#twodimensional

[govindhtech]

Aubry Andre Harper Model Quantised Currents Survive Problems

Aubry Andre Harper Model

A recent study shown that quantised currents can continue in disordered materials when the protective energy gaps that were thought to be necessary are erased, challenging topological protection in quantum systems. A driven Aubry-André-Harper (AAH) chain, a basic model for quasiperiodic systems, demonstrates this paradoxical persistence, which could revolutionise quantum state preparation and allow new investigations of odd quantum phenomena.

The durability of topological properties like precise, quantised currents has been attributed to symmetry-forbidden transitions or energy gaps between occupied and empty quantum states. Thouless pumps, a key example of topological phases where slow time-periodic modulation causes quantised charge transport, were thought to break down in periodic systems if disorder decreased energy gaps. Research by Emmanuel Gottlob, Ulrich Schneider, Dan S. Borgnia, and Robert-Jan Slager shows that quasiperiodic systems don't always do this.

Knowing the Aubry-André-Harper (AAH) Model

The work focusses on the almost Mathieu operator, the one-dimensional Aubry-André-Harper (AAH) lattice. It is a basic model of quasiperiodic systems since its structure is orderly but not recurring in space. The main components of the AAH Hamiltonian are an onsite cosine potential ($\hat{V}(\varphi)$) and a nearest-neighbor hopping term ($\hat{J}$) that allows particles to traverse across neighbouring sites.

A crucial feature of the Aubry Andre Harper Model is the irrational parameter $\beta$. The hopping term's translation invariance is compromised by this irrationality, giving it peculiar quantum properties. For $|V/J| > 1$, the system's eigenfunctions demonstrate Anderson localisation, which means particles are limited to certain regions based on the ratio of potential strength $V$ to hopping strength $J$, even without extra disorder.

The researchers assess the AAH model's spectral properties using a “configuration-space” approach. Each lattice site $i$ is assigned a unit circle angle by the formula $\theta_i = 2\pi\beta i + \varphi \mod 2\pi$ in this abstract space Since $\beta$ is irrational and each site has a unique $\theta$ value, this mapping reliably populates the unit circle. This method is crucial because it avoids the lack of a Brillouin zone in quasiperiodic lattices, which is used to calculate topological invariants in periodic.

When there is no hopping ($J/V = 0$), the Aubry Andre Harper Model is dense on a specific energy interval. Similar onsite energies in surrounding sites provide resonances with a small hopping amplitude ($J/V \ll 1$). These resonances divide the continuous spectrum into discrete energy bands by creating pairs of spectral gaps. The AAH spectrum is a “nowhere-dense Cantor set,” defined by an unending, fractal hierarchy of these gaps, not continuous. The gap-labelling theorem reliably quantifies the IDoS inside these bands, where each gap has an integer Chern number.

Thouless Pumping and Unprecedented Robustness

Thouless pumping modulates a Hamiltonian slowly, continuously, and regularly. The AAH model achieves this by linearly raising phase $\varphi$ while keeping a constant pumping rate. This produces a quantised charge transfer proportional to the band's Chern number. In contrast to periodic systems, which only quantise charge per pump cycle, the quasiperiodic AAH model quantises time-independent current.

This study's discovery that quantised currents remain while chaos closes energy gaps is groundbreaking. Because local disorder convolves with the clean spectrum, unperturbed spectral gaps smaller than the disorder strength collapse in the AAH chain. Contrary to widespread assumption, quantised currents only break down at much higher critical disorder intensities and survive long after this gap closure. A band with a Chern number of +4 remained quantised even when the disorder strength was more than an order of magnitude bigger than the clean gaps.

A local picture based on Landau-Zener (avoided-crossing) transitions in the configuration space explains this remarkable robustness. When phase $\varphi$ changes, all localised states in the Aubry Andre Harper Model resonate with another state, possibly far distant in real space. If the pumping rate is slow enough (adiabatic), a Landau-Zener transition causes quantised transport.

