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A V Zolotaryuk ◽  
Yaroslav Zolotaryuk

Abstract A heterostructure composed of N parallel homogeneous layers is studied in the limit as their widths l1, . . . , lN shrink to zero. The problem is investigated in one dimension and the piecewise constant potential in the Schrödinger equation is given by the strengths V1, . . . , VN as functions of l1, . . . , lN, respectively. The key point is the derivation of the conditions on the functions V1(l1), . . . , VN(lN) for realizing a family of one-point interactions as l1, . . . , lN tend to zero along available paths in the N-dimensional space. The existence of equations for a squeezed structure, the solution of which determines the system parameter values, under which the non-zero tunneling of quantum particles through a multi-layer structure occurs, is shown to exist and depend on the paths. This tunneling appears as a result of an appropriate cancellation of divergences.

2022 ◽  
Vol 5 (1) ◽  
pp. 01-03
Sadique Hussain

Nanoparticles (NPs) have attracted a lot of attention in the fields of electronics, biology, and astronautics because of their unique physicochemical and electrical characteristics. NPs are materials with at least one dimension of fewer than 100 nanometres that are commercially manufactured (Bahadar et al., 2016; Vishwakarma et al., 2010). In the medical field, drugs, proteins, DNA, and monoclonal antibodies are all being delivered via NPs(Hussain et al., 2021).

2022 ◽  
pp. 1118-1140
Gargi Banerjee

The aim of this chapter is to provide quantitative techniques and guidance for analyzing different problems related to the measurement of diversity and inclusion practices present in organizations. The example of only one dimension of diversity; viz Gender diversity is given in this chapter. However, these Quantitative tools can be used to explore other facets of diversity as well. In this way, this chapter shall seek to provide a basic understanding of how to analyze and study the data collected for research on Diversity and Inclusion practices in organizations.

2022 ◽  
Vol 258 ◽  
pp. 05009
Stéphane Delorme ◽  
Thierry Gousset ◽  
Roland Katz ◽  
Pol-Bernard Gossiaux

We investigate the real-time dynamics of a correlated heavy quarkantiquark pair inside the Quark-Gluon Plasma using new quantum master equations derived from first QCD principles and based on the work of Blaizot & Escobedo [4]. The full equations are directly numerically solved in one-dimension to reduce computing costs and is used to gain insight on the dynamics in both a static and evolving medium following a Björken-like temperature evolution. The effect of the initial state on the dynamics is also studied.

2022 ◽  
Vol 2022 (1) ◽  
Pouria Dadras

Abstract In this paper, we consider the evolution of the thermofield-double state under the double-traced operator that connects its both sides. We will compute the entanglement entropy of the resulting state using the replica trick for the large N field theory. To leading order, it can be computed from the two-point function of the theory, where, in CFTs, it is fixed by the symmetries. Due to the exponential decay of the interaction, the entanglement entropy saturates about the thermal time after the interaction is on. Next, we restrict ourselves to one dimension and assume that the theory at strong coupling is effectively described by the Schwarzian action. We then compute the coarse-grained entropy of the resulting state using the four-point function. The equality of the two entropies implies that the double-traced operators in our theory act coherently. In AdS/CFT correspondence where the thermofield-double state corresponds to a two-sided black hole, the action of a double-traced operator corresponds to shrinking or expanding the black hole in the bulk.

2022 ◽  
Vol 2022 (1) ◽  
Peng Cheng ◽  
Ruben Minasian ◽  
Stefan Theisen

Abstract We revisit the relation between the anomalies in four and six dimensions and the Chern-Simons couplings one dimension below. While the dimensional reduction of chiral theories is well-understood, the question which three and five-dimensional theories can come from a general circle reduction, and are hence liftable, is more subtle. We argue that existence of an anomaly cancellation mechanism is a necessary condition for liftability. In addition, the anomaly cancellation and the CS couplings in six and five dimensions respectively determine the central charges of string-like BPS objects that cannot be consistently decoupled from gravity, a.k.a. supergravity strings. Following the completeness conjecture and requiring that their worldsheet theory is unitary imposes bounds on the admissible theories. We argue that for the anomaly-free six-dimensional theories it is more advantageous to study the unitarity constraints obtained after reduction to five dimensions. In general these are slightly more stringent and can be cast in a more geometric form, highly reminiscent of the Kodaira positivity condition (KPC). Indeed, for the F-theoretic models which have an underlying Calabi-Yau threefold these can be directly compared. The unitarity constraints (UC) are in general weaker than KPC, and maybe useful in understanding the consistent models without F-theoretic realisation. We catalogue the cases when UC is more restrictive than KPC, hinting at more refined hidden structure in elliptic Calabi-Yau threefolds with certain singularity structure.

2021 ◽  
pp. 33-48
Nancy T. Ammerman

This chapter builds on the assertion that spirituality is best understood as one dimension of the larger phenomenon of lived religious practice, rather than as a phenomenon separate from or opposed to religion. Spirituality is situated in a multidimensional analysis that also includes embodiment, materiality, emotion, aesthetics, morality, and narrative. By analyzing spirituality as a distinct dimension of religious practice, we can see the internal dynamics among all the dimensions. Understanding spirituality and religion at this micro level is incomplete, however, without attention to the distinct legal and cultural contexts around the world. This chapter elaborates on four ideal-typical macrosocial contexts that each shape quite differently the practice of religion and its spiritual dimensions: entangled, established, institutionalized, and interstitial contexts. These contexts identify differences in modal expectations for the fields within which religious practices will be found and the modes of regulation that will constrain religious action.

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