negative Fourier components of the interaction potential. Finally,
we make a connection between the class of models at hand and the system of
infinite-dimensional hard spheres, when the limits of interaction steepness and
space dimension are both taken to infinity in a particularly described fashion.Comment: 19 pages, 5 figures, submitted to J. Chem. Phys; new version: minor
changes in structure of pape
Spin Effects in a Quantum Ring
Recent experiments are reviewed that explore the spin states of a ring-shaped
many-electron quantum dot. Coulomb-blockade spectroscopy is used to access the
spin degree of freedom. The Zeeman effect observed for states with successive
electron number allows to select possible sequences of spin ground states of
the ring. Spin-paired orbital levels can be identified by probing their
response to magnetic fields normal to the plane of the ring and electric fields
caused by suitable gate voltages. This narrows down the choice of ground-state
spin sequences. A gate-controlled singlet--triplet transition is identified and
the size of the exchange interaction matrix element is determined.Comment: 13 pages, 3 figures, Proceedings of the QD2004 conference in Banf
Objektorientierte Modellierung am Beispiel eines Mikrosystems zur Messung von Beschleunigungen
Mean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms
Continuous-time Markov chains with alarms (ACTMCs) allow for alarm events
that can be non-exponentially distributed. Within parametric ACTMCs, the
parameters of alarm-event distributions are not given explicitly and can be
subject of parameter synthesis. An algorithm solving the -optimal
parameter synthesis problem for parametric ACTMCs with long-run average
optimization objectives is presented. Our approach is based on reduction of the
problem to finding long-run average optimal strategies in semi-Markov decision
processes (semi-MDPs) and sufficient discretization of parameter (i.e., action)
space. Since the set of actions in the discretized semi-MDP can be very large,
a straightforward approach based on explicit action-space construction fails to
solve even simple instances of the problem. The presented algorithm uses an
enhanced policy iteration on symbolic representations of the action space. The
soundness of the algorithm is established for parametric ACTMCs with
alarm-event distributions satisfying four mild assumptions that are shown to
hold for uniform, Dirac and Weibull distributions in particular, but are
satisfied for many other distributions as well. An experimental implementation
shows that the symbolic technique substantially improves the efficiency of the
synthesis algorithm and allows to solve instances of realistic size.Comment: This article is a full version of a paper accepted to the Conference
on Quantitative Evaluation of SysTems (QEST) 201
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