476 research outputs found
Correlation functions in the non-relativistic AdS/CFT correspondence
We study the correlation functions of scalar operators in the theory defined
as the holographic dual of the Schroedinger background with dynamical exponent
z=2 at zero temperature and zero chemical potential. We offer a closed
expression of the correlation functions at tree level in terms of Fourier
transforms of the corresponding n-point functions computed from pure AdS in the
lightcone frame. At the loop level this mapping does not hold and one has to
use the full Schroedinger background, after proper regularization. We
explicitly compute the 3-point function comparing it with the specific 3-point
function of the non-relativistic theory of cold atoms at unitarity. We find
agreement of both 3-point functions, including the part not fixed by the
symmetry, up to an overall normalization constant.Comment: 32 pages, 7 figures; v2: typos corrected, references added and
additional discussion about the case of compact number-direction, includes
new appendix with the computations of the 2 and 3 point function for the
compact number-direction case. The general results remain the same. Version
published in Phys.Rev.
Probabilistic Models for Integration Error in the Assessment of Functional Cardiac Models
This paper studies the numerical computation of integrals, representing estimates or predictions, over the output of a computational model with respect to a distribution over uncertain inputs to the model. For the functional cardiac models that motivate this work, neither nor possess a closed-form expression and evaluation of either requires 100 CPU hours, precluding standard numerical integration methods. Our proposal is to treat integration as an estimation problem, with a joint model for both the a priori unknown function and the a priori unknown distribution . The result is a posterior distribution over the integral that explicitly accounts for dual sources of numerical approximation error due to a severely limited computational budget. This construction is applied to account, in a statistically principled manner, for the impact of numerical errors that (at present) are confounding factors in functional cardiac model assessment
SO(2,1) conformal anomaly: Beyond contact interactions
The existence of anomalous symmetry-breaking solutions of the SO(2,1)
commutator algebra is explicitly extended beyond the case of scale-invariant
contact interactions. In particular, the failure of the conservation laws of
the dilation and special conformal charges is displayed for the two-dimensional
inverse square potential. As a consequence, this anomaly appears to be a
generic feature of conformal quantum mechanics and not merely an artifact of
contact interactions. Moreover, a renormalization procedure traces the
emergence of this conformal anomaly to the ultraviolet sector of the theory,
within which lies the apparent singularity.Comment: 11 pages. A few typos corrected in the final versio
Galilean Conformal and Superconformal Symmetries
Firstly we discuss briefly three different algebras named as nonrelativistic
(NR) conformal: Schroedinger, Galilean conformal and infinite algebra of local
NR conformal isometries. Further we shall consider in some detail Galilean
conformal algebra (GCA) obtained in the limit c equal to infinity from
relativistic conformal algebra O(d+1,2) (d - number of space dimensions). Two
different contraction limits providing GCA and some recently considered
realizations will be briefly discussed. Finally by considering NR contraction
of D=4 superconformal algebra the Galilei conformal superalgebra (GCSA) is
obtained, in the formulation using complex Weyl supercharges.Comment: 16 pages, LateX; talk presented at XIV International Conference
"Symmetry Methods in Physics", Tsakhkadzor, Armenia, August 16-22, 201
Exact results on the dynamics of multi-component Bose-Einstein condensate
We study the time-evolution of the two dimensional multi-component
Bose-Einstein condensate in an external harmonic trap with arbitrary
time-dependent frequency. We show analytically that the time-evolution of the
total mean-square radius of the wave-packet is determined in terms of the same
solvable equation as in the case of a single-component condensate. The dynamics
of the total mean-square radius is also the same for the rotating as well as
the non-rotating multi-component condensate. We determine the criteria for the
collapse of the condensate at a finite time. Generalizing our previous work on
a single-component condensate, we show explosion-implosion duality in the
multi-component condensate.Comment: Two-column 6 pages, RevTeX, no figures(v1); Added an important
reference, version to appear in Physical Review A (v2
Seelische Belastung bei Menschen mit umweltbezogenen Störungen: Ein Vergleich zwischen Selbstbild und Fremdeinschätzung
Zusammenfassung: Umweltbezogene Gesundheitsstörungen stellen wissenschaftlich und klinisch ein diagnostisches und therapeutisches Konfliktfeld dar. Ein hoher subjektiver Leidensdruck, ein somatisches Krankheitsmodell sowie das Festhalten an einer Umweltursache gefährden die therapeutische Beziehung, wenn die Krankheitsmodelle von Arzt und Patient nicht übereinstimmen. Unsere Untersuchung greift diese empirisch noch kaum erforschte Diskrepanz auf, indem sie die Selbsteinschätzung von Patienten mit umweltbezogenen Krankheitsstörungen (n=61) systematisch der Fremdeinschätzung durch ein multidisziplinäres Expertenteam gegenüberstellt. Die Resultate weisen darauf hin, dass in Selbst- und Fremdeinschätzung psychisch unauffällige Probanden wenig psychiatrische Störungen zeigen, über stabile psychische Strukturen verfügen und v.a. unter umweltbedingten oder medizinischen Ursachen leiden. Wenn Selbst- und Fremdeinschätzung beide eine psychische Auffälligkeit beschreiben, sind entsprechend psychiatrische Störungen gehäuft, psychische Strukturen labil, und die Beschwerden werden psychiatrisch verursacht. Divergieren Selbst- und Fremdeinschätzung, erlaubt die Fremdeinschätzung akkuratere Aussagen bezüglich der psychiatrischen Diagnosen, der innerpsychischen Struktur und der Ursachenzuschreibun
Kinetics of phase-separation in the critical spherical model and local scale-invariance
The scaling forms of the space- and time-dependent two-time correlation and
response functions are calculated for the kinetic spherical model with a
conserved order-parameter and quenched to its critical point from a completely
disordered initial state. The stochastic Langevin equation can be split into a
noise part and into a deterministic part which has local scale-transformations
with a dynamical exponent z=4 as a dynamical symmetry. An exact reduction
formula allows to express any physical average in terms of averages calculable
from the deterministic part alone. The exact spherical model results are shown
to agree with these predictions of local scale-invariance. The results also
include kinetic growth with mass conservation as described by the
Mullins-Herring equation.Comment: Latex2e with IOP macros, 28 pp, 2 figures, final for
Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities
We perform the complete group classification in the class of nonlinear
Schr\"odinger equations of the form
where is an arbitrary
complex-valued potential depending on and is a real non-zero
constant. We construct all the possible inequivalent potentials for which these
equations have non-trivial Lie symmetries using a combination of algebraic and
compatibility methods. The proposed approach can be applied to solving group
classification problems for a number of important classes of differential
equations arising in mathematical physics.Comment: 10 page
Cardiac cell modelling: Observations from the heart of the cardiac physiome project
In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field
Symmetry based determination of space-time functions in nonequilibrium growth processes
We study the space-time correlation and response functions in nonequilibrium
growth processes described by linear stochastic Langevin equations. Exploiting
exclusively the existence of space and time dependent symmetries of the
noiseless part of these equations, we derive expressions for the universal
scaling functions of two-time quantities which are found to agree with the
exact expressions obtained from the stochastic equations of motion. The
usefulness of the space-time functions is illustrated through the investigation
of two atomistic growth models, the Family model and the restricted Family
model, which are shown to belong to a unique universality class in 1+1 and in
2+1 space dimensions. This corrects earlier studies which claimed that in 2+1
dimensions the two models belong to different universality classes.Comment: 18 pages, three figures included, submitted to Phys. Rev.
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