We establish a simpliied form of the axisymmetric Fokker-Planck-Landau operator. In doing so, we derive a weak formulation of this operator on which we get directly the conservation properties and the decay of the entropy as it is the case for the three dimensional operator 6]. A symmetrized version of this formulation leads to a class of numerical schemes which satisfy these physical propertie...

We introduce a new quantity, called pseudo-entropy, as generalization of entanglement entropy via postselection. expect this quantity to provide class order parameters in quantum many-body systems. In the anti--de Sitter space (AdS)/conformal field theory (CFT) correspondence, is dual areas minimal area surfaces time-dependent Euclidean spaces which are asymptotically AdS. call geometric comput...

We analyze properties of the quantum conditional amplitude operator @Phys. Rev. Lett. 79, 5194 ~1997!#, which plays a role similar to that of the conditional probability in classical information theory. The spectrum of the conditional operator that characterizes a quantum bipartite system is shown to be invariant under local unitary transformations and reflects its inseparability. More specific...

This paper explores distance measures based on genetic operators for genetic programming using tree structures. The consistency between genetic operators and distance measures is a crucial point for analytical measures of problem difficulty, such as fitness distance correlation, and for measures of population diversity, such as entropy or variance. The contribution of this paper is the explorat...

The gyrokinetic linearized exact Fokker-Planck collision operator is obtained in a form suitable for plasma gyrokinetic equations, for arbitrary mass ratio. The linearized Fokker-Planck operator includes both the test-particle and field-particle contributions, and automatically conserves particles, momentum, and energy, while ensuring non-negative entropy production. Finite gyroradius effects i...

Discerning possible candidates for measuring distances between quantum states is a subject of perennial interest. Many of these measures were first defined as distances between probability distributions and subsequently employed as distance-measures in Hilbert space. Let H be the Hilbert space associated with a quantum system and let S be the set of all states, i.e. the set of self-adjoint, (se...

We consider the linear inverse problem of reconstructing an unknown finite measure μ from a noisy observation of a generalized moment of μ defined as the integral of a continuous and bounded operator Φ with respect to μ. Motivated by various applications, we focus on the case where the operator Φ is unknown; instead, only an approximation Φm to it is available. An approximate maximum entropy so...

A paradigm for describing dynamical systems that have both Hamiltonian and dissipative parts is presented. Features of generalized Hamiltonian systems and metric systems are combined to produce what are called metriplectic systems. The phase space for metriplectic systems is equipped with a bracket operator that has an antisymmetric Poisson bracket part and a symmetric dissipative part. Flows a...

We study the behavior of an open quantum system, with an N-dimensional space of states, whose density matrix evolves according to a nonunitary map defined in two steps: A unitary step, where the system evolves with an evolution operator obtained by quantizing a classically chaotic map (baker's map and Harper's map are the two examples we consider). A nonunitary step where the evolution operator...

The pure quantum entanglement is generalized to the case of mixed compound states on an operator algebra to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized by quantum couplings which are described as transpose-CP, but not Completely Positive (CP), trace-normalized linear positive maps of the algebra. The entangled (total) informa...