Stabilization of 1D solitons by fractional derivatives in systems with quintic nonlinearity

We study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under “fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index $$\alpha$$ α . We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Laplacian (corresponding to Lévy index $$\alpha =2$$ α = 2 ), the soliton is unstable, even infinitesimal difference $$\alpha$$ α from 2 immediately stabilizes the soliton texture. Our analytical and numerical investigations of $$\omega (N)$$ ω ( N ) dependence ($$\omega$$ ω is soliton frequency and N its mass) show (within the famous Vakhitov–Kolokolov criterion) the stability of our soliton texture in the fractional $$\alpha <2$$ α < 2 case. Direct numerical analysis of the linear stability problem of soliton texture also confirms this point. We show analytically and numerically that fractional Schrödinger equation with quintic nonlinearity admits the existence of (stable) soliton textures at $$2/3<\alpha <2$$ 2 / 3 < α < 2 , which is in accord with existing literature data. These results may be relevant to both Bose–Einstein condensates in cold atomic gases and optical solitons in the disordered media.

Spatial Unfurling

This chapter examines the perceptual and aesthetic properties of “spatial unfurling,” an effect achieved by moving the camera across space rather than into it, such as in lateral tracking shots. By emphasizing the flatness of the screen and the boundaries of the frame, spatial unfurling lacks the feeling of kinesthesia characteristic of forward camera movement. As a result, spatial unfurling illustrates the limitations of the long-held truism in film theory that camera movement produces an illusion of our own embodied movement through space. By critiquing the logic of this truism as it appears in phenomenological film theory, and by examining the perceptual effects of spatial unfurling in narrative and experimental films such as Mauvais Sang (Carax, 1986), La région centrale (Snow, 1971), and Georgetown Loop (Jacobs, 1996), this chapter argues for a phenomenological account of camera movement that forgoes analogies with bodily movement and instead emphasizes one’s perceptual encounter with the screen.

A Nickelate Renaissance

The 2019 discovery of high temperature superconductivity in layered nickelate films, Nd1-xSrNiO2, has galvanized a community that has been studying nickelates for more than 30 years both as cuprate analogs and in their own right. On the surface, infinite layer nickelates, and their multilayer analogs, should be promising candidates based on our understanding of cuprates: square planar coordination and a parent d9 configuration that places a single hole in a dx2-y2 planar orbital makes nickelates seem poised for superconductivity. But creating crystals and films of sufficient quality of this d9 configuration in Ni1+ has proven to be a synthetic challenge, only recently overcome. These crystalline specimens are opening windows that shed new light on the cuprate-nickelate analogy and reveal nuances that leave the relationship between cuprates and nickelates very much an area open to debate. This Perspective gives a qualitative, phenomenological account of these newly discovered superconductors and multilayer members of the infinite layer nickelate family. The focus is on our current understanding of electronic and magnetic properties of these materials as well as some future opportunities, explored from the viewpoint of synthetic challenges and some suggested developments in materials discovery and growth to make further progress in this rejuvenated field.

Zen Buddhism and the Phenomenology of Mysticism

In this paper, I use a comparative analysis of mysticism in Zen and the Abrahamic faiths to formulate a phenomenological account of mysticism “as such.” I argue that, while Zen Buddhism is distinct from other forms of mystical experience in important ways, it can still be fit into a general phenomenological category of mystical experience. First, I explicate the phenomenological accounts of mysticism provided by Anthony Steinbock and Angela Bello. Second, I offer an account of Zen mysticism which both coheres with and problematizes these accounts, arguing that Zen demonstrates the inadequacy of these accounts as descriptions of mysticism as a universal religious category. Lastly, I use this investigation to propose that Zen mysticism does generally cohere with the mystical experiences of other religions, but only if we devise a new formula for speaking phenomenologically about mystical experience as such which captures this phenomenon in all of its manifestations.

Stabilization of 1D Solitons By Fractional Derivatives In Systems With Quintic Nonlinearity

We study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under ”fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index α. We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Lapla-cian (corresponding to Lévy index α = 2), the soliton is unstable, even infinitesimal difference α from 2 immediately stabilizes the soliton texture. Our analytical and numerical investigations of ω(N) dependence (ω is soliton frequency and N its mass) show (within the famous Vakhitov-Kolokolov criterion) the stability of our soliton texture in the fractional α < 2 case. Direct numerical analysis of the linear stability problem of soliton texture also confirms this point. We show analytically and numerically that fractional Schrödinger equation with quintic nonlinearity admits the existence of (stable) soliton textures at 2/3 < α < 2, which is in accord with existing literature data. These results may be relevant to both Bose-Einstein condensates in cold atomic gases and optical solitons in the disordered media.

