246 research outputs found
From thermal to excited-state quantum phase transitions ---the Dicke model
We study the thermodynamics of the full version of the Dicke model, including
all the possible values of the total angular momentum , with both
microcanonical and canonical ensembles. We focus on how the excited-state
quantum phase transition, which only appears in the microcanonical description
of the maximum angular momentum sector, , change to a standard thermal
phase transition when all the sectors are taken into account. We show that both
the thermal and the excited-state quantum phase transitions have the same
origin; in other words, that both are two faces of the same phenomenon. Despite
all the logarithmic singularities which characterize the excited-state quantum
phase transition are ruled out when all the -sectors are considered, the
critical energy (or temperature) still divides the spectrum in two regions: one
in which the parity symmetry can be broken, and another in which this symmetry
is always well defined.Comment: Submitted to PRE. Comments are welcome. V2: Updated to match
published versio
Entropy, chaos and excited-state quantum phase transitions in the Dicke model
We study non-equilibrium processes in an isolated quantum system ---the Dicke
model--- focusing on the role played by the transition from integrability to
chaos and the presence of excited-state quantum phase transitions. We show that
both diagonal and entanglement entropies are abruptly increased by the onset of
chaos. Also, this increase ends in both cases just after the system crosses the
critical energy of the excited-state quantum phase transition. The link between
entropy production, the development of chaos and the excited-state quantum
phase transition is more clear for the entanglement entropy. On the contrary,
the heat dissipated by the process is affected neither by the onset of chaos,
nor by the excited-state quantum phase transition.Comment: 12 pages, 9 figures, RevTex 4.
Approximated integrability of the Dicke model
A very approximate second integral of motion of the Dicke model is identified
within a broad region above the ground state, and for a wide range of values of
the external parameters. This second integral, obtained from a Born Oppenheimer
approximation, classifies the whole regular part of the spectrum in bands
labelled by its corresponding eigenvalues. Results obtained from this
approximation are compared with exact numerical diagonalization for finite
systems in the superradiant phase, obtaining a remarkable accord. The region of
validity of our approach in the parameter space, which includes the resonant
case, is unveiled. The energy range of validity goes from the ground state up
to a certain upper energy where chaos sets in, and extends far beyond the range
of applicability of a simple harmonic approximation around the minimal energy
configuration. The upper energy validity limit increases for larger values of
the coupling constant and the ratio between the level splitting and the
frequency of the field. These results show that the Dicke model behaves like a
two-degree of freedom integrable model for a wide range of energies and values
of the external parameters.Comment: 6 pages, 3 figures. Second version with added text, references and
some new figure
Decoherence induced by an interacting spin environment in the transition from integrability to chaos
We investigate the decoherence properties of a central system composed of two
spins 1/2 in contact with a spin bath. The dynamical regime of the bath ranges
from a fully integrable integrable limit to complete chaoticity. We show that
the dynamical regime of the bath determines the efficiency of the decoherence
process. For perturbative regimes, the integrable limit provides stronger
decoherence, while in the strong coupling regime the chaotic limit becomes more
efficient. We also show that the decoherence time behaves in a similar way. On
the contrary, the rate of decay of magnitudes like linear entropy or fidelity
does not depend on the dynamical regime of the bath. We interpret the latter
results as due to a comparable complexity of the Hamiltonian for both the
integrable and the fully chaotic limits.Comment: Submitted to Phys. Rev.
