Disorder and Interaction in 2D: Exact diagonalization study of the Anderson-Hubbard-Mott model

We investigate, by numerically calculating the charge stiffness, the effects of random diagonal disorder and electron-electron interaction on the nature of the ground state in the 2D Hubbard model through the finite size exact diagonalization technique. By comparing with the corresponding 1D Hubbard model results and by using heuristic arguments we conclude that it is \QTR{it}{unlikely} that there is a 2D metal-insulator quantum phase transition although the effect of interaction in some range of parameters is to substantially enhance the non-interacting charge stiffness.Comment: 13 pages, 2 figures Revised version. Accepted for publication in Phys. Rev. Let

Correlated charge polarization in a chain of coupled quantum dots

Coherent charge transfer in a linear array of tunnel-coupled quantum dots, electrostatically coupled to external gates, is investigated using the Bethe ansatz for a symmetrically biased Hubbard chain. Charge polarization in this correlated system is shown to proceed via two distinct processes: formation of bound states in the metallic phase, and charge transfer processes corresponding to a superposition of antibound states at opposite ends of the chain in the Mott-insulating phase. The polarizability in the insulating phase of the chain exhibits a universal scaling behavior, while the polarization charge in the metallic phase of the model is shown to be quantized in units of $e/2$.Comment: 9 pages, 3 figures, 1 tabl

Antiturcica Iterata – another Look at Croatian anti-Turkish Writings during the Renaissance

