Spectral Properties of Disordered Interacting Non-Hermitian Systems

Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian interacting disordered Hamiltonians and attempt to analyze their chaotic behavior or lack of it through the lens of the recently introduced non-hermitian analog of the spectral form factor and the complex spacing ratio. We consider three widely relevant non-hermitian models which are unique in their ways and serve as excellent platforms for such investigations. Two of the models considered are short-ranged and have different symmetries. The third model is long-ranged, whose hermitian counterpart has itself become a subject of growing interest. All these models exhibit a deep connection with the non-hermitian Random Matrix Theory of corresponding symmetry classes at relatively weak disorder. At relatively strong disorder, the models show the absence of complex eigenvalue correlation, thereby, corresponding to Poisson statistics. Our thorough analysis is expected to play a crucial role in understanding disordered open quantum systems in general.Comment: 12 pages, 15 figures, 3 table

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25

Impact of dephasing probes on incommensurate lattices

We investigate open quantum dynamics for a one-dimensional incommensurate Aubry-Andr\'{e}-Harper lattice chain, a part of which is initially filled with electrons and is further connected to dephasing probes at the filled lattice sites. This setup is akin to a step-initial configuration where the non-zero part of the step is subjected to dephasing. We investigate the quantum dynamics of local electron density, the scaling of the density front as a function of time both inside and outside of the initial step, and the growth of the total number of electrons outside the step. We analyze these quantities in all three regimes, namely, the de-localized, critical, and localized phases of the underlying lattice. Outside the initial step, we observe that the density front spreads according to the underlying nature of single-particle states of the lattice, for both the de-localized and critical phases. For the localized phase, the spread of the density front hints at a logarithmic behaviour in time that has no parallel in the isolated case (\emph{i.e.}, in the absence of probes). Inside the initial step, due to the presence of the probes, the density front spreads in a diffusive manner for all the phases. This combination of rich and different dynamical behaviour, outside and inside the initial step, results in the emergence of mixed dynamical phases. While the total occupation of electrons remains conserved, the value outside or inside the initial step turns out to have a rich dynamical behaviour. Our work is widely adaptable and has interesting consequences when disordered/quasi-disordered systems are subjected to a thermodynamically large number of probes.Comment: 18 pages, 8 figure

Study of Thermo-Sensitive In-Situ Gels for Ocular Delivery

The aim of the present study was the development of thermo-sensitive in-situ gels for in-vitro evaluation of ophthalmic delivery systems of ketorolac tromethamine (KT), based on methylcellulose (MC) in combination with hydroxypropylmethyl cellulose (HPMC). The gel temperature of 1% MC solution was observed at 60°C. It was found that 6% oral rehydration salt without dextrose (ORS) was capable to reduce the gel temperature below physiological temperature. HPMC was added to increase viscosity and drug release time. The results indicated a large increase in viscosity at 37°C with addition of HPMC whch provided sustained release of the drug over a 4h period. From in-vitro release studies, it could be concluded that the developed systems were thus a better alternative to conventional eye drops

Studies on synthesis and characterization of magnesia based refractory aggregates developed from Indian magnesite

The present work intends to study the properties of magnesia based refractory aggregates developed from Indian magnesite by changing lime/silica ratio. The material has been sintered in the temperature range of 1550C - 1700C. The sintered samples are characterized in terms of bulk density, apparent porosity, true density, percentage densification, mechanical, thermo-mechanical properties like cold modulus of rupture, hot modulus of rupture and thermal shock resistance and structural properties by XRD. The developed microstructures at different temperatures are studied through FESEM study and compositional analysis of the developed phases is done by EDX study

Development and in vitro evaluation of Letrozole loaded biodegradable nanoparticles for breast cancer therapy

The objectives of our study were to prepare and evaluate a biodegradable nanoparticulate system of Letrozole (LTZ) intended for breast cancer therapy. LTZ loaded poly(lactide-co-glycolide) nanoparticles (LTZ-PLGA-NPs) were prepared by emulsion-solvent evaporation method using methylene chloride and polyvinyl alcohol. Percentage of drug (with respect to polymer) was selected as formulation variable. LTZ-PLGA-NPs were characterized by particle size, zeta potential, infrared spectra, drug entrapment efficiency and in vitro release. Sonication was done with an ultrasound pulse sonicator at 70 W, 30 kHz for 90 sec to produce stable NPs of mean size range from 64 nm to 255 nm with high entrapment efficiency (68% to 82%). Percentage of drug significantly influenced particle size, entrapment efficiency and release (pOs objetivos de nosso estudo foram preparar e avaliar o sistema de nanopartícula biodegradável de letrozol na terapia de câncer mamário. Nanopartículas de poli(lactídeo-co-glicolídeo) carregadas com LTZ (LTZ-PLGA-NPs) foram preparadas pelo método de emulsão-evaporação de solvente, utilizando dicloro metano e álcool polivinílico. A porcentagem do fármaco (com relação ao polímero) foi selecionada como variável da formulação. LTZ-PLGA-NPs foram caracterizadas pelo tamanho da partícula, potencial zeta, espectros no infravermelho, eficiência de inclusão e liberação in vitro. A sonicação foi realizada com sonicador de ultrassom, de pulso a 70W e 30 kHz por 90 segundos para produzir NPs estáveis, de faixa de tamanho médio de 64 nm a 266 nm, com alta eficiência de inclusão (68% a 82%). A porcentagem do fármaco foi significativamente influenciada pelo tamanho da partícula, eficiência de inclusão e liberação (