The AAH spectrum's fractal nature (Cantor set) and Anderson localisation are crucial. If these resonances are ordered, the quantised current is unaffected by the phase winding varying between subsequent Landau-Zener processes in disorder. Quantisation breaks down only when the disorder disrupts this order and particles are back-reflected. To protect quantised currents from long-range tunnelling, a high pumping rate is necessary. This suggests that local resonance stability, not clean energy gap magnitude, limits robustness.

Prepare for New Quantum Technologies

The experimental implications of this discovery are significant. The researchers present a dependable method for preparing quantum computing with chosen Chern numbers that can be immediately applied to cold atom and photonic research. Such configurations can achieve the Aubry Andre Harper Model by superimposing optical lattices. As phase is pumped, atomic clouds can be spatially separated into Chern number-corresponding regions. This method is reliable even with small energy gaps around target bands.

By applying this protocol to a 2D lattice of 1D AAH chains, states with a well-defined “real” 2D Chern number can be created. The integer and fractional quantum Hall effects may open up new experimental avenues for studying quantum Hall physics in conventional condensed matter systems with flat bands, high Chern numbers, and non-local interactions.

In summary

A new protection mechanism for Thouless pumping in quasiperiodic systems reveals untapped topological richness and inspires a rethinking of topological defence without translation invariance. Systems with various incommensurate frequencies, moiré van der Waals structures as solid-state platforms for these exciting new quantum phenomena, and the local Landau-Zener image and global mobility gaps will be investigated in future studies.

[imagella-blog]

Four eagles from Greek mythology in black and white

Phoenix Tattoo #GreekMythology #Eagles #PsychologicalSymbols #FerraniaP30 #Gothcore #DarkDesign #TwoDimensional

[monkeyssalad-blog]

Lyda Borelli by Aldo Mazza by Truus, Bob & Jan too! Via Flickr: Italian postcard. Ed. [Mona Lisa], 1809. Pastel by Aldo Mazza. Aldo Mazza (Milano, 6 July 1880 - Gavirate, 26 juli 1964) was an Italian painter, illustrator of children's books, caricaturist for satirical magazines, and poster designer. Mazza came from a family of painters. Both his grandfather Giuseppe and his great-uncle Salvatore had been renowned painters. When he was 16, Mazza enrolled to the Accademia delle Belle Arte di Brera, where he was taught by Cesare Tallone and dedicated himself to painting, while also illustrating children's books for the editor Vallardi. His first commission was the making of satirical designs for the journal Guerin Meschino, which he did for over twenty years. Afterward, he would also design illustrations for Il Numero, L'Illustrazione italiana, Il Secolo (from 1924), and Il Pasquino. In 1914 he would participate in the Great Italian Exhibition of Caricature and Humor, organized by Il Numero. He initially specialized in a realist, colorful style, rejecting the artistic avant-garde. In 1905 he married Paola Farnesi. In 1908 he illustrated La canzoniere della nonna and starts his career in chromo-lithography, working for e.g. Sonzogno, Bertelli, Ricordi, making caricatural posters, as well as a poster for stage actress Dina Galli. In 1915 Mazza joined the army when Italy joined the Allied Forces during the First World War. He continued his work though, designing patriotic posters e.g. for the National Loans, and painted landscapes in Dalmatia and Libya. He also painted abandoned poor children and started a contract with the daily Il Secolo. In a sketchy style he made several portraits of stage actors such as Lyda Borelli and Dina Galli, of which several were also issued as postcards. Yet, in the same style he also drew anonymous fashionable ladies, or used the style for stage companies such as the Borelli-Piperno-Gandusio company, founded in 1913, or the company Galli-Guasti-Ciarli-Bracci. He worked as a poster designer mainly for the Bologna firm Chappuis, for the Arti grafiche Bertarelli and for Ricordi, producing about sixty posters, including advertising and political ones; he also designed theater posters, calendars (the 1917 one, for the Unione Cooperativa di Milano, is famous) and postcards in chromolithography. Companies for which he made his billboard posters were e.g.: the Neapolitan clothing company Mele, Fernet-Branca liquor, Birra Italia, Shell lubricants, Ganzini photography items, Bianchi bicycles, the department store La Rinascente, Credito Italiano, Magazzini Vittoria, etc. Remarkable is also his poster for the 1911 World Fair in Turin, as well as his posters promoting tourism in Italy. Mazza knew the painter and designer Marcello Dudovich. From him he gradually adopted the taste for the twodimensional and strong contrasts in colors. After the war, Mazza started to design posters with audacious designs, influenced by the futurists, the new sportive culture (e.g. dynamic posters with racing cars), and the fascist climate. As a painter, Mazza initially worked in the divisionist style. He specialized in (often women's) portraits, flowers, and landscapes. He contributed to exhibitions such as those by the Venice Biennale, Brera, the Lombard watercolorists, and the Mostra del ritratto femminile contemporaneo (Monza, 1924), while in 1935 he was given a personal exhibition at the Gallery Pesaro in Milan. Today, postcards and calendars by Mazza can be found at the Raccolta Bertirelli in Milan, his posters at the Salce Collection in Treviso, while the Museo nazionale della scienza e della tecnologia Leonardo da Vinci di Milano owns several paintings by Mazza, his grandfather and great-uncle. Sources: Italian Wikipedia, www.youtube.com/watch?v=-bmov5Cc0gM. Lyda Borelli (1887-1959) was already an acclaimed stage actress before she became the first diva of the Italian silent cinema. The fascinating film star caused a craze among female fans called 'Borellismo'.