Otpor »Turcima«, održavanje granice prema Osmanskome Carstvu, jedna je od dominantnih tema u ranonovovjekovnoj Hrvatskoj. Sukladno tome, »turska tema« prisutna je i u književnosti. Problematizirana je u velikom vremenskom rasponu, na različitim jezicima, u različitim žanrovima, s različitim intencijama. Važnu podskupinu tekstova ove tematike – izravne i neizravne pozive na otpor osmanskim napadima i osvajanjima u razdoblju 1436-1600 – ovdje smo pokušali popisati što potpunije i što konzistentnije. Uvodno dajemo pregled istraživanja i interpretacija hrvatskoga protuturskog korpusa od 1945. do 2014. Potom upozoravamo na probleme vezane uz konstituiranje korpusa i iznosimo načela po kojima smo korpus uspostavili. Zatim opisujemo korpus prema očuvanosti popisanih tekstova, prema pisanom mediju u kojem su prenošeni (rukopisi ili tiskovine), prema jeziku (latinski, hrvatski, talijanski), načinu izražavanja (proza, poezija), književnim vrstama, kronologiji (upozoravamo i na diskontinuitete, na godine kad se javlja manje protuturskih tekstova), te prema prostorima koji su u tekstovima posebno isticani. Razmatramo i autore, prema broju tekstova, prema porijeklu i društvenom statusu. Naposljetku skiciramo sinoptičku interpretaciju korpusa, posebnu pozornost poklanjajući tekstovima koji se pojavljuju istodobno ili su vremenski bliski. Bibliografska skica hrvatskog protuturskog korpusa prilog je radu, a dostupna je i kao baza podataka na internetu.In the 15th and 16th centuries, Croatian writing about the Ottoman threat was both a reaction to the continuous crisis of several states, their societies, and culture, and an attempt to overcome this crisis by developing new ideas and new ways of consolidating the society. It has been claimed that this desperate attempt laid the foundations of modern Croatia. To be able to identify continuities and discontinuities of the so-called Croatian anti-Turkish writings, we have compiled a list of as many such works as possible. In Croatian literary history, the anti-Turkish writings seem to have first been presented as a group by Mihovil Kombol in 1945. In 1974, Marin Franičević tried to consider together texts from this group written in different languages (Latin and Croatian). In 1983, Vedran Gligo selected and published a canonical collection of sixteen (Latin) »anti-Turkish speeches« from the Renaissance. At the same time, Tomislav Raukar interpreted the anti-Turkish theme as a stimulus to Early Modern Croatia. In 2004, Davor Dukić proposed an imagological interpretation of the anti-Turkish corpus. All researchers, however, worked with a restricted number of texts, and there was not even an estimate of the actual size of the corpus. To construe a corpus with some pretence to comprehensiveness, we had to establish whether (and to what degree) a text addresses the anti-Turkish theme, whether it could be considered a »Croatian« text, whether it could be considered a literary and a public as opposed to a documentary or a private text). Such considerations led us to exclude some famous texts (such as Judita by Marko Marulić),while including e. g. an Oratio contra Turcam which Ivan Pergošić reprinted from the book by Johannes Avenarius. The fuzzy boundaries between confidentiality and publicity have been demonstrated by the fate of reports by the papal nuntio Antonius Fabregues, whose official dispatches about the Battle of Krbava field have appeared also in print as propagandistic broadsheets. In our corpus, a Croatian anti-Turkish work is a text urging Christian action against the Turks in defence of Dalmatia, Croatia, Hungary, and Christian Europe as a whole, written by an author significantly connected with Croatia, and calling to arms either by direct appeals or by a more indirect strategy of reporting, celebrating and lamenting events in the Christian-Turkish struggle. The corpus currently comprises basic bibliographic data on 141 texts written between 1436 and 1600. It exists as a list (see the Appendix to the article) and as a database published by the TeMrežaH project (temrezah.ffzg.unizg.hr/antiturcica-biblio.html). We have included data on a few texts that are not preserved, and on texts by unknown authors. Ninety-four texts first appeared as manuscripts, 44 in print (two exist in roughly contemporaneous handwritten and printed versions). Two texts (poems in Croatian from 1565 and 1596) were first printed almost a hundred years after the events they describe (in 1655). One hundred and four texts are in Latin, 26 in Croatian, nine in Italian; 75 texts are in prose, 66 in verse. An especially active period of production falls in 1493-1548 (when three fifths of all texts in the corpus were written). There are three longer periods of silence, when just a few anti-Turkish texts appear: the years 1504-1509, 1546-1560, 1575-1591. Christian Europe is the central topic in 46 texts, the Kingdom of Hungary in 31, Croatia itself in 20, Dalmatia (and Dubrovnik) in 20, the Levant in 15, the Venetian Republic in 11; this distribution follows the geopolitical situation of Croatian regions during the Renaissance, but Croatia and Dalmatia are treated in about the same number of texts, while the Kingdom of Hungary was thematised significantly more often than Venice. The texts were written by 61 authors (seven are anonymous), 40 of which wrote just one text; fourteen are known as authors only because of their anti-Turkish works. The five authors with most anti-Turkish texts are Fran Trankvil Andreis, Damjan Beneša, Marko Marulić, Ludovik Paskalić, Ivan Vitez od Sredne. Beneša and Paskalić were absent from the Croatian »canon« of anti-Turkish authors. Four of the authors are not Croatian by birth (Tideo Acciarini, Antonio Fabregues, Francesco Marcello, Bernard Zane), but they were all connected to Dalmatia by office, as teachers, diplomats or Church officials. Most of the authors can be regarded as humanists (17) or priests (24, or 34 including priests serving as diplomats); there were 15 diplomats, five of them lay persons. The authors whose anti-Turkish writings appear during the longest chronological span are Fran Trankvil Andreis from Trogir (53 years), Mavro Vetranović from Dubrovnik (writing in Croatian over 45 years), and Frano Božićević Natalis from Split (35 years). A chronological analysis also reveals two main generations of anti-Turkish writers. The first one was active during 1500-1535, and the second during 1520-1570. Among the authors those from Dalmatia and Dubrovnik prevail; they belong mostly to the civic patriciate, to the lesser nobility, or even to the general citizenry. A synoptic analysis of dates, genres, authors and contexts suggests a discontinuity in the corpus of Croatian anti-Turkish writings: some time after 1530-1540 public speeches and appeals disappear, to be replaced by administrative reports to the authorities of the Habsburg empire, by sensational testimonies about travels or battles, and by highly individual »grassroots« entreaties, often, seemingly, without significant political support, often without the benefit of print or of larger print runs. The discontinuity may be connected with the agony of the Kingdom of Hungary and Croatia (after the Battle of Mohács), and with the gradual disappearance of the generation of Croatian humanists that had tried to play significant roles in this kingdom

Tight focusing of laser light using a chromium Fresnel zone plate

Funding: Russian Scientific Foundation (17-19-01186).Using near-field scanning microscopy, we demonstrate that a 15-µm zone plate fabricated in a 70-nm chromium film sputtered on a glass substrate and having a focal length and outermost zone's width equal to the incident wavelength λ = 532 nm, focuses a circularly polarized Gaussian beam into a circular subwavelength focal spot whose diameter at the full-width of half-maximum intensity is FWHM = 0.47λ. This value is in near-accurate agreement with the FDTD-aided numerical estimate of FWHM = 0.46λ. When focusing a Gaussian beam linearly polarized along the y-axis, an elliptic subwavelength focal spot is experimentally found to measure FWHMx = 0.42λ (estimated value FWHMx = 0.40λ) and FWHMy = 0.64λ. The subwavelength focal spots presented here are the tightest among all attained so far for homogeneously polarized beams by use of non-immersion amplitude zone plates.PostprintPeer reviewe

