Double bracket dissipation in kinetic theory for particles with anisotropic interactions

We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double bracket approach (Double Bracket Vlasov, or DBV). The moments of the DBV equation lead to a nonlocal form of Darcy's law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double bracket kinetic equations is expressed as Lie-Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density--orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.Comment: 19 pages; no figures. Submitted to Proc. Roy. Soc.

Inverse moment problem for elementary co-adjoint orbits

We give a solution to the inverse moment problem for a certain class of Hessenberg and symmetric matrices related to integrable lattices of Toda type.Comment: 13 page

Gradual efficiency improvement through a sequence of targets

The goal in efficiency analysis is not only to evaluate a decision-making unit (DMU) performance, but also to find an efficient target which provides information on inputs reduction and outputs increment values that are necessary to remove inefficiencies for each inefficient DMU. In data envelopment analysis (DEA), the target unit is located on the efficient frontier and possibly far from the unit under assessment. Therefore, in practice performance improvement seems to be disappointing or even impossible to achieve in only one step for some inefficient DMUs. In this regard, finding intermediate targets is of great importance in benchmarking literature. In this article, we find a sequence of targets instead of a single target for each inefficient unit. In our method, the intermediate target at each step has three properties: (I) the intermediate targets and the unit under evaluation are all similar in size; (II) efficiency scores are ascending through the sequence of targets; (III) the target unit at each step is close to the special part of the efficient frontier as much as possible. These properties lead to finding a target that is more achievable in real applications

Random Hamiltonian in thermal equilibrium

A framework for the investigation of disordered quantum systems in thermal equilibrium is proposed. The approach is based on a dynamical model--which consists of a combination of a double-bracket gradient flow and a uniform Brownian fluctuation--that `equilibrates' the Hamiltonian into a canonical distribution. The resulting equilibrium state is used to calculate quenched and annealed averages of quantum observables.Comment: 8 pages, 4 figures. To appear in DICE 2008 conference proceeding

The importance of personally relevant knowledge for pandemic risk prevention behavior: A multimethod analysis and two-country validation

Copyright © 2021 The Author(s). Pandemics threaten world stability; however, spread is mitigated with prevention behaviors. We introduce “personally relevant knowledge” to explain the knowledge–behavior gap (i.e., objective and subjective knowledge on information acquisition and behavioral change). Hypotheses are derived from prior knowledge literature, economic psychology, and relevance theory. Multimethod analysis (survey data, partial least squares structural equation path modeling [PLS-SEM], and an asymmetric information theoretic statistical analysis) is applied to H1N1 data from the USA and Australia. Personally relevant knowledge is an important addition to prior knowledge conceptualizations, and information theory uncovers asymmetric variable relationships concerning the knowledge–behavior gap, not captured by PLS-SEM.Center for Risk Management and Insurance Research, University of Texas at Austin

Knee joint neuromuscular activation performance during muscle damage and superimposed fatigue

This study examined the concurrent effects of exercise-induced muscle damage and superimposed acute fatigue on the neuromuscular activation performance of the knee flexors of nine males (age: 26.7 ± 6.1yrs; height 1.81 ± 0.05m; body mass 81.2 ± 11.7kg [mean ± SD]). Measures were obtained during three experimental conditions: (i) FAT-EEVID, involving acute fatiguing exercise performed on each assessment occasion plus a single episode of eccentric exercise performed on the first occasion and after the fatigue trial; (ii) FAT, involving the fatiguing exercise only and; (iii) CON consisting of no exercise. Assessments were performed prior to (pre) and at lh, 24h, 48h, 72h, and 168h relative to the eccentric exercise. Repeated-measures ANOVAs showed that muscle damage within the FAT-EEVID condition elicited reductions of up to 38%, 24%) and 65%> in volitional peak force, electromechanical delay and rate of force development compared to baseline and controls, respectively (F[io, 80] = 2.3 to 4.6; p to 30.7%>) following acute fatigue (Fp; i6] = 4.3 to 9.1; p ; Fp, iq = 3.9; p <0.05). The safeguarding of evoked muscle activation capability despite compromised volitional performance might reveal aspects of capabilities for emergency and protective responses during episodes of fatigue and antecedent muscle damaging exercise

Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde

A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom

Empirical Determination of Bang-Bang Operations

Strong and fast "bang-bang" (BB) pulses have been recently proposed as a means for reducing decoherence in a quantum system. So far theoretical analysis of the BB technique relied on model Hamiltonians. Here we introduce a method for empirically determining the set of required BB pulses, that relies on quantum process tomography. In this manner an experimenter may tailor his or her BB pulses to the quantum system at hand, without having to assume a model Hamiltonian.Comment: 14 pages, 2 eps figures, ReVTeX4 two-colum

NMR Techniques for Quantum Control and Computation

Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to a new level, motivated by the interest in quantum information processing. NMR has been the workhorse for the experimental implementation of quantum protocols, allowing exquisite control of systems up to seven qubits in size. Here, we survey and summarize a broad variety of pulse control and tomographic techniques which have been developed for and used in NMR quantum computation. Many of these will be useful in other quantum systems now being considered for implementation of quantum information processing tasks.Comment: 33 pages, accepted for publication in Rev. Mod. Phys., added subsection on T_{1,\rho} (V.A.6) and on time-optimal pulse sequences (III.A.6), redid some figures, made many small changes, expanded reference