190 research outputs found
Localization and Causality for a free particle
Theorems (most notably by Hegerfeldt) prove that an initially localized
particle whose time evolution is determined by a positive Hamiltonian will
violate causality. We argue that this apparent paradox is resolved for a free
particle described by either the Dirac equation or the Klein-Gordon equation
because such a particle cannot be localized in the sense required by the
theorems.Comment: 9 pages,no figures,new section adde
Analytic theory of ground-state properties of a three-dimensional electron gas at varying spin polarization
We present an analytic theory of the spin-resolved pair distribution
functions and the ground-state energy of an electron gas
with an arbitrary degree of spin polarization. We first use the Hohenberg-Kohn
variational principle and the von Weizs\"{a}cker-Herring ideal kinetic energy
functional to derive a zero-energy scattering Schr\"{o}dinger equation for
. The solution of this equation is implemented
within a Fermi-hypernetted-chain approximation which embodies the Hartree-Fock
limit and is shown to satisfy an important set of sum rules. We present
numerical results for the ground-state energy at selected values of the spin
polarization and for in both a paramagnetic and a fully
spin-polarized electron gas, in comparison with the available data from Quantum
Monte Carlo studies over a wide range of electron density.Comment: 13 pages, 8 figures, submitted to Phys. Rev.
Fast energy transfer mediated by multi-quanta bound states in a nonlinear quantum lattice
By using a Generalized Hubbard model for bosons, the energy transfer in a
nonlinear quantum lattice is studied, with special emphasis on the interplay
between local and nonlocal nonlinearity. For a strong local nonlinearity, it is
shown that the creation of v quanta on one site excites a soliton band formed
by bound states involving v quanta trapped on the same site. The energy is
first localized on the excited site over a significant timescale and then
slowly delocalizes along the lattice. As when increasing the nonlocal
nonlinearity, a faster dynamics occurs and the energy propagates more rapidly
along the lattice. Nevertheless, the larger is the number of quanta, the slower
is the dynamics. However, it is shown that when the nonlocal nonlinearity
reaches a critical value, the lattice suddenly supports a very fast energy
propagation whose dynamics is almost independent on the number of quanta. The
energy is transfered by specific bound states formed by the superimposition of
states involving v-p quanta trapped on one site and p quanta trapped on the
nearest neighbour sites, with p=0,..,v-1. These bound states behave as
independent quanta and they exhibit a dynamics which is insensitive to the
nonlinearity and controlled by the single quantum hopping constant.Comment: 28 pages, 8 figure
Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two
We consider the billiard dynamics in a non-compact set of R^d that is
constructed as a bi-infinite chain of translated copies of the same
d-dimensional polytope. A random configuration of semi-dispersing scatterers is
placed in each copy. The ensemble of dynamical systems thus defined, one for
each global realization of the scatterers, is called `quenched random Lorentz
tube'. Under some fairly general conditions, we prove that every system in the
ensemble is hyperbolic and almost every system is recurrent, ergodic, and
enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure
Enhancement of fusion rates due to quantum effects in the particles momentum distribution in nonideal media
This study concerns a situation when measurements of the nonresonant
cross-section of nuclear reactions appear highly dependent on the environment
in which the particles interact. An appealing example discussed in the paper is
the interaction of a deuteron beam with a target of deuterated metal Ta. In
these experiments, the reaction cross section for d(d,p)t was shown to be
orders of magnitude greater than what the conventional model predicts for the
low-energy particles. In this paper we take into account the influence of
quantum effects due to the Heisenberg uncertainty principle for particles in a
non-ideal medium elastically interacting with the medium particles. In order to
calculate the nuclear reaction rate in the non-ideal environment we apply both
the Monte Carlo technique and approximate analytical calculation of the Feynman
diagram using nonrelativistic kinetic Green's functions in the medium which
correspond to the generalized energy and momentum distribution functions of
interacting particles. We show a possibility to reduce the 12-fold integral
corresponding to this diagram to a fivefold integral. This can significantly
speed up the computation and control accuracy. Our calculations show that
quantum effects significantly influence reaction rates such as p +7Be, 3He
+4He, p +7Li, and 12C +12C. The new reaction rates may be much higher than the
classical ones for the interior of the Sun and supernova stars. The possibility
to observe the theoretical predictions under laboratory conditions is
discussed
Self-consistent Overhauser model for the pair distribution function of an electron gas in dimensionalities D=3 and D=2
We present self-consistent calculations of the spin-averaged pair
distribution function for a homogeneous electron gas in the paramagnetic
state in both three and two dimensions, based on an extension of a model that
was originally proposed by A. W. Overhauser [Can. J. Phys. {\bf 73}, 683
(1995)] and further evaluated by P. Gori-Giorgi and J. P. Perdew [Phys. Rev. B
{\bf 64}, 155102 (2001)]. The model involves the solution of a two-electron
scattering problem via an effective Coulombic potential, that we determine
within a self-consistent Hartree approximation. We find numerical results for
that are in excellent agreement with Quantum Monte Carlo data at low and
intermediate coupling strength , extending up to in
dimensionality D=3. However, the Hartree approximation does not properly
account for the emergence of a first-neighbor peak at stronger coupling, such
as at in D=2, and has limited accuracy in regard to the spin-resolved
components and . We also
report calculations of the electron-electron s-wave scattering length, to test
an analytical expression proposed by Overhauser in D=3 and to present new
results in D=2 at moderate coupling strength. Finally, we indicate how this
approach can be extended to evaluate the pair distribution functions in
inhomogeneous electron systems and hence to obtain improved
exchange-correlation energy functionals.Comment: 14 pages, 7 figuers, to apear in Physical Review
Intra-abdominal hypertension and abdominal compartment syndrome in pancreatitis, paediatrics, and trauma
Peer reviewe
Many body physics from a quantum information perspective
The quantum information approach to many body physics has been very
successful in giving new insight and novel numerical methods. In these lecture
notes we take a vertical view of the subject, starting from general concepts
and at each step delving into applications or consequences of a particular
topic. We first review some general quantum information concepts like
entanglement and entanglement measures, which leads us to entanglement area
laws. We then continue with one of the most famous examples of area-law abiding
states: matrix product states, and tensor product states in general. Of these,
we choose one example (classical superposition states) to introduce recent
developments on a novel quantum many body approach: quantum kinetic Ising
models. We conclude with a brief outlook of the field.Comment: Lectures from the Les Houches School on "Modern theories of
correlated electron systems". Improved version new references adde
Relaxation channels of two-vibron bound states in \alpha-helix proteins
Relaxation channels for two-vibron bound states in an anharmonic alpha-helix
protein are studied. It is pointed out that the relaxation originates in the
interaction between the dressed anharmonic vibrons and the remaining phonons.
This interaction is responsible for the occurrence of transitions between
two-vibron eigenstates mediated by both phonon absorption and phonon emission.
At biological temperature, it is shown that the relaxation rate does not
significantly depends on the nature of the two-vibron state involved in the
process. Therefore, the lifetime for both bound and free states is of the same
order of magnitude and ranges between 0.1 and 1.0 ps for realistic parameters.
By contrast, the relaxation channels strongly depend on the nature of the
two-vibron states which is a consequence of the breather-like behavior of the
two-vibron bound states.Comment: octobre 2003 - soumis Phys. Rev.
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