Comment on "Measuring the Orbital Angular Momentum of a Single Photon"

Optical modes with different orbital angular momentums (OAMs) per photon may be sorted by Mach-Zehnder interferometers incorporated with beam rotators, without resorting to OAM mode converters.Comment: 1 page, 1 figur

Coherent Resonant Tunneling Through an Artificial Molecule

Coherent resonant tunneling through an artificial molecule of quantum dots in an inhomogeneous magnetic field is investigated using an extended Hubbard model. Both the multiterminal conductance of an array of quantum dots and the persistent current of a quantum dot molecule embedded in an Aharanov-Bohm ring are calculated. The conductance and persistent current are calculated analytically for the case of a double quantum dot and numerically for larger arrays using a multi-terminal Breit-Wigner type formula, which allows for the explicit inclusion of inelastic processes. Cotunneling corrections to the persistent current are also investigated, and it is shown that the sign of the persistent current on resonance may be used to determine the spin quantum numbers of the ground state and low-lying excited states of an artificial molecule. An inhomogeneous magnetic field is found to strongly suppress transport due to pinning of the spin-density-wave ground state of the system, and giant magnetoresistance is predicted to result from the ferromagnetic transition induced by a uniform external magnetic field.Comment: 23 pages, 12 figure

Microlens-aided focusing of linearly and azimuthally polarized laser light

Funding: Russian Foundation for Basic Research (RFBR) (14-29-07133, 14-07-97039, 15-07-01174, 15-47-02492, 15-37-20723, 16-07-00990, 16-47-630483); Ministry of Education and Science of the Russian Federation (NSh-4128.2016.9, MK-9019.2016.2); European Research Council (337508).We have investigated a four-Sector transmission Polarization Converter (4-SPC) for a wavelength of 633 nm, that enables the conversion of a linearly polarized incident beam into a mixture of linearly and azimuthally polarized beams. It was numerically shown that by placing a Fresnel zone plate of focal length 532 nm immediately after the 4-SPC, the incident light can be focused into an oblong subwavelength focal spot whose size is smaller than the diffraction limit (with width and breadth, respectively, measuring FWHM = 0.28λ and FWHM = 0.45λ, where λ is the incident wavelength and FWHM stands for full-width at half maximum of the intensity). After passing through the 4-SPC, light propagates in free space over a distance of 300 μm before being focused by a Fresnel zone plate (ZP), resulting in focal spot measuring 0.42λ and 0.81λ. The focal spot was measured by a near-field microscope SNOM, and the transverse E-field component of the focal spot was calculated to be 0.42λ and 0.59λ. This numerical result was verified experimentally, giving a focal spot of smaller and larger size, respectively, measuring 0.46λ and 0.57λ. To our knowledge, this is the first implementation of polarization conversion and subwavelength focusing of light using a pair of transmission micro-optic elements.PostprintPeer reviewe

Delocalizing effect of the Hubbard repulsion for electrons on a two-dimensional disordered lattice

We study numerically the ground-state properties of the repulsive Hubbard model for spin-1/2 electrons on two-dimensional lattices with disordered on-site energies. The projector quantum Monte Carlo method is used to obtain very accurate values of the ground-state charge density distributions with $N_p$ and $N_p+1$ particles. The difference in these charge densities allows us to study the localization properties of an added particle. The results obtained at quarter-filling on finite clusters show that the Hubbard repulsion has a strong delocalizing effect on the electrons in disordered 2D lattices. However, numerical restrictions do not allow us to reach a definite conclusion about the existence of a metal-insulator transition in the thermodynamic limit in two-dimensions.Comment: revtex, 7 pages, 7 figure

The relativistic impulse approximation for the exclusive electrodisintegration of the deuteron

The electrodisintegration of the deuteron in the frame of the Bethe-Salpeter approach with a separable kernel of the nucleon-nucleon interaction is considered. This conception keeps the covariance of a description of the process. A comparison of relativistic and nonrelativistic calculations is presented. The factorization of the cross section of the reaction in the impulse approximation is obtained by analytical calculations. It is shown that the photon-neutron interaction plays an important role.Comment: 31 pages, 14 figures, 1 tabl