41,272 research outputs found
A quantum Mermin--Wagner theorem for quantum rotators on two--dimensional graphs
This is the first of a series of papers considering symmetry properties of
quantum systems over 2D graphs or manifolds, with continuous spins, in the
spirit of the Mermin--Wagner theorem. In the model considered here (quantum
rotators) the phase space of a single spin is a dimensional torus, and
spins (or particles) are attached to sites of a graph satisfying a special
bi-dimensionality property. The kinetic energy part of the Hamiltonian is minus
a half of the Laplace operator. We assume that the interaction potential is
C-smooth and invariant under the action of a connected Lie group {\ttG}.
A part of our approach is to give a definition (and a construction) of a class
of infinite-volume Gibbs states for the systems under consideration (the class
\fG). This class contains the so-called limit Gibbs states, with or without
boundary conditions. We use ideas and techniques originated from various past
papers, in combination with the Feynman--Kac representation, to prove that any
state lying in the class \fG (defined in the text) is {\ttG}-invariant. An
example is given where the interaction potential is singular and there exists a
Gibbs state which is not {\ttG}-invariant.
In the next paper under the same title we establish a similar result for a
bosonic model where particles can jump from a vertex of the graph to one of its
neighbors (a generalized Hubbard model).Comment: 27 page
Energy-efficient coding with discrete stochastic events
We investigate the energy efficiency of signaling mechanisms that transfer information by means of discrete stochastic events, such as the opening or closing of an ion channel. Using a simple model for the generation of graded electrical signals by sodium and potassium channels, we find optimum numbers of channels that maximize energy efficiency. The optima depend on several factors: the relative magnitudes of the signaling cost (current flow through channels), the fixed cost of maintaining the system, the reliability of the input, additional sources of noise, and the relative costs of upstream and downstream mechanisms. We also analyze how the statistics of input signals influence energy efficiency. We find that energy-efficient signal ensembles favor a bimodal distribution of channel activations and contain only a very small fraction of large inputs when energy is scarce. We conclude that when energy use is a significant constraint, trade-offs between information transfer and energy can strongly influence the number of signaling molecules and synapses used by neurons and the manner in which these mechanisms represent information
Metal-insulator transition in an aperiodic ladder network: an exact result
We show, in a completely analytical way, that a tight binding ladder network
composed of atomic sites with on-site potentials distributed according to the
quasiperiodic Aubry model can exhibit a metal-insulator transition at multiple
values of the Fermi energy. For specific values of the first and second
neighbor electron hopping, the result is obtained exactly. With a more general
model, we calculate the two-terminal conductance numerically. The numerical
results corroborate the analytical findings and yield a richer variety of
spectrum showing multiple mobility edges.Comment: 4 pages, 3 figure
Spin-correlations and magnetic structure in an Fe monolayer on 5d transition metal surfaces
We present a detailed first principles study on the magnetic structure of an
Fe monolayer on different surfaces of 5d transition metals. We use the
spin-cluster expansion technique to obtain parameters of a spin model, and
predict the possible magnetic ground state of the studied systems by employing
the mean field approach and in certain cases by spin dynamics calculations. We
point out that the number of shells considered for the isotropic exchange
interactions plays a crucial role in the determination of the magnetic ground
state. In the case of Ta substrate we demonstrate that the out-of-plane
relaxation of the Fe monolayer causes a transition from ferromagnetic to
antiferromagnetic ground state. We examine the relative magnitude of nearest
neighbour Dzyaloshinskii-Moriya (D) and isotropic (J) exchange interactions in
order to get insight into the nature of magnetic pattern formations. For the
Fe/Os(0001) system we calculate a very large D/J ratio, correspondingly, a spin
spiral ground state. We find that, mainly through the leading isotropic
exchange and Dzyaloshinskii-Moriya interactions, the inward layer relaxation
substantially influences the magnetic ordering of the Fe monolayer. For the
Fe/Re(0001) system characterized by large antiferromagnetic interactions we
also determine the chirality of the N\'eel-type ground state.Comment: 15 pages, 8 figures, 2 table
Explicit Representations for the T-Matrix on Unphysical Energy Sheets and Resonances in Two- and Three-Body Systems
We discuss the structure of the two- and three-body T-matrices, scattering
matrices, and resolvents continued to the unphysical energy sheets. Our
conclusions arise due to the representations that have been found for
analytically continued momentum-space kernels of the T-operators. These
representations are explicitly written only in terms of the physical-sheet
kernels of the T-matrix itself. One of advantages of the representations in the
three-body case is that they show which portions of the physical-sheet
three-body scattering matrix are ``responsible'' for the resonances associated
with a particular unphysical sheet. A resonance appears to be the energy where
the correspondingly truncated scattering matrix (taken on the physical sheet)
has eigenvalue zero. We also mention applications of this approach to some
specific three-body systems, based on the Faddeev differential equations.Comment: Based on a lecture given at the International Workshop ``Critical
Stability of Few-Body Quantum Systems'' (Dresden, October 17--22, 2005
- …