Search results for "phase space"
showing 10 items of 176 documents
Coulomb-interacting billiards in circular cavities
2013
We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a more …
Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space
2005
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally to Boltzmann-Gibbs standard thermostatistics while, in the latter, Tsallis thermostatistics is straightforwardly obtained as the most appropriate formalism. We first focus on the microcanonical ensemble stressing the importance of the limit $t \to \infty$ on the form of the microcanonical measure. Interestingly, this approach leads to interpret the entropic index $q$ as the box-counting dimension of the (microcanonical) phase space when fractality is considered.
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.
Standard forms and entanglement engineering of multimode Gaussian states under local operations
2007
We investigate the action of local unitary operations on multimode (pure or mixed) Gaussian states and single out the minimal number of locally invariant parametres which completely characterise the covariance matrix of such states. For pure Gaussian states, central resources for continuous-variable quantum information, we investigate separately the parametre reduction due to the additional constraint of global purity, and the one following by the local-unitary freedom. Counting arguments and insights from the phase-space Schmidt decomposition and in general from the framework of symplectic analysis, accompany our description of the standard form of pure n-mode Gaussian states. In particula…
Digit replacement: A generic map for nonlinear dynamical systems
2016
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attracto…
Diffusive neural network
2002
Abstract A non-connectionist model of a neuronal network based on passive diffusion of neurotransmitters is presented as an alternative to hard-wired artificial neural networks. Classic thermodynamical approach shows that the diffusive network is capable of exhibiting asymptotic stability and a dynamics resembling that of a chaotic system. Basic computational capabilities of the net are discussed based on the equivalence with a Turing machine. The model offers a way to represent mass-sustained brain functions in terms of recurrent behaviors in the phase space.
Analysis of an Experimental Model of In Vitro Cardiac Tissue Using Phase Space Reconstruction
2014
International audience; The in vitro cultures of cardiac cells represent valuable models to study the mechanism of the arrhythmias at the cellular level. But the dynamics of these experimental models cannot be characterized precisely, as they include a lot of parameters that depend on experimental conditions. This paper is devoted to the investigation of the dynamics of an in vitro model using a phase space reconstruction. Our model, based on the heart cells of new born rats, generates electrical field potentials acquired using a microelectrode technology, which are analyzed in normal and under external stimulation conditions. Phase space reconstructions of electrical field potential signal…
Molecular alignment echoes probe collision-induced rotational-speed changes
2020
International audience; We show that the decays with pressure of the rotational alignment echoes induced in N 2 O-He gas mixtures by two ultrashort laser pulses with various delays show detailed information about collision-induced changes of the rotational speed of the molecules. Measurements and classical calculations consistently demonstrate that collisions reduce the echo amplitude all the more efficiently when the echo appears late. We quantitatively explain this behavior by the filamentation of the classical rotational phase space induced by the first pulse and the narrowing of the filaments with time. The above mentioned variation of the echo decay then reflects the ability of collisi…
Hybrid optical-digital method for local-displacement analysis by use of a phase-space representation.
2010
A method for evaluating the local deformation or displacement of an object in speckle metrology is described. The local displacements of the object in one direction are digitally coded in a one-dimensional specklegram. By optically performing the local spectrum of this pattern, one simultaneously achieves information about the local displacement and its spatial position. The good performance of this technique is demonstrated with computer-generated test signals.
Biomolecular-solvent stereodynamic coupling probed by deuteration.
1983
Thermodynamic interpretation of experiments with isotopically perturbed solvent supports the view that solvent stereodynamics is directly relevant to thermodynamic stability of biomolecules. According with the current understanding of the structure of the aqueous solvent, in any stereodynamic configuration of the latter, connectivity pathways are identifiable for their topologic and order properties. Perturbing the solvent by isotopic substitution or, e.g., by addition of co-solvents, can therefore be viewed as reinforcing or otherwise perturbing these topologic structures. This microscopic model readily visualizes thermodynamic interpretation. In conclusion, the topologic stereodynamic str…