[instantcaramel]

If we bring back the gay best friend trope, can we please do it with an actor who is actually gay?

and I thought Twitter is the site where nobody has any humor….

a) I also don‘t think it‘s a bad trope, I‘d rather have representation among minor characters than not at all if they‘re not just twodimensional jokes

b) last time I checked Phil never publicly said he‘s heterosexual and we‘re getting to a point where we‘re having a serious discussion about if people need to come out. I am glad when actors do, more people are out than I ever could have imagined as a kid - but look at what happened with the forced outing of the Heartstopper kid? And Nicholas Galitzine has a girlfriend, are we all going to boycott Red White Royal Blue now because he isn‘t gay enough hm?

[hardrockerhippie]

I have tons of interests. I just don't feel the need to talk about any and all of them on tumblr. It's not that i deliberately hide anything. I am just a multidimensional person and this is a twodimensional blog on the internet. And i do have friends that i talk to.

[codingprolab]

ECE220 Machine Problem 2 Translating and Printing a Student’s Schedule

Your task this week is to write an LC-3 program that translates a student’s daily schedule from a list to a twodimensional matrix of pointers (memory addresses, in this case to names of events), then prints the schedule as shown to the right. Your program must make use of the subroutines that you wrote for MP1 last week. Not counting those subroutines (nor comments, blank lines, and so forth),…

[bedlessbug]

jgb - death of affect

By eradicating all inflections of subjectivity from his narrative, Ballard seems to be seeking a Barthesian ‘degree zero’ of writing which had already been adumbrated in the anxietyfree psychological landscapes of his early novels and short stories. Ballard’s style — which is consistently blank, neutral and stripped of all the conventional artifices of fiction — bears an interesting relation to the ‘objective style’

an ability to sustain the dispassionate gaze of the scientist and, as we shall see, a fascination with objects and human beings that exist above all in a closed relation to themselves, to the detriment of the metaphoric and symbolic aura of traditional, ‘humanist’ fiction.

the erosion of human relationships and the individual self into a state of twodimensional anonymity.

his rejection of the metaphysical ‘depth’ of traditional art and of its accompanying tendency to represent the subject as a unified, self-present whole.

