Search results for "Theorem"

Nearly-integrable dissipative systems and celestial mechanics

2010

The influence of dissipative effects on classical dynamical models of Celestial Mechanics is of basic importance. We introduce the reader to the subject, giving classical examples found in the literature, like the standard map, the Hénon map, the logistic mapping. In the framework of the dissipative standard map, we investigate the existence of periodic orbits as a function of the parameters. We also provide some techniques to compute the breakdown threshold of quasi-periodic attractors. Next, we review a simple model of Celestial Mechanics, known as the spin-orbit problem which is closely linked to the dissipative standard map. In this context we present the conservative and dissipative KA…

Continuous variable quantum teleportation with non-Gaussian resources

2007

We investigate continuous variable quantum teleportation using non-Gaussian states of the radiation field as entangled resources. We compare the performance of different classes of degaussified resources, including two-mode photon-added and two-mode photon-subtracted squeezed states. We then introduce a class of two-mode squeezed Bell-like states with one-parameter dependence for optimization. These states interpolate between and include as subcases different classes of degaussified resources. We show that optimized squeezed Bell-like resources yield a remarkable improvement in the fidelity of teleportation both for coherent and nonclassical input states. The investigation reveals that the …

Comment on "Direct linear term in the equation of state of plasmas"

2015

In a recent paper [Phys. Rev. E 91, 013108 (2015)], Kraeft et al. criticize known exact results on the equation of state of quantum plasmas, which have been obtained independently by several authors. They argue about a difference in the definition of the direct two-body function Q(x), which appears in virial expansions of thermodynamical quantities, but Q(x) is not a measurable quantity in itself. Differences in definitions of intermediate quantities are irrelevant, and only differences in physical quantities are meaningful. Beyond Kraeft et al.'s broad statement that there is no agreement at order ρ(5/2) in the virial equation for the pressure, we show that their published results for this…

Symmetries and Symmetry Groups in Quantum Physics

2013

When one talks about discrete or continuous groups which are to describe symmetries of quantum systems, one must first identify the objects on which the elements of these groups are acting.

Radial conformal motions in Minkowski space–time

1999

A study of radial conformal Killing fields (RCKF) in Minkowski space-time is carried out, which leads to their classification into three disjointed classes. Their integral curves are straight or hyperbolic lines admitting orthogonal surfaces of constant curvature, whose sign is related to the causal character of the field. Otherwise, the kinematic properties of the timelike RCKF are given and their applications in kinematic cosmology is discussed.

Linear response theory: many-body formulation

2013

Fluctuations, response and aging dynamics in a simple glass-forming liquid out of equilibrium

1999

By means of molecular dynamics computer simulations we investigate the out of equilibrium relaxation dynamics of a simple glass former, a binary Lennard-Jones system, after a quench to low temperatures. We study both one time quantities and two-times correlation functions. Two-times correlation functions show a strong time and waiting time $t_w$ dependence. For large $t_w$ and times corresponding to the early $\beta$-relaxation regime the correlators approach the Edwards-Anderson value by means of a power-law in time. at long times $\tau$ the correlation functions can be expressed as $C_{\rm AG}(h(t_w+\tau)/h(t_w))$ and compute the function $h(t)$. This function is found to show a $t$-depen…

Birkhoff's theorem and perturbations in $f(R)$ theories

2012

Invited contribution to Annalen der Physik (Expert Opinion).

Algebraic Quantization, Good Operators and Fractional Quantum Numbers

1995

The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the ``failure" of the Ehrenfest theorem is clarified in terms of the already defined notion of {\it good} (and {\it bad}) operators. The analysis of ``constrained" Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring ``anomal…

The Poisson Bracket Structure of the SL(2, R)/U(1) Gauged WZNW Model with Periodic Boundary Conditions

2000

The gauged SL(2, R)/U(1) Wess-Zumino-Novikov-Witten (WZNW) model is classically an integrable conformal field theory. A second-order differential equation of the Gelfand-Dikii type defines the Poisson bracket structure of the theory. For periodic boundary conditions zero modes imply non-local Poisson brackets which, nevertheless, can be represented by canonical free fields.