6,724 research outputs found
Emergence of equilibrium thermodynamic properties in quantum pure states. II. Analysis of a spin model system
A system composed of identical spins and described by a quantum mechanical
pure state is analyzed within the statistical framework presented in Part I of
this work. We explicitly derive the typical values of the entropy, of the
energy, and of the equilibrium reduced density matrix of a subsystem for the
two different statistics introduced in Part I. In order to analyze their
consistency with thermodynamics, these quantities of interest are evaluated in
the limit of large number of components of the isolated system. The main
results can be summarized as follows: typical values of the entropy and of the
equilibrium reduced density matrix as functions of the internal energy in the
fixed expectation energy ensemble do not satisfy the requirement of
thermodynamics. On the contrary, the thermodynamical description is recovered
from the random pure state ensemble (RPSE), provided that one considers systems
large enough. The thermodynamic limit of the considered properties for the spin
system reveals a number of important features. First canonical statistics (and
thus, canonical typicality as long as the fluctuations around the average value
are small) emerges without the need of assuming the microcanonical space for
the global pure state. Moreover, we rigorously prove (i) the equivalence of the
"global temperature," derived from the entropy equation of state, with the
"local temperature" determining the canonical state of the subsystems; and (ii)
the equivalence between the RPSE typical entropy and the canonical entropy for
the overall system.Comment: 30 pages, 10 figure
Interplay between valence and core excitation mechanisms in the breakup of halo nuclei
The phenomenon of core excitation in the breakup of a two-body halo nucleus
is investigated. We show that this effect plays a significant role in the
reaction dynamics and, furthermore, its interference with the valence
excitation mechanism has sizable and measurable effects on the breakup angular
distributions. These effects have been studied in the resonant breakup of 11Be
on a carbon target, populating the resonances at 1.78 MeV (5/2+) and 3.41 MeV
(3/2+). The calculations have been performed using a recently extension of the
DWBA method, which takes into account the effect of core excitation in both the
structure of the halo nucleus and in the reaction mechanism. The calculated
angular distributions have been compared with the available data [Fukuda et
al., Phys. Rev. C70,054606]. Although each of these resonances is dominated by
one of the two considered mechanisms, the angular patterns of these resonances
depend in a very delicate way on the interference between them. This is the
first clear evidence of this effect but the phenomenon is likely to occur in
other similar reactions.Comment: 5 pages, 2 figures, (Version to appear in Physical Review Letters
Determining distributions of weakly bound nuclei from breakup cross sections using Continuum Discretized Coupled Channels calculations. Application to Be
A novel method to extract the strength of a weakly bound nucleus from
experimental Coulomb dissociation data is proposed. The method makes use of
continuum discretized coupled channels (CDCC) calculations, in which both
nuclear and Coulomb forces are taken into account to all orders. This is a
crucial advantage with respect to the standard procedure based on the
Equivalent Photon Method (EPM) which does not properly take into account
nuclear distortion, higher order coupling effects, or Coulomb-nuclear
interference terms. The procedure is applied to the Be nucleus using two
sets of available experimental data at different energies, for which seemingly
incompatible have been reported using the EPM. We show that the present
procedure gives consistent strengths, thus solving the aforementioned
long-standing discrepancy between the two measurements.Comment: Submitted for publicatio
Signatures of Anderson localization and delocalized random quantum states
We consider the notion of equilibration for an isolated quantum system
exhibiting Anderson localization. The system is assumed to be in a pure state,
i.e., described by a wave-function undergoing unitary dynamics. We focus on the
simplest model of a 1D disordered chain and we analyse both the dynamics of an
initially localized state and the dynamics of quantum states drawn at random
from the ensemble corresponding to the minimum knowledge about the initial
state. While in the former case the site distribution remains confined in a
limited portion of the chain, the site distribution of random pure state
fluctuates around an equilibrium average that is delocalized over the entire
chain. A clear connection between the equilibration observed when the system is
initialized in a fully localized state and the amplitude of dynamical
fluctuations of a typical random pure state is established
Correlated adaptation of agents in a simple market: a statistical physics perspective
We discuss recent work in the study of a simple model for the collective
behaviour of diverse speculative agents in an idealized stockmarket, considered
from the perspective of the statistical physics of many-body systems. The only
information about other agents available to any one is the total trade at time
steps. Evidence is presented for correlated adaptation and phase
transitions/crossovers in the global volatility of the system as a function of
appropriate information scaling dimension. Stochastically controlled
irrationally of individual agents is shown to be globally advantageous. We
describe the derivation of the underlying effective stochastic differential
equations which govern the dynamics, and make an interpretation of the results
from the point of view of the statistical physics of disordered systems.Comment: 15 Pages. 5 figure
Beyond quantum microcanonical statistics
Descriptions of molecular systems usually refer to two distinct theoretical
frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of
an isolated system which is determined to calculate molecular properties and to