In Wesselman’s paintings, he writes, ‘the bland surface defuses the subject’ (AE 55), reducing it to an abstract, flat silhouette from which every mark of human presence fades. Likewise, Ballard’s Atrocity Exhibition — in which language and the self constantly seem on the verge of becoming engulfed in the claustrophobic angles and curves of the subject’s architectural environment — explores the consciousnesses of human beings who tend to surrender to the world of objects and even tend to ‘become mere extensions of the geometries of situations’ (AE 87). ATOMIC BOMB!

neutralized into a space beyond good and evil which reflects the latent desire of the postmodern consciousness to achieve, at least at a metaphorical level, ‘the total fusion and nondifferentiation of all matter’ (AE 33):

between bodily and objective geometries, as well as the boundaries between the organic and the nonorganic.

The ‘continuous present’ in which most of Ballard’s characters evolve echoes the author's own interpretation of the mannequin-like figures in Giorgio de Chirico’s painting The Disquieting Muses as ‘human beings from whom all time has been eroded, and reduced to the essence of their own geometries’ (UGM 86).”

Ballard’s preoccupation with the mass media and the possibility that the new technological landscape may trigger unconscious drives is central to the grammar of pornography and violence that runs through the whole collection.

the insanity of Ballard’s patients, far from being due to their failure to make contact with the outside world, results from an excess of awareness which makes it impossible for them to cope with what Dr Nathan calls ‘the phenomenology of the universe, the specific and independent existence of separate objects and events, however trivial and inoffensive these may seem’:

Ballard’s proposition that ‘sexual intercourse can no longer be regarded as a personal and isolated activity, but is seen to be a vector in a public complex involving automobile styling, politics and mass communications’ points to ‘the nonsexual roots of sexuality’

The main target of Ballard’s critique is of course the media culture itself and its tendency to trivialize cruelty and package violence into a commercial product.

Ballard is therefore neither a moralist nor an apologist, but a visionary observer of what he perceives as the cold post-morality of a fragmented, narcissistic age.

For Ballard, the gradual numbing of our emotional responses to mediatized violence has led to various forms of physical and mental alienation, including a phenomenon the author memorably called the ‘death of affect’ (AE 77, R/S 96).

As Ballard recently suggested in The Kindness of Women, our gradual alienation from any kind of direct (that is, unmediated) response to experience — combined with the unlimited expansion of the mind's possibilities afforded to us by modern technology — has left us “free to pursue our own psychopathologies as a game’ (KW 221). PORNOGRAPHY

Still, the images of sexual perversion which abound in Ballard’s Atrocity Exhibition and Crash (which he called the first ‘technological’ porn novel) are almost entirely deprived of erotic content, as they are always depicted in strictly technical terms. The aseptic abstractness of Ballard’s vignettes is best understood in the light of Dr Nathan’s remark, in ‘The Assassination Weapon’, that ‘science is the ultimate pornography, analytic activity whose main aim is to isolate objects or events from their contexts in time and space’ (AE 36). QUOTE THIS HERE! SCIENCE OF ATOMIC BOMB IMAGE, ISOLATED, NEVER TO BE JOINED WITH THE MASS OF NIGHTS DARKNESS AGAIN

[cat-tenyx]

japanese letters doing a transformers and turning into twodimensional car

[ankitcodinghub]

CSE131 - Homework #9 Solved

Objective : Learn how to use array and combine with for and while loops to implement some operations. 9.1 Write a program to use the rand() function to generate two twodimensional arrays of size 3*3, then output these matrices and implement addition, subtraction and multiplication operations. Hint: random between 0 ~ 100. Output: 9.2 Write a program let the user to input two numbers as the…

[virtualizetechnologies0]

VIRTUALIZE TECHNOLOGIES: REVOLUTIONIZING THE 2D METAVERSE  

VIRTUALIZE TECHNOLOGIES: REVOLUTIONIZING THE 2D METAVERSE  

At Virtualize Technologies, we are shaping the future of digital interaction by creating innovative experiences in the 2D metaverse. Combining creativity with cuttingedge technology, we specialize in designing virtual spaces where users can connect, explore, and engage seamlessly. Whether it’s for gaming, education, or social platforms, our team transforms ideas into interactive 2D metaverse environments that captivate audiences worldwide.  

