457 research outputs found
Further study of the Over-Barrier Model to compute charge exchange processes
In this paper we study theoretically the process of electron capture between
one-optical-electron atoms (e.g. hydrogenlike or alkali atoms) and ions at
low-to-medium impact velocities () working on a modification
of an already developed classical In this work we present an improvement over
the Over Barrier Model (OBM) described in a recent paper [F. Sattin, Phys. Rev.
A {\bf 62}, 042711 (2000)]. We show that: i) one of the two free parameters
there introduced actually comes out consistently from the starting assumptions
underlying the model; ii) the modified model thus obtained is as much accurate
as the former one. Furthermore, we show that OBMs are able to accurately
predict some recent results of state selective electron capture, at odds with
what previously supposed.Comment: RevTeX, 7 pages, 4 eps figures. To appear in Physical Review A
(2001-september issue
Decay of the metastable phase in d=1 and d=2 Ising models
We calculate perturbatively the tunneling decay rate of the
metastable phase in the quantum d=1 Ising model in a skew magnetic field near
the coexistence line at T=0. It is shown that
oscillates in the magnetic field due to discreteness of the excitation
energy spectrum. After mapping of the obtained results onto the extreme
anisotropic d=2 Ising model at , we verify in the latter model the
droplet theory predictions for the free energy analytically continued to the
metastable phase. We find also evidence for the discrete-lattice corrections in
this metastable phase free energy.Comment: 4 pages, REVTe
Drag forces on inclusions in classical fields with dissipative dynamics
We study the drag force on uniformly moving inclusions which interact
linearly with dynamical free field theories commonly used to study soft
condensed matter systems. Drag forces are shown to be nonlinear functions of
the inclusion velocity and depend strongly on the field dynamics. The general
results obtained can be used to explain drag forces in Ising systems and also
predict the existence of drag forces on proteins in membranes due to couplings
to various physical parameters of the membrane such as composition, phase and
height fluctuations.Comment: 14 pages, 7 figure
Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
In this paper, we review theoretical and experimental research on rare region
effects at quantum phase transitions in disordered itinerant electron systems.
After summarizing a few basic concepts about phase transitions in the presence
of quenched randomness, we introduce the idea of rare regions and discuss their
importance. We then analyze in detail the different phenomena that can arise at
magnetic quantum phase transitions in disordered metals, including quantum
Griffiths singularities, smeared phase transitions, and cluster-glass
formation. For each scenario, we discuss the resulting phase diagram and
summarize the behavior of various observables. We then review several recent
experiments that provide examples of these rare region phenomena. We conclude
by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative
Ising chain fixed, references added, v3: final version as publishe
The signed loop approach to the Ising model: foundations and critical point
The signed loop method is a beautiful way to rigorously study the
two-dimensional Ising model with no external field. In this paper, we explore
the foundations of the method, including details that have so far been
neglected or overlooked in the literature. We demonstrate how the method can be
applied to the Ising model on the square lattice to derive explicit formal
expressions for the free energy density and two-point functions in terms of
sums over loops, valid all the way up to the self-dual point. As a corollary,
it follows that the self-dual point is critical both for the behaviour of the
free energy density, and for the decay of the two-point functions.Comment: 38 pages, 7 figures, with an improved Introduction. The final
publication is available at link.springer.co
Ultracold Atoms in 1D Optical Lattices: Mean Field, Quantum Field, Computation, and Soliton Formation
In this work, we highlight the correspondence between two descriptions of a
system of ultracold bosons in a one-dimensional optical lattice potential: (1)
the discrete nonlinear Schr\"{o}dinger equation, a discrete mean-field theory,
and (2) the Bose-Hubbard Hamiltonian, a discrete quantum-field theory. The
former is recovered from the latter in the limit of a product of local coherent
states. Using a truncated form of these mean-field states as initial
conditions, we build quantum analogs to the dark soliton solutions of the
discrete nonlinear Schr\"{o}dinger equation and investigate their dynamical
properties in the Bose-Hubbard Hamiltonian. We also discuss specifics of the
numerical methods employed for both our mean-field and quantum calculations,
where in the latter case we use the time-evolving block decimation algorithm
due to Vidal.Comment: 14 pages, 2 figures; to appear in Journal of Mathematics and
Computers in Simulatio
More is the Same; Phase Transitions and Mean Field Theories
This paper looks at the early theory of phase transitions. It considers a
group of related concepts derived from condensed matter and statistical
physics. The key technical ideas here go under the names of "singularity",
"order parameter", "mean field theory", and "variational method".
In a less technical vein, the question here is how can matter, ordinary
matter, support a diversity of forms. We see this diversity each time we
observe ice in contact with liquid water or see water vapor, "steam", come up
from a pot of heated water. Different phases can be qualitatively different in
that walking on ice is well within human capacity, but walking on liquid water
is proverbially forbidden to ordinary humans. These differences have been
apparent to humankind for millennia, but only brought within the domain of
scientific understanding since the 1880s.
A phase transition is a change from one behavior to another. A first order
phase transition involves a discontinuous jump in a some statistical variable
of the system. The discontinuous property is called the order parameter. Each
phase transitions has its own order parameter that range over a tremendous
variety of physical properties. These properties include the density of a
liquid gas transition, the magnetization in a ferromagnet, the size of a
connected cluster in a percolation transition, and a condensate wave function
in a superfluid or superconductor. A continuous transition occurs when that
jump approaches zero. This note is about statistical mechanics and the
development of mean field theory as a basis for a partial understanding of this
phenomenon.Comment: 25 pages, 6 figure
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