scholarly journals Explicit construction of a unitary double product integral

2011 ◽  
Vol 96 ◽  
pp. 215-236
Author(s):  
R. L. Hudson ◽  
Paul Jones
2021 ◽  
Vol 11 (10) ◽  
pp. 4420
Author(s):  
Panayotis Panayotaros

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis.


1991 ◽  
Vol 55 (5) ◽  
pp. 2042-2076 ◽  
Author(s):  
O. V. Manturov
Keyword(s):  

2020 ◽  
Vol 32 (5) ◽  
pp. 1315-1336
Author(s):  
Gianfranco Casnati ◽  
Ozhan Genc

AbstractWe deal with instanton bundles on the product {\mathbb{P}^{1}\times\mathbb{P}^{2}} and the blow up of {\mathbb{P}^{3}} along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.


2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Tomáš Brauner

Abstract We initiate the classification of nonrelativistic effective field theories (EFTs) for Nambu-Goldstone (NG) bosons, possessing a set of redundant, coordinate-dependent symmetries. Similarly to the relativistic case, such EFTs are natural candidates for “exceptional” theories, whose scattering amplitudes feature an enhanced soft limit, that is, scale with a higher power of momentum at long wavelengths than expected based on the mere presence of Adler’s zero. The starting point of our framework is the assumption of invariance under spacetime translations and spatial rotations. The setup is nevertheless general enough to accommodate a variety of nontrivial kinematical algebras, including the Poincaré, Galilei (or Bargmann) and Carroll algebras. Our main result is an explicit construction of the nonrelativistic versions of two infinite classes of exceptional theories: the multi-Galileon and the multi-flavor Dirac-Born-Infeld (DBI) theories. In both cases, we uncover novel Wess-Zumino terms, not present in their relativistic counterparts, realizing nontrivially the shift symmetries acting on the NG fields. We demonstrate how the symmetries of the Galileon and DBI theories can be made compatible with a nonrelativistic, quadratic dispersion relation of (some of) the NG modes.


2021 ◽  
Vol 28 (Supplement_1) ◽  
Author(s):  
LE Estrada Martinez ◽  
JA Lara Vargas ◽  
JA Pineda Juarez ◽  
JD Morales Portano ◽  
JB Gomez Alvarez ◽  
...  

Abstract Funding Acknowledgements Type of funding sources: None. Introduction  Due to the increase in global prevalence of degenerative valve disease, aortic stenosis (AS) has played a preponderant role in the cardiovascular scenario, especially in patients undergoing transcatheter aortic valve replacement (TAVR). An alternative management for this patients are the cardiac rehabilitation programs (CRP); however, their effect has not been completely understood, both in exercise capacity and quality of life, but neither in the improvement of cardiopulmonary performance and other cardiovascular outcomes.  Purpose: To evaluate the effect of the CRP on exercise tolerance and cardiopulmonary performance in patients with AS undergoing TAVR.  Methods: A cohort study was conducted including 26 patients with AS undergoing TAVR and divided into an intervention group who performed a 4-week supervised training program in the Cardiac Rehabilitation Service and a control group to whom instructions and recommendations to performed unsupervised exercise at home were given. Demographic and clinical data (VO2Max, METS12, oxygen pulse, heart rate, double product, left ventricular ejection fraction, body mass index) were collected at baseline and after a 4-week follow-up. Results: 15 patients were included in the intervention group and 11 patients in the control group. There were no baseline significant differences between groups. After the intervention, significant differences were observed in the METS 12 final gain variable between the control and intervention group (4.55 vs 3.1 p = 0.01). Intergroup analysis showed significant differences (percentage changes) in the intervention group with an increase of METS12 (67.4%, p = 0.001), oxygen pulse (18.21%, p = 0.01), final METS (39.47% p = 0.001) and a decrease in VO2 recovery time (-12.5%, p = 0.05), in the ergometric performance index by heart rate (-38.17%, p = 0.001) and by double product (-38.1%, p = 0.001). Conclusions  A 4-week cardiac rehabilitation program is effective to improve exercise tolerance and cardiopulmonary response in patients with AS undergoing TAVR; improvement was statistically significant in METS12, oxygen pulse, VO2 recovery time, METS-load and ergometric performance index for heart rate and double product. METS12 final gain was statistically significant in intervention group in comparison with the control group. Abstract Figure. Control vs Intervention Group (METS12)


2014 ◽  
Vol 29 (03n04) ◽  
pp. 1430001 ◽  
Author(s):  
V. K. DOBREV

We give a review of some group-theoretical results related to nonrelativistic holography. Our main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall the interpretation of nonrelativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. One important result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory, and that these operators and the bulk-to-boundary operators are intertwining operators. Further, we recall the fact that there is a hierarchy of equations on the boundary, invariant with respect to Schrödinger algebra. We also review the explicit construction of an analogous hierarchy of invariant equations in the bulk, and that the two hierarchies are equivalent via the bulk-to-boundary intertwining operators. The derivation of these hierarchies uses a mechanism introduced first for semisimple Lie groups and adapted to the nonsemisimple Schrödinger algebra. These require development of the representation theory of the Schrödinger algebra which is reviewed in some detail. We also recall the q-deformation of the Schrödinger algebra. Finally, the realization of the Schrödinger algebra via difference operators is reviewed.


2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yi Liao ◽  
Xiao-Dong Ma

Abstract We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $$ {\left.384\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.10\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.4\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.236\right|}_{\Delta B=\pm 1}^{\Delta L=\mp 1} $$ 384 Δ B = 0 Δ L = ± 2 + 10 Δ B = ± 2 Δ L = 0 + 4 Δ B = ± 1 Δ L = ± 3 + 236 Δ B = ± 1 Δ L = ∓ 1 operators without referring to fermion generations, and $$ {\left.44874\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.2862\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.486\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.42234\right|}_{\Delta B=\mp 1}^{\Delta L=\pm 1} $$ 44874 Δ B = 0 Δ L = ± 2 + 2862 Δ B = ± 2 Δ L = 0 + 486 Δ B = ± 1 Δ L = ± 3 + 42234 Δ B = ∓ 1 Δ L = ± 1 operators when three generations of fermions are referred to, where ∆L, ∆B denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.


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