High resolution simulations of the head-on collision of white dwarfs
The direct impact of white dwarfs has been suggested as a plausible channel
for type Ia supernovae. In spite of their (a priori) rareness, in highly
populated globular clusters and in galactic centers, where the amount of white
dwarfs is considerable, the rate of violent collisions between two of them
might be non-negligible. Even more, there are indications that binary white
dwarf systems orbited by a third stellar-mass body have an important chance to
induce a clean head-on collision. Therefore, this scenario represents a source
of contamination for the supernova light-curves sample that it is used as
standard candles in cosmology, and it deserves further investigation. Some
groups have conducted numerical simulations of this scenario, but their results
show several differences. In this paper we address some of the possible sources
of these differences, presenting the results of high resolution hydrodynamical
simulations jointly with a detailed nuclear post-processing of the nuclear
abundances, to check the viability of white dwarf collisions to produce
significant amounts of 56Ni. To that purpose, we use a 2D-axial symmetric
smoothed particle hydrodynamic code to obtain a resolution considerably higher
than in previous studies. In this work, we also study how the initial mass and
nuclear composition affect the results. The gravitational wave emission is also
calculated, as this is a unique signature of this kind of events. All
calculated models produce a significant amount of 56Ni, ranging from 0.1 Msun
to 1.1 Msun, compatible not only with normal-Branch type Ia supernova but also
with the subluminous and super-Chandrasekhar subset. Nevertheless, the
distribution mass-function of white dwarfs favors collisions among 0.6-0.7 Msun
objects, leading to subluminous events.Comment: 24 pages, 12 figures, accepted for publication in MNRA
Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians
Using a new class of exactly solvable models based on the pairing
interaction, we show that it is possible to construct integrable Hamiltonians
with a Wigner distribution of nearest neighbor level spacings. However, these
Hamiltonians involve many-body interactions and the addition of a small
integrable perturbation very quickly leads the system to a Poisson
distribution. Besides this exceptional cases, we show that the accumulated
distribution of an ensemble of random integrable two-body pairing hamiltonians
is in perfect agreement with the Poisson limit. These numerical results for
quantum integrable Hamiltonians provide a further empirical confirmation to the
work of the Berry and Tabor in the semiclassical limit.Comment: 5 pages, 4 figures, LaTeX (RevTeX 4) Content changed, References
added Accepted for publication in PR
Fluctuations in the level density of a Fermi gas
We present a theory that accurately describes the counting of excited states
of a noninteracting fermionic gas. At high excitation energies the results
reproduce Bethe's theory. At low energies oscillatory corrections to the
many--body density of states, related to shell effects, are obtained. The
fluctuations depend non-trivially on energy and particle number. Universality
and connections with Poisson statistics and random matrix theory are
established for regular and chaotic single--particle motion.Comment: 4 pages, 1 figur
Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition
We study the ergodic side of the many-body localization transition in its
standard model, the disordered Heisenberg quantum spin chain. We show that the
Thouless energy, extracted from long-range spectral statistics and the
power-spectrum of the full momentum distribution fluctuations, is not large
enough to guarantee thermalization. We find that both estimates coincide and
behave non-monotonically, exhibiting a strong peak at an intermediate value of
the disorder. Furthermore, we show that non-thermalizing initial conditions
occur well within the ergodic phase with larger probability than expected.
Finally, we propose a mechanism, driven by the Thouless energy and the presence
of anomalous events, for the transition to the localized phase.Comment: 14 pages, 9 figures. Accepted preprint; to appear in Phys. Rev.
Signatures of a critical point in the many-body localization transition
Disordered interacting spin chains that undergo a many-body localization
transition are characterized by two limiting behaviors where the dynamics are
chaotic and integrable. However, the transition region between them is not
fully understood yet. We propose here a possible finite-size precursor of a
critical point that shows a typical finite-size scaling and distinguishes
between two different dynamical phases. The kurtosis excess of the diagonal
fluctuations of the full one-dimensional momentum distribution from its
microcanonical average is maximum at this singular point in the paradigmatic
disordered - model. For system sizes accessible to exact
diagonalization, both the position and the size of this maximum scale linearly
with the system size. Furthermore, we show that this singular point is found at
the same disorder strength at which the Thouless and the Heisenberg energies
coincide. Below this point, the spectral statistics follow the universal random
matrix behavior up to the Thouless energy. Above it, no traces of chaotic
behavior remain, and the spectral statistics are well described by a
generalized semi-Poissonian model, eventually leading to the integrable
Poissonian behavior. We provide, thus, an integrated scenario for the many-body
localization transition, conjecturing that the critical point in the
thermodynamic limit, if it exists, should be given by this value of disorder
strength.Comment: 19 pages, 8 figures, comments are welcom
Thouless energy challenges thermalization on the ergodic side of the many-body localization transition
We study the ergodic side of the many-body localization transition in its standard model, the disordered Heisenberg quantum spin chain. We show that the Thouless energy, extracted from long-range spectral statistics and the power-spectrum of the full momentum distribution fluctuations, is not large enough to guarantee thermalization. We find that both estimates coincide and behave nonmonotonically, exhibiting a strong peak at an intermediate value of the disorder. Furthermore, we show that nonthermalizing initial conditions occur well within the ergodic phase with larger probability than expected. Finally, we propose a mechanism, driven by the Thouless energy and the presence of anomalous events, for the transition to the localized phase
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