What is the 2D Metaverse?  

The 2D metaverse is a digital space where people can interact through avatars, engage in activities, and explore virtual environments—all within a twodimensional framework. It’s accessible, userfriendly, and perfect for businesses and platforms looking to enhance their digital presence.  

From creating social hubs to immersive virtual classrooms, the 2D metaverse offers endless possibilities for interaction and innovation. At Virtualize Technologies, we bring these concepts to life with custom solutions tailored to meet your specific needs.  

 Why Choose Virtualize Technologies for 2D Metaverse Development?  

1. Expertise in 2D Design  

   Our team has extensive experience in creating visually stunning and interactive 2D environments that engage users.  

2. Custom Solutions  

   We design metaverse experiences that align with your brand identity and user expectations, ensuring every project is unique.  

3. CrossPlatform Compatibility  

   Our 2D metaverse solutions are optimized for various platforms, including web, mobile, and desktop, ensuring accessibility for all users.  

4. Seamless Interactions  

  We prioritize userfriendly interfaces and smooth navigation, making every virtual experience enjoyable and immersive.  

 Our 2D Metaverse Services  

 Game Development  

   We craft interactive 2D metaverse games with engaging storylines and seamless multiplayer experiences.  

 Social Platforms  

   Build virtual spaces for users to connect, chat, and collaborate in realtime.  

 Educational Solutions  

   Create virtual classrooms and training environments to enhance learning in an interactive and engaging way.  

 Event Hosting  

   Design 2D metaverse venues for hosting virtual events, conferences, and exhibitions.  

 How We Develop Your 2D Metaverse  

1. Planning and Conceptualization  

   We work closely with you to understand your vision and define the goals of your 2D metaverse project.  

2. Design and Development  

   Our team creates immersive visuals, intuitive interfaces, and engaging features to bring your virtual world to life.  

3. Testing and Optimization  

   Rigorous testing ensures your 2D metaverse runs smoothly and provides a flawless user experience.  

4. Launch and Support  

   After launch, we offer ongoing support to keep your virtual environment updated and functional.  

 Step Into the 2D Metaverse with Us  

The 2D metaverse is transforming how we connect, collaborate, and entertain. At Virtualize Technologies, we are committed to building virtual spaces that captivate and inspire.  

Ready to explore the possibilities of the 2D metaverse? Contact Virtualize Technologies today and let’s create your next immersive virtual experience together!  

[gods-fear-what-cant-be-controled]

Holy shit do you even care about anything outside of things pertaining to you and the "background noise" of thousands of instances of existence or do you think being the main character of your own story means every side character is twodimensional snd everything outside your main quest is environment padding

[eternalxblossom]

Hey i love your blog specially your faking it recap. I know its been so long since faking it but i have a question do you think karma loved amy way more than amy loved karma? Because i was watching it and i felt like karma cared about amy way more! Do you think the reason karma didn't want to be with Amy was because she was afraid that somehow their relationship couldn't work out and she would lose amy and she didn't want to risk that? So although she would love to be with Amy she decided to not go to that road because at least she have amy as a friend. If some how amy assured karma that they friendship isn't at risk that if their relationship couldn't workout they could go back to being best friends im sure karma didn't hesitate to be with Amy. I just wanted to say that Amy was so important to karma that she couldn't risk losing her. And also i don't buy the idea that carter wanted Amy and karma go back to being friends after they date. I think he said oh amy and karma will date so viewers don't get sad and he said oh and then they will go back being friends so he don't spoil the series if someday faking it get a revival. So he basically said karmy will happen and will not happen. But by saying karmy will happen we all know that karma was really loved amy romantically all along.