consider the time evolution according to the unitary Schr\"odinger equation. On
the other hand a mixed state, i.e. a statistical density matrix, is the
standard formalism to account for thermal equilibrium, as postulated in the
microcanonical quantum statistics. In the present paper an alternative
treatment relying on a statistical analysis of the possible wavefunctions of an
isolated system is presented. In analogy with the classical ergodic theory, the
time evolution of the wavefunction determines the probability distribution in
the phase space pertaining to an isolated system. However, this alone cannot
account for a well defined thermodynamical description of the system in the
macroscopic limit, unless a suitable probability distribution for the quantum
constants of motion is introduced. We present a workable formalism assuring the
emergence of typical values of thermodynamic functions, such as the internal
energy and the entropy, in the large size limit of the system. This allows the
identification of macroscopic properties independently of the specific
realization of the quantum state. A description of material systems in
agreement with equilibrium thermodynamics is then derived without constraints
on the physical constituents and interactions of the system. Furthermore, the
canonical statistics is recovered in all generality for the reduced density
matrix of a subsystem
Pilot-wave quantum theory with a single Bohm's trajectory
The representation of a quantum system as the spatial configuration of its
constituents evolving in time as a trajectory under the action of the
wave-function, is the main objective of the Bohm theory. However, its standard
formulation is referred to the statistical ensemble of its possible
trajectories. The statistical ensemble is introduced in order to establish the
exact correspondence (the Born's rule) between the probability density on the
spatial configurations and the quantum distribution, that is the squared
modulus of the wave-function. In this work we explore the possibility of using
the pilot wave theory at the level of a single Bohm's trajectory. The pilot
wave theory allows a formally self-consistent representation of quantum systems
as a single Bohm's trajectory, but in this case there is no room for the Born's
rule at least in its standard form. We will show that a correspondence exists
between the statistical distribution of configurations along the single Bohm's
trajectory and the quantum distribution for a subsystem interacting with the
environment in a multicomponent system. To this aim, we present the numerical
results of the single Bohm's trajectory description of the model system of six
confined rotors with random interactions. We find a rather close correspondence
between the coordinate distribution of one rotor along its trajectory and the
time averaged marginal quantum distribution for the same rotor. This might be
considered as the counterpart of the standard Born's rule. Furthermore a
strongly fluctuating behavior with a fast loss of correlation is found for the
evolution of each rotor coordinate. This suggests that a Markov process might
well approximate the evolution of the Bohm's coordinate of a single rotor and
it is shown that the correspondence between coordinate distribution and quantum
distribution of the rotor is exactly verified
Description of the LiLi transfer reaction using structure overlaps from a full three-body model
Recent data on the differential angular distribution for the transfer
reaction Li(p,d)Li at MeV in inverse kinematics are
analysed within the DWBA reaction framework, using the overlap functions
calculated within a three-body model of Li. The weight of the different
Li configurations in the system's ground state is obtained from the
structure calculations unambiguously. The effect of the Li spin in the
calculated observables is also investigated. We find that, although all the
considered models succeed in reproducing the shape of the data, the magnitude
is very sensitive to the content of wave in the Li
ground-state wave function. Among the considered models, the best agreement
with the data is obtained when the Li ground state contains a 31\%
of wave in the -Li subsystem. Although this model takes into
account explicitly the splitting of the and resonances due to the
coupling of the wave to the spin of the core, a similar
degree of agreement can be achieved with a model in which the Li spin is
ignored, provided that it contains a similar p-wave content.Comment: 8 pages, 3 figures. Final versio
Linking structure and dynamics in reactions with Borromean nuclei: the LiLi case
One-neutron removal reactions induced by two-neutron Borromean
nuclei are studied within a Transfer-to-the-Continuum (TC) reaction framework,
which incorporates the three-body character of the incident nucleus. The
relative energy distribution of the residual unbound two-body subsystem, which
is assumed to retain information on the structure of the original three-body
projectile, is computed by evaluating the transition amplitude for different
neutron-core final states in the continuum. These transition amplitudes depend
on the overlaps between the original three-body ground-state wave function and
the two-body continuum states populated in the reaction, thus ensuring a
consistent description of the incident and final nuclei. By comparing different
Li three-body models, it is found that the LiLi
relative energy spectrum is very sensitive to the position of the and
states in Li and to the partial wave content of these
configurations within the Li ground-state wave function. The possible
presence of a low-lying resonance is discussed. The coupling of the
single particle configurations with the non-zero spin of the Li core,
which produces a spin-spin splitting of the states, is also studied. Among the
considered models, the best agreement with the available data is obtained with
a Li model that incorporates the actual spin of the core and contains
31\% of -wave content in the -Li subsystem, in accord
with our previous findings for the Li(p,d)Li transfer reaction,
and a near-threshold virtual state.Comment: 7 pages, 4 figures, submitted to PL
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