The Hamilton--Jacobi Theory and the Analogy between Classical and Quantum Mechanics

We review here some conventional as well as less conventional aspects of the time-independent and time-dependent Hamilton-Jacobi (HJ) theory and of its connections with Quantum Mechanics. Less conventional aspects involve the HJ theory on the tangent bundle of a configuration manifold, the quantum HJ theory, HJ problems for general differential operators and the HJ problem for Lie groups.Comment: 42 pages, LaTeX with AIMS clas

Wigner distributions for finite dimensional quantum systems: An algebraic approach

We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space', and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail.Comment: Latex, 13 page

Phase-space descriptions of operators and the Wigner distribution in quantum mechanics II. The finite dimensional case

A complete solution to the problem of setting up Wigner distribution for N-level quantum systems is presented. The scheme makes use of some of the ideas introduced by Dirac in the course of defining functions of noncommuting observables and works uniformly for all N. Further, the construction developed here has the virtue of being essentially input-free in that it merely requires finding a square root of a certain N^2 x N^2 complex symmetric matrix, a task which, as is shown, can always be accomplished analytically. As an illustration, the case of a single qubit is considered in some detail and it is shown that one recovers the result of Feynman and Wootters for this case without recourse to any auxiliary constructs.Comment: 14 pages, typos corrected, para and references added in introduction, submitted to Jour. Phys.

Null Phase Curves and Manifolds in Geometric Phase Theory

Bargmann invariants and null phase curves are known to be important ingredients in understanding the essential nature of the geometric phase in quantum mechanics. Null phase manifolds in quantum-mechanical ray spaces are submanifolds made up entirely of null phase curves, and so are equally important for geometric phase considerations. It is shown that the complete characterization of null phase manifolds involves both the Riemannian metric structure and the symplectic structure of ray space in equal measure, which thus brings together these two aspects in a natural manner.Comment: 10 pages, 1 figur

Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems. A unitary group approach

We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study the effect of degeneracies on geometric phases for three-level systems. This is shown to lead to a highly nontrivial generalization of the result for two-level systems in which degeneracy results in a "monopole" structure in parameter space. The rich structures that arise are related to the geometry of adjoint orbits in SU(3). The limiting case of a two-level degeneracy in a three-level system is shown to lead to the known monopole structure.Comment: Latex, 27 p

One-step synthesis of metal/oxide nanocomposites by gas phase condensation

Metallic nanoparticles (NPs), either supported on a porous oxide framework or finely dispersed within an oxide matrix, find applications in catalysis, plasmonics, nanomagnetism and energy conversion, among others. The development of synthetic routes that enable to control the morphology, chemical composition, crystal structure and mutual interaction of metallic and oxide phases is necessary in order to tailor the properties of this class of nanomaterials. With this work, we aim at developing a novel method for the synthesis of metal/oxide nanocomposites based on the assembly of NPs formed by gas phase condensation of metal vapors in a He/O2 atmosphere. This new approach relies on the independent evaporation of two metallic precursors with strongly different oxidation enthalpies. Our goal is to show that the precursor with less negative enthalpy gives birth to metallic NPs, while the other to oxide NPs. The selected case study for this work is the synthesis of a Fe-Co/TiOx nanocomposite, a system of great interest for its catalytic and magnetic properties. By exploiting the new concept, we achieve the desired target, i.e., a nanoscale dispersion of metallic alloy NPs within titanium oxide NPs, the structure of which can be tailored into TiO1-\u3b4 or TiO2 by controlling the synthesis and processing atmosphere. The proposed synthesis technique is versatile and scalable for the production of many NPs-assembled metal/oxide nanocomposites

Entanglement and nonclassicality for multi-mode radiation field states

Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multi-mode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beamsplitters, in a transparent manner. For single mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beamsplitter, these conditions turn exactly into signatures of NPT entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two--mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beamsplitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three--mode beamsplitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.Comment: Latex, 46 page

Late-Stage Molecular Editing Enabled by Ketone Chain-Walking Isomerization

Herein, a method for the isomerization of ketones in a manner akin to the chain-walking reaction of alkenes is described. Widely available and inexpensive pyrrolidine and elemental sulfur are deployed as catalysts to achieve this reversible transformation. Key to the utility of this approach was the elucidation of a stereochemical model to determine the thermodynamically favored product of the reaction and the kinetic selectivity observed. With the distinct selectivity profile of our ketone chain-walking process, the isomerization of various steroids was demonstrated to rapidly access novel steroids with "unnatural" oxidation patterns.ISSN:0002-7863ISSN:1520-512

Screening of Aroma-Producing Performance of Anticlostridial Lacticaseibacillus casei Strains

The cheesemaking industry is increasingly interested in using adjunct cultures with potential aromatic and anticlostridial activities. In this study, 34 Lb. paracasei and 2 Lb. rhamnosus strains were isolated from a semi-hard cheese and characterized for their proteolytic, esterase, and anticlostridial activity. Moreover, the strains were inoculated in a curd-based medium and the volatile compounds in the headspace of samples were evaluated by solid-phase microextraction–GC–MS analysis. Proteolytic activity was present in 30 strains, whereas only one Lb. paracasei strain showed esterase activity. All strains inhibited Cl. sporogenes, Cl. beijerinckii, and Cl. butyricum, and 18 isolates inhibited at least one Cl. tyrobutyricum strain. Principal component analysis and clustering analysis based on the volatilome grouped strains into three groups. One of these groups was characterized by high amounts of acids and esters and clustered with control samples inoculated with commercial starter cultures, suggesting similarity in the aroma profile. Strains belonging to this group with inhibitory effects against Cl. tyrobutyricum might be exploited as autochthonous adjunct cultures for the reduction of late-blowing defects in semi-hard cheeses