Search results for "Mathematical physics"
showing 10 items of 2687 documents
Generation of Non-Classical States through QND-like Processes
2007
In the spirit of quantum nondemolition measurement we show that repeatedly measuring the atomic state of a trapped ion subjected to suitable vibronic couplings it is possible to extract interesting nonclassical states. The possibility of generating angular momentum Schrödinger cat is demonstrated.
Three-mode two-boson Jaynes–Cummings model in trapped ions
2006
In this paper, we analyse a two-boson three-mode Jaynes–Cummings model which can be implemented in the context of trapped ions. The symmetries of the Hamiltonian are brought to light and analysed in detail in order to solve the eigenvalue problem. The calculation of the time evolution operator shows the possibility of realizing interesting applications, such as the generation of nonclassical states.
(Regular) pseudo-bosons versus bosons
2012
We discuss in which sense the so-called {\em regular pseudo-bosons}, recently introduced by Trifonov and analyzed in some details by the author, are related to ordinary bosons. We repeat the same analysis also for {\em pseudo-bosons}, and we analyze the role played by certain intertwining operators, which may be bounded or not.
Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings
1994
Recently we presented a new technique for numerical simulations of colloidal hard-sphere systems and showed its high efficiency. Here, we extend our calculations to the treatment of both 2- and 3-dimensional monodisperse and 3-dimensional polydisperse systems (with sampled finite Gaussian size distribution of particle radii), focusing on equilibrium pair distribution functions and structure factors as well as volume fractions of random close packing (RCP). The latter were determined using in principle the same technique as Woodcock or Stillinger had used. Results for the monodisperse 3-dimensional system show very good agreement compared to both pair distribution and structure factor predic…
Mond's conjecture for maps between curves
2017
A theorem by D. Mond shows that if f:(C,0)→C2,0 is finite and has has degree one onto its image (Y, 0), then the Ae-codimension is less than or equal to the image Milnor number μI(f), with equality if and only if (Y, 0) is weighted homogeneous. Here we generalize this result to the case of a map germ f:(X,0)→C2,0, where (X, 0) is a plane curve singularity.
From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture
2020
Abstract In this paper we study the joint convexity/concavity of the trace functions Ψ p , q , s ( A , B ) = Tr ( B q 2 K ⁎ A p K B q 2 ) s , p , q , s ∈ R , where A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of ( p , q , s ) ∈ R 3 for Ψ p , q , s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of ( α , z ) for α-z Renyi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψ p…
Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects
2016
We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up $Z'$ along the cubic of the irreducible holomorphic symplectic eightfold $Z$, described by the four authors, is isomorphic to an irreducible component of a moduli space of Gieseker stable torsion sheaves or rank three torsion free sheaves. For a very general such cubic fourfold, we show that $Z$ is isomorphic to a connected component of a moduli space of tilt-stable objects in the derived category and to a moduli space of Bridgeland stable objects in the Kuznetsov component. Moreover, the contraction between $Z'$ and $Z$ i…
TOPOLOGICAL PARTIAL *-ALGEBRAS: BASIC PROPERTIES AND EXAMPLES
1999
Let [Formula: see text] be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space [Formula: see text]. Then [Formula: see text] is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of [Formula: see text]. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of potential topological partial *-algebras, either function spaces (lattices of Lp spaces on [0, 1] or on ℝ, amalgam spaces), or partial *-algebras of operators (operators on a partial inner product space, O*-algebras).
Fibre Bundle for Spin and Charge in General Relativity
2000
The Lorentzian and spin structures of general relativity are shown to allow a natural extension, by means of which the set of possible electromagnetic bundles is linked to the topology and geometry of the underlying causal structure. Further, both the Dirac operator and the electromagnetic potential are obtainable from a single linear connection 1-form.
Exact controllability to trajectories for entropy solutions to scalar conservation laws in several space dimensions
2019
We describe a new method which allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a natural geometric condition.