Search results for "Names"
showing 10 items of 6843 documents
Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence
2014
In this paper, we use a non-equilibrium thermodynamic framework to generalize a previous nonlocal model of counterflow superfluid turbulence to incorporate some new coupled terms which may be relevant in the evolution of inhomogeneous vortex tangles. The theory chooses as fundamental fields the energy density, the heat flux, and the averaged vortex line length per unit volume. The constitutive quantities are assumed to depend on the fundamental fields and on their first spatial derivatives, allowing us to describe thermal dissipation, vortex diffusion and a new contribution to vortex formation. The restrictions on the constitutive relations are deduced from the entropy principle, using the …
Efficient Simulation of Multivariate Binomial and Poisson Distributions
1998
Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the mult…
Erratum to “Simulation of BSDEs with jumps by Wiener Chaos expansion” [Stochastic Process. Appl. 126 (2016) 2123–2162]
2017
Abstract We correct Proposition 2.9 from “Simulation of BSDEs with jumps by Wiener Chaos expansion” published in Stochastic Processes and their Applications, 126 (2016) 2123–2162. The proposition which provides an expression for the expectation of products of multiple integrals (w.r.t. Brownian motion and compensated Poisson process) requires a stronger integrability assumption on the kernels than previously stated. This does not affect the remaining results of the article.
Non-self-adjoint Hamiltonians with complex eigenvalues
2016
Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In particular, we consider the functional structure related to systems living in finite-dimensional Hilbert spaces, and we show that certain intertwining relations can be deduced also in this case if we introduce suitable antilinear operators. We also analyze a simple model, computing the transition probabilities in the broken and in the unbroken regime.
Explicit near-symplectic mappings of Hamiltonian systems with Lie-generating functions
2008
The construction of explicit near-symplectic mappings for generic Hamiltonian systems with the utilization of Lie transforms is presented. The method is mathematically rigorous and systematically extended to high order with respect to a perturbation parameter. The explicit mappings are compared to their implicit counterparts, which use mixed-variable generating functions, in terms of conservation of invariant quantities, calculation speed and accurate construction of Poincare surfaces of sections. The comparative study considers a wide range of parameters and initial conditions for which different time scales are involved due to large differences between internal and external frequencies of…
Gibbs states defined by biorthogonal sequences
2016
Motivated by the growing interest on PT-quantum mechanics, in this paper we discuss some facts on generalized Gibbs states and on their related KMS-like conditions. To achieve this, we first consider some useful connections between similar (Hamiltonian) operators and we propose some extended version of the Heisenberg algebraic dynamics, deducing some of their properties, useful for our purposes.
Partial inner product spaces, metric operators and generalized hermiticity
2013
Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is, the simplest case of a partial inner product space (PIP space). Next, we introduce several generalizations of the notion of similarity between operators and explore to what extend they preserve spectral properties. Then we apply some of the previous results to operators on a particular PIP space, namely, a scale of Hilbert spaces generated by a metric operator. Finally, we reformulate the notion of pseudo-hermitian operators in the preceding formalism.
Hamiltonians defined by biorthogonal sets
2017
In some recent papers, the studies on biorthogonal Riesz bases has found a renewed motivation because of their connection with pseudo-hermitian Quantum Mechanics, which deals with physical systems described by Hamiltonians which are not self-adjoint but still may have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed is some previous papers. However, in many physical models, one has to deal not with o.n. bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of $\mat…
Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes
2000
A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space $\eufrak{h}$ and it is shown that they satisfy similar properties as the derivation and divergence operator on the Wiener space over $\eufrak{h}$. The derivation operator is then used to give sufficient conditions for the existence of smooth Wigner densities for pairs of operators satisfying the canonical commutation relations. For $\eufrak{h}=L^2(\mathbb{R}_+)$, the divergence operator is shown to coincide with the Hudson-Parthasarathy quantum stochastic integral for adapted integrable processes and with the non-causal…
Unitary Representations of Quantum Superpositions of two Coherent States and beyond
2013
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad hoc introduced set of hermitian operators, leads to the definition of new basis in the oscillator Hilbert space, extending in a natural way the displaced Fock states basis. The potential development of our method and our results are briefly outlined.