456 research outputs found
Two remarks on generalized entropy power inequalities
This note contributes to the understanding of generalized entropy power
inequalities. Our main goal is to construct a counter-example regarding
monotonicity and entropy comparison of weighted sums of independent identically
distributed log-concave random variables. We also present a complex analogue of
a recent dependent entropy power inequality of Hao and Jog, and give a very
simple proof.Comment: arXiv:1811.00345 is split into 2 papers, with this being on
Dynamics and transport near quantum-critical points
The physics of non-zero temperature dynamics and transport near
quantum-critical points is discussed by a detailed study of the O(N)-symmetric,
relativistic, quantum field theory of a N-component scalar field in spatial
dimensions. A great deal of insight is gained from a simple, exact solution of
the long-time dynamics for the N=1 d=1 case: this model describes the critical
point of the Ising chain in a transverse field, and the dynamics in all the
distinct, limiting, physical regions of its finite temperature phase diagram is
obtained. The N=3, d=1 model describes insulating, gapped, spin chain
compounds: the exact, low temperature value of the spin diffusivity is
computed, and compared with NMR experiments. The N=3, d=2,3 models describe
Heisenberg antiferromagnets with collinear N\'{e}el correlations, and
experimental realizations of quantum-critical behavior in these systems are
discussed. Finally, the N=2, d=2 model describes the superfluid-insulator
transition in lattice boson systems: the frequency and temperature dependence
of the the conductivity at the quantum-critical coupling is described and
implications for experiments in two-dimensional thin films and inversion layers
are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical
properties of unconventional magnetic systems", Geilo, Norway, April 2-12,
1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be
published. 46 page
The role of multiple marks in epigenetic silencing and the emergence of a stable bivalent chromatin state
We introduce and analyze a minimal model of epigenetic silencing in budding
yeast, built upon known biomolecular interactions in the system. Doing so, we
identify the epigenetic marks essential for the bistability of epigenetic
states. The model explicitly incorporates two key chromatin marks, namely H4K16
acetylation and H3K79 methylation, and explores whether the presence of
multiple marks lead to a qualitatively different systems behavior. We find that
having both modifications is important for the robustness of epigenetic
silencing. Besides the silenced and transcriptionally active fate of chromatin,
our model leads to a novel state with bivalent (i.e., both active and
silencing) marks under certain perturbations (knock-out mutations, inhibition
or enhancement of enzymatic activity). The bivalent state appears under several
perturbations and is shown to result in patchy silencing. We also show that the
titration effect, owing to a limited supply of silencing proteins, can result
in counter-intuitive responses. The design principles of the silencing system
is systematically investigated and disparate experimental observations are
assessed within a single theoretical framework. Specifically, we discuss the
behavior of Sir protein recruitment, spreading and stability of silenced
regions in commonly-studied mutants (e.g., sas2, dot1) illuminating the
controversial role of Dot1 in the systems biology of yeast silencing.Comment: Supplementary Material, 14 page
Two-Particle-Self-Consistent Approach for the Hubbard Model
Even at weak to intermediate coupling, the Hubbard model poses a formidable
challenge. In two dimensions in particular, standard methods such as the Random
Phase Approximation are no longer valid since they predict a finite temperature
antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The
Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as
particle conservation, the Pauli principle, the local moment and local charge
sum rules. The self-energy formula does not assume a Migdal theorem. There is
consistency between one- and two-particle quantities. Internal accuracy checks
allow one to test the limits of validity of TPSC. Here I present a pedagogical
review of TPSC along with a short summary of existing results and two case
studies: a) the opening of a pseudogap in two dimensions when the correlation
length is larger than the thermal de Broglie wavelength, and b) the conditions
for the appearance of d-wave superconductivity in the two-dimensional Hubbard
model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems",
Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages.
Misprint in Eq.(23) corrected (thanks D. Bergeron
Associations of familial risk factors with social fears and social phobia: evidence for the continuum hypothesis in social anxiety disorder?
