Localized Thermal States

It is believed that thermalization in closed systems of interacting particles can occur only when the eigenstates are fully delocalized and chaotic in the preferential (unperturbed) basis of the total Hamiltonian. Here we demonstrate that at variance with this common belief the typical situation in the systems with two-body inter-particle interaction is much more complicated and allows to treat as thermal even eigenstates that are not fully delocalized. Using a semi-analytical approach we establish the conditions for the emergence of such thermal states in a model of randomly interacting bosons. Our numerical data show an excellent correspondence with the predicted properties of {\it localized thermal eigenstates}.Comment: Proceedings of the 5th Conference on Nuclei and Mesoscopic Physics, NMP17, East Lansing (USA

Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator

We study quench dynamics in the many-body Hilbert space using two isolated systems with a finite number of interacting particles: a paradigmatic model of randomly interacting bosons and a dynamical (clean) model of interacting spins-$1/2$. For both systems in the region of strong quantum chaos, the number of components of the evolving wave function, defined through the number of principal components $N_{pc}$ (or participation ratio), was recently found to increase exponentially fast in time [Phys. Rev. E 99, 010101R (2019)]. Here, we ask whether the out-of-time ordered correlator (OTOC), which is nowadays widely used to quantify instability in quantum systems, can manifest analogous time-dependence. We show that $N_{pc}$ can be formally expressed as the inverse of the sum of all OTOC's for projection operators. While none of the individual projection-OTOC's shows an exponential behavior, their sum decreases exponentially fast in time. The comparison between the behavior of the OTOC with that of the $N_{pc}$ helps us better understand wave packet dynamics in the many-body Hilbert space, in close connection with the problems of thermalization and information scrambling.Comment: 11 pages, 7 figure

Steiner's formula in the Heisenberg group

Steiner's tube formula states that the volume of an ∈-neighborhood of a smooth regular domain in ℝn is a polynomial of degree n in the variable ∈ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ∈-neighborhood with respect to the Heisenberg metric is an analytic function of ∈ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms

On The Dynamic Programming Approach To Incentive Constraint Problems

In this paper we study a class of infinite horizon optimal control problems with incentive constraints in the discrete time case. More specifically, we establish suffcient conditions under which the value function associated to such problems satisfies the Dynamic Programming Principle.In this paper we study a class of infinite horizon optimal control problems with incentive constraints in the discrete time case. More specifically, we establish suffcient conditions under which the value function associated to such problems satisfies the Dynamic Programming Principle.Non-Refereed Working Papers / of national relevance onl

On the ordeal of quinolone preparation via cyclisation of aryl-enamines; synthesis and structure of ethyl 6-methyl-7-iodo-4-(3-iodo-4-methylphenoxy)-quinoline-3-carboxylate

Recent studies directed to the design of compounds targeting the bc(1) protein complex of Plasmodium falciparum, the parasite responsible for most lethal cases of malaria, identified quinolones (4-oxo-quinolines) with low nanomolar inhibitory activity against both the enzyme and infected erythrocytes. The 4-oxo-quinoline 3-ester chemotype emerged as a possible source of potent bc(1) inhibitors, prompting us to expand the library of available analogs for SAR studies and subsequent lead optimization. We now report the synthesis and structural characterization of unexpected ethyl 6-methyl-7-iodo-4-(3-iodo-4-methylphenoxy)quinoline-3-carboxylate, a 4-aryloxy-quinoline 3-ester formed during attempted preparation of 6-methyl-7-iodo-4-oxo-quinoline-3-carboxylate (4-oxo-quinoline 3-ester). We propose that the 4-aryloxy-quinoline 3-ester derives from 6-methyl-7-iodo-4-hydroxy-quinoline-3-carboxylate (4-hydroxy-quinoline 3-ester), the enol form of 6-methyl-7-iodo-4-oxo-quinoline-3-carboxylate. Formation of the 4-aryloxy-quinoline 3-ester confirms the impact of quinolone/hydroxyquinoline tautomerism, both on the efficiency of synthetic routes to quinolones and on pharmacologic profiles. Tautomers exhibit different cLogP values and interact differently with the enzyme active site. A structural investigation of 6-methyl-7-iodo-4-oxo-quinoline-3-carboxylate and 6-methyl-7-iodo-4-hydroxy-quinoline-3-carboxylate, using matrix isolation coupled to FTIR spectroscopy and theoretical calculations, revealed that the lowest energy conformers of 6-methyl-7-iodo-4-hydroxy-quinoline-3-carboxylate, lower in energy than their most stable 4-oxo-quinoline tautomer by about 27 kJ mol(-1), are solely present in the matrix, while the most stable 4-oxo-quinoline tautomer is solely present in the crystalline phase.Fundacao para a Ciencia e Tecnologia (FCT - Portugal) [UID/Multi/04326/2013]; QREN-COMPETE-UE; CCMAR; FCT [SFRH/BD/81821/2011, RECI/BBB-BQB/0230/2012, UI0313/QUI/2013, UID/FIS/04564/2016]; FEDER/COMPETE-UE; [PTDC/QEQ-QFI/3284/2014 - POCI-01-0145-FEDER-016617]info:eu-repo/semantics/publishedVersio