Shared action: An existential phenomenological account

Drawing on recent phenomenological discussions of collective intentionality and existential phenomenological accounts of agency, this article proposes a novel interpretation of shared action. First, I argue that we should understand action on the basis of how an environment pre-reflectively solicits agents to behave based on (a) the affordances or goals inflected by their abilities and dispositions and (b) their self-referential commitment to a project that is furthered by these affordances. Second, I show that this definition of action is sufficiently flexible to account for not only individual action (in which both (a) and (b) refer only to an individual) but also several distinct subtypes of shared action. My thesis is that behaviour counts as shared action if and only if it is caused by a solicitation in which either (a) the goals, or (b) the commitments, or both (a) goals and (b) commitments are joint, i.e., depend on several individuals. We thereby get three distinct subtypes of shared actions: (i) jointly coordinated individually committed action, (ii) individually coordinated jointly committed action, and (iii) jointly coordinated jointly committed action.

Adjacent Histories

In this conversation, composed through written correspondence, Julie Beth Napolin and Amanda Armstrong-Price discuss aspects of Denise Riley’s “Am I That Name?” in light of contemporary feminist debates, including debates within black feminism and transfeminism. The authors begin by considering the significance of Riley’s unconventional title, outlining what might be at stake—and what might be occluded—in the title’s allusion to Sojourner Truth’s interjection, “Ain’t I a woman?” Allusion and juxtaposition form key aspects of Riley’s approach to historical representation, which involves reading sources on sex and gender for what they say about adjacent historical categories and constellating discrepant historical situations in ways that speak to ongoing conundrums about identity and alliance. With respect to the latter, the authors consider the historical situation—in feminism and more generally—that occasioned Riley’s 1988 work while also reading her work in relation to the challenges of our current moment. Riley’s phenomenological account of the inconstancy of gendered being is read for its resonances with contemporary transfeminist work while her broader oeuvre is brought to bear on some of the scraps of phobic common sense—the voices without mouths—that circulate online and work to forestall what remain urgent acts of alliance.

Mimesis and Experience: A Platonic Perspective on Ricoeur's Time and Narrative

Ricoeur's Time and Narrative is duly cited in footnotes but does not seem to have had a strong impact on anglophone narratology. One of the reasons for this is certainly Ricoeur's emphasis on plot, which does not harmonize with the focus on consciousness in cognitive narratology. This article suggests that a reconsideration of the concept of mimesis could help build a bridge between Ricoeur's phenomenological approach and cognitive studies in narrative. More specifically, it argues that Plato's discussion of poetry in the Republic, unanimously criticized by modern scholars, can enrich Ricoeur's concept of mimesis. While Ricoeur follows Aristotle, who ties mimesis to plot, Plato, in Republic 2 and 3, considers mimesis an act of impersonation and thereby paves the way to the level of character, on which cognitive narratologists tend to focus. This article first offers a new reading of the Republic's examination of poetry, trying to show that Plato's account of the effects of poetry on the listeners’ souls resonates with current cognitive approaches. Equipped with this reading, it then turns to Ricoeur again. Ricoeur's description of mimesis III, the reader's adoption of the narrative configuration of time in life, remains vague and abstract. Through its focus on the impact of characters on audiences, Plato's idea of mimesis permits us to integrate a cognitivist perspective into Ricoeur's phenomenological account.

Empathy and Togetherness Online Compared to IRL: A Phenomenological Account

In this paper I aim to show with the aid of philosophers Edith Stein and Peter Goldie, how empathy and other social feelings are instantiated and developed in real life versus on the Internet. The examples of on-line communication show both how important the embodied aspects of empathy are and how empathy may be possible also in the cases of encountering personal stories rather than personal bodies. Since video meetings, social media, online gaming and other forms of interaction via digital technologies are taking up an increasing part of our time, it is important to understand how such forms of social intercourse are different from in real life (IRL) meetings and why they can accordingly foster not only new communal bonds but also hatred and misunderstanding.