We examined parental psychopathology and family environment in subthreshold and DSM-IV threshold conditions of social anxiety disorder (SAD) in a representative cohort sample of 1,395 adolescents. Offspring and parental psychopathology was assessed using the DIA-X/M-CIDI; recalled parental rearing and family functioning via questionnaire. Diagnostic interviews in parents were supplemented by family history reports from offspring. The cumulative lifetime incidence was 23.07% for symptomatic SAD, and 18.38 and 7.41% for subthreshold and threshold SAD, respectively. The specific parent-to-offspring association for SAD occurred for threshold SAD only. For subthreshold and threshold SAD similar associations were found with other parental anxiety disorders, depression and substance use disorders. Parental rearing behaviour, but not family functioning, was associated with offspring threshold SAD, and although less strong and less consistent, also with subthreshold SAD. Results suggest a continued graded relationship between familial risk factors and offspring SAD. Parental psychopathology and negative parental styles may be used defining high-risk groups to assign individuals with already subthreshold conditions of SAD to early intervention programs
A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry
We present here a review of the fundamental topics of Hartree-Fock theory in
Quantum Chemistry. From the molecular Hamiltonian, using and discussing the
Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock
equations for the electronic problem. Special emphasis is placed in the most
relevant mathematical aspects of the theoretical derivation of the final
equations, as well as in the results regarding the existence and uniqueness of
their solutions. All Hartree-Fock versions with different spin restrictions are
systematically extracted from the general case, thus providing a unifying
framework. Then, the discretization of the one-electron orbitals space is
reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition
of the basic underlying concepts related to the construction and selection of
Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we
close the review with a section in which the most relevant modern developments
(specially those related to the design of linear-scaling methods) are commented
and linked to the issues discussed. The whole work is intentionally
introductory and rather self-contained, so that it may be useful for non
experts that aim to use quantum chemical methods in interdisciplinary
applications. Moreover, much material that is found scattered in the literature
has been put together here to facilitate comprehension and to serve as a handy
reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and
subeqn package
Parental alcohol use and adolescent school adjustment in the general population: Results from the HUNT study
<p>Abstract</p> <p>Background</p> <p>This study investigates the relationship between parental drinking and school adjustment in a total population sample of adolescents, with independent reports from mothers, fathers, and adolescents. As a group, children of alcohol abusers have previously been found to exhibit lowered academic achievement. However, few studies address which parts of school adjustment that may be impaired. Both a genetic approach and social strains predict elevated problem scores in these children. Previous research has had limitations such as only recruiting cases from clinics, relying on single responders for all measures, or incomplete control for comorbid psychopathology. The specific effects of maternal and paternal alcohol use are also understudied.</p> <p>Methods</p> <p>In a Norwegian county, 88% of the population aged 13-19 years participated in a health survey (N = 8984). Among other variables, adolescents reported on four dimensions of school adjustment, while mothers and fathers reported their own drinking behaviour. Mental distress and other control variables were adjusted for. Multivariate analysis including generalized estimation equations was applied to investigate associations.</p> <p>Results</p> <p>Compared to children of light drinkers, children of alcohol abusers had moderately elevated attention and conduct problem scores. Maternal alcohol abuse was particularly predictive of such problems. Children of abstainers did significantly better than children of light drinkers. Controlling for adolescent mental distress reduced the association between maternal abuse and attention problems. The associations between parental reported drinking and school adjustment were further reduced when controlling for the children's report of seeing their parents drunk, which itself predicted school adjustment. Controlling for parental mental distress did not reduce the associations.</p> <p>Conclusions</p> <p>Parental alcohol abuse is an independent risk factor for attention and conduct problems at school. Some of the risk associated with mothers' drinking is likely to be mediated by adolescent mental distress. Despite lowered adjustment on the externalizing dimensions, children of alcohol abusers report that they enjoy being at school as much as other children.</p
Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
We review recent theoretical work on two closely related issues: excitation
of an isolated quantum condensed matter system driven adiabatically across a
continuous quantum phase transition or a gapless phase, and apparent relaxation
of an excited system after a sudden quench of a parameter in its Hamiltonian.
Accordingly the review is divided into two parts. The first part revolves
around a quantum version of the Kibble-Zurek mechanism including also phenomena
that go beyond this simple paradigm. What they have in common is that
excitation of a gapless many-body system scales with a power of the driving
rate. The second part attempts a systematic presentation of recent results and
conjectures on apparent relaxation of a pure state of an isolated quantum
many-body system after its excitation by a sudden quench. This research is
motivated in part by recent experimental developments in the physics of
ultracold atoms with potential applications in the adiabatic quantum state
preparation and quantum computation.Comment: 117 pages; review accepted in Advances in Physic
Relative entanglement entropies in 1 + 1-dimensional conformal field theories
We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy S(\u3c11\u2016\u3c10) between two given reduced density matrices \u3c11 and \u3c10 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr(\u3c11\u3c1n 1210) and define a set of R\'enyi relative entropies Sn(\u3c11\u2016\u3c10). We compute these quantities for integer values of the parameter n and derive via the replica limit, the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator i 02\u3d5, both with respect to the ground state and to the state generated by chiral vertex operators. These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement. \ua9 2017, The Author(s)
The Hubbard model within the equations of motion approach
The Hubbard model has a special role in Condensed Matter Theory as it is
considered as the simplest Hamiltonian model one can write in order to describe
anomalous physical properties of some class of real materials. Unfortunately,
this model is not exactly solved except for some limits and therefore one
should resort to analytical methods, like the Equations of Motion Approach, or
to numerical techniques in order to attain a description of its relevant
features in the whole range of physical parameters (interaction, filling and
temperature). In this manuscript, the Composite Operator Method, which exploits
the above mentioned analytical technique, is presented and systematically
applied in order to get information about the behavior of all relevant
properties of the model (local, thermodynamic, single- and two- particle ones)
in comparison with many other analytical techniques, the above cited known
limits and numerical simulations. Within this approach, the Hubbard model is
shown to be also capable to describe some anomalous behaviors of the cuprate
superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference
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