386 research outputs found
The genesis of the quantum theory of the chemical bond
An historical overview is given of the relevant steps that allowed the
genesis of the quantum theory of the chemical bond, starting from the
appearance of the new quantum mechanics and following later developments till
approximately 1931. General ideas and some important details are discussed
concerning molecular spectroscopy, as well as quantum computations for simple
molecular systems performed within perturbative and variational approaches, for
which the Born-Oppenheimer method provided a quantitative theory accounting for
rotational, vibrational and electronic states. The novel concepts introduced by
the Heitler-London theory, complemented by those underlying the method of the
molecular orbitals, are critically analyzed along with some of their relevant
applications. Further improvements in the understanding of the nature of the
chemical bond are also considered, including the ideas of one-electron and
three-electron bonds introduced by Pauling, as well as the generalizations of
the Heitler-London theory firstly performed by Majorana, which allowed the
presence of ionic structures into homopolar compounds and provided the
theoretical proof of the stability of the helium molecular ion. The study of
intermolecular interactions, as developed by London, is finally examined.Comment: amsart, 34 pages, 2 figure
Modification of the Bloch law in ferromagnetic nanostructures
The temperature dependence of magnetization in ferromagnetic nanostructures
(e.g., nanoparticles or nanoclusters) is usually analyzed by means of an
empirical extension of the Bloch law sufficiently flexible for a good fitting
to the observed data and indicates a strong softening of magnetic coupling
compared to the bulk material. We analytically derive a microscopic
generalization of the Bloch law for the Heisenberg spin model which takes into
account the effects of size, shape and various surface boundary conditions. The
result establishes explicit connection to the microscopic parameters and
differs significantly from the existing description. In particular, we show
with a specific example that the latter may be misleading and grossly
overestimates magnetic softening in nanoparticles. It becomes clear why the
usual dependence appears to be valid in some nanostructures, while
large deviations are a general rule. We demonstrate that combination of
geometrical characteristics and coupling to environment can be used to
efficiently control magnetization and, in particular, to reach a magnetization
higher than in the bulk material.Comment: 7 pages, 4 figure
Role of the attractive intersite interaction in the extended Hubbard model
We consider the extended Hubbard model in the atomic limit on a Bethe lattice
with coordination number z. By using the equations of motion formalism, the
model is exactly solved for both attractive and repulsive intersite potential
V. By focusing on the case of negative V, i.e., attractive intersite
interaction, we study the phase diagram at finite temperature and find, for
various values of the filling and of the on-site coupling U, a phase transition
towards a state with phase separation. We determine the critical temperature as
a function of the relevant parameters, U/|V|, n and z and we find a reentrant
behavior in the plane (U/|V|,T). Finally, several thermodynamic properties are
investigated near criticality.Comment: 7 pages, 7 figures. EPJB Topical Issue on Novel Quantum Phases and
Mesoscopic Physics in Quantum Gase
Quantum dynamics of a binary mixture of BECs in a double well potential: an Holstein-Primakoff approach
We study the quantum dynamics of a binary mixture of Bose-Einstein
condensates (BEC) in a double-well potential starting from a two-mode
Bose-Hubbard Hamiltonian. Focussing on the regime where the number of atoms is
very large, a mapping onto a SU(2) spin problem together with a
Holstein-Primakoff transformation is performed. The quantum evolution of the
number difference of bosons between the two wells is investigated for different
initial conditions, which range from the case of a small imbalance between the
two wells to a coherent spin state. The results show an instability towards a
phase-separation above a critical positive value of the interspecies
interaction while the system evolves towards a coherent tunneling regime for
negative interspecies interactions. A comparison with a semiclassical approach
is discussed together with some implications on the experimental realization of
phase separation with cold atoms.Comment: 12 pages, 7 figures, accepted for publication in J. Phys.
A conformal field theory description of magnetic flux fractionalization in Josephson junction ladders
We show how the recently proposed effective theory for a Quantum Hall system
at "paired states" filling v=1 (Mod. Phys. Lett. A 15 (2000) 1679; Nucl. Phys.
B641 (2002) 547), the twisted model (TM), well adapts to describe the
phenomenology of Josephson Junction ladders (JJL) in the presence of defects.
In particular it is shown how naturally the phenomenon of flux
fractionalization takes place in such a description and its relation with the
discrete symmetries present in the TM. Furthermore we focus on closed
geometries, which enable us to analyze the topological properties of the ground
state of the system in relation to the presence of half flux quanta.Comment: 16 pages, 2 figure, Latex, revised versio
Majorana and the theoretical problem of photon-electron scattering
Relevant contributions by Majorana regarding Compton scattering off free or
bound electrons are considered in detail, where a (full quantum) generalization
of the Kramers-Heisenberg dispersion formula is derived. The role of
intermediate electronic states is appropriately pointed out in recovering the
standard Klein-Nishina formula (for free electron scattering) by making
recourse to a limpid physical scheme alternative to the (then unknown) Feynman
diagram approach. For bound electron scattering, a quantitative description of
the broadening of the Compton line was obtained for the first time by
introducing a finite mean life for the excited state of the electron system.
Finally, a generalization aimed to describe Compton scattering assisted by a
non-vanishing applied magnetic field is as well considered, revealing its
relevance for present day research.Comment: latex, amsart, 10 pages, 1 figur
Quantum Bose Josephson Junction with binary mixtures of BECs
We study the quantum behaviour of a binary mixture of Bose-Einstein
condensates (BEC) in a double-well potential starting from a two-mode
Bose-Hubbard Hamiltonian. We focus on the small tunneling amplitude regime and
apply perturbation theory up to second order. Analytical expressions for the
energy eigenvalues and eigenstates are obtained. Then the quantum evolution of
the number difference of bosons between the two potential wells is fully
investigated for two different initial conditions: completely localized states
and coherent spin states. In the first case both the short and the long time
dynamics is studied and a rich behaviour is found, ranging from small amplitude
oscillations and collapses and revivals to coherent tunneling. In the second
case the short-time scale evolution of number difference is determined and a
more irregular dynamics is evidenced. Finally, the formation of Schroedinger
cat states is considered and shown to affect the momentum distribution.Comment: 14 pages, 4 figure
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