Oh wow, a Faking It ask, I haven't gotten one of those in forever, le sigh :( Thank you for appreciating my dumb recaps! I wouldn't necessarily say that Karma loved Amy 'more', not the word I would use, but I would say Karma never really had too many friends outside of Amy, or, however many she had, they never filled that space in her heart the same way. So the moment Amy branched out and started doing things on her own (leaving for the summer, photography), she felt left out so she lashed out. I think whenever Karma felt confused about Amy, she overcompensated and projected everything onto the first dude she saw lmfao.

I've been saying it forever, the only way Karmy would work was if they both let their guard down and admitted how important they are to each other and talked about their fear of losing each other openly. I've always wanted a serious convo on that.

Also I must disagree with your optimistic view on Carter. He has been misleading the Karmy fans for years and used us to keep getting the show renewed. I don't believe he ever had any intention of having them get together AND last. Unfortunately, he would have sent the most stupid message across - that love and friendship can't coexist. He even said they would have realized they lost what made them 'them' in some interview, which is utter bullshit.

If someone gave me the writing rights for the show, let's just say I would have found a way to do it realistically. I honestly think, and I will keep saying this, they needed more WLW consultants on the show. Even if Carter himself is gay, female dynamics have a level of nuance I don't think he was ever able to convey properly. It's precisely why Karma's POV was never shown right, to the point where other people filled in the blanks just to make her out into a 'heartless bitch' or 'twodimensional character' (both far from the truth).

[imagella-blog]

Purple roses clip art image in bold, cartoonish style

Rose Tattoo #purpleroses #clipart #boldlines #darkpink #twodimensional #garyhume #elaboratedetail #64:27 #purpleflowers #cartoonart

[babyawacs]

.@blackberry .@swiftonsecurity .@swiftonsecuriti #mandelbrot #busted.@mathematics @harvardmath .@harvard   #cc @darpa #usstratcom‎ .@us_stratcom .@gchq .@nsagov caniget info on injecting a boolean separator between the static part and the dynamic part o.f fractals ifithelped ie ringlattic e redring greenring inconcept but on fractals  withandwithout utilising 3dimensional mathemathics then on a twod imensional lattice‎

.@blackberry #mandelbrot #busted.@mathematics @harvardmath .@harvard #cc @darpa #usstratcom‎ .@us_stratcom .@gchq .@nsagov caniget info on injecting a boolean separator between the static part and the dynamic part of fractals ifithelped ie ringlattice redring greenring inconcept but on fractals withandwithout utilising 3dimensional mathemathics then on a twodimensional lattice‎ I am Christian…

[leanstooneside]

The Who

◊ 14 THEO

◊ FOUR YEARS

◊ 30 SECS

◊ II: MORE

◊ 2011 JANUARY

◊ 6 CICCARIELLO

◊ 9 PETER

◊ THREEDIMENSIONAL ENVIRONMENT

◊ ONE DILEMMA

◊ FEW COMMERCIALS

◊ 1ST ED

◊ FIRST PROOF

◊ 2010 LONDON

◊ 198513; THEY

◊ A FEW

◊ TEN YEARS

◊ 5 SECS

◊ 8 PETER

◊ THIRTEEN TALKS

◊ FIVE KINGDOMS

◊ ONE WORD

◊ 2008 WORK

◊ 2008 DRAFT

◊ TWODIMENSIONAL PERSPECTIVAL

[nightmaretist]

There's paintings as well, in the permanent collection as well as in the temporary one. Sculpted works and installations are quite interesting as well, so I do think you should give it a shot. Art should not merely be twodimensional, after all. [...] Not in this current collection, but there must be something in the archives.

Sculpted? Bit heavier to "borrow" sadly Hmm [...] I'm more of a painting than a sculpture [...] connoisseur, but maybe it's finally time I branch out, see what the other side has to offer. I'm sure your work will be something to watch out for, of course. I'm not a bird person either but I won't mind becoming one. Do you have more [...] water-inspired works, though?