Search results for "phase space"

Approximating hidden chaotic attractors via parameter switching.

2018

In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …

Heteroclinic contours and self-replicated solitary waves in a reaction–diffusion lattice with complex threshold excitation

2008

Abstract The space–time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. Heteroclinic orbits defining traveling wave front solutions are investigated in a moving frame system. A heteroclinic contour formed by separatrix manifolds of two saddle-foci is found in the phase space. The existence of such structure indicates the appearance of complex wave patterns in the network. Such solutions have been confirmed and analyzed numerically. Complex homoclinic orbits found in the neighborhood of the heteroclinic contour define …

Action-Angle Variables

2001

In the following we will assume that the Hamiltonian does not depend explicitly on time; ∂H/∂t = 0. Then we know that the characteristic function W(q i , P i ) is the generator of a canonical transformation to new constant momenta P i , (all Q i , are ignorable), and the new Hamiltonian depends only on the P i ,: H = K = K(P i ). Besides, the following canonical equations are valid: $$ \dot Q_i = \frac{{\partial K}} {{\partial P_i }} = v_i = const. $$ (1) $$ \dot P_i = \frac{{\partial K}} {{\partial Q_i }} = 0. $$ (2)

Simulating quantum-optical phenomena with optical lattices

2011

Cold atoms trapped in optical lattices have been proved to be very versatile quantum systems in which a large class of many-body condensed-matter Hamiltonians can be simulated [1].

Anharmonicity deformation and curvature in supersymmetric potentials

1994

An algebraic description of the class of 1D supersymmetric shape invariant potentials is investigated in terms of the shape-invariant-potential (SIP) deformed algebra, the generators of which act both on the dynamical variable and on the parameters of the potentials. The phase space geometry associated with SIP's is studied by means of a coherent state (SIP-CS) path integral and the ray metric of the SIP-CS manifold. The anharmonicity of SIP's results in a inhomogeneous phase space manifold with one Killing vector and with a modified symplectic Kahler structure, and it induces a non constant curvature into the generalized phase space. Analogous results from the phase space geometry of someq…

Kinematically corrected correlation functions for inclusive reactions

1972

Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large

2015

The analysis of the stability and numerical simulation of Costas loop circuits for high-frequency signals is a challenging task. The problem lies in the fact that it is necessary to simultaneously observe very fast time scale of the input signals and slow time scale of phase difference between the input signals. To overcome this difficult situation it is possible, following the approach presented in the classical works of Gardner and Viterbi, to construct a mathematical model of Costas loop, in which only slow time change of signal?s phases and frequencies is considered. Such a construction, in turn, requires the computation of phase detector characteristic, depending on the waveforms of th…

Scaling behaviour of non-hyperbolic coupled map lattices

2006

Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order which exhibit strongest possible chaotic behaviour for small coupling constants a. We prove that the expectations of arbitrary observables scale with \sqrt{a} in the low-coupling limit, contrasting the hyperbolic case which is known to scale with a. Moreover we prove that there are log-periodic oscillations of period \log N^2 modulating the \sqrt{a}-dependence of a given expectation value.…

Kinetic transport theory with quantum coherence

2008

We derive transport equations for fermions and bosons in spatially or temporally varying backgrounds with special symmetries, by use of the Schwinger-Keldysh formalism. In a noninteracting theory the coherence information is shown to be encoded in new singular shells for the 2-point function. Imposing this phase space structure to the interacting theory leads to a a self-consistent equation of motion for a physcial density matrix, including coherence and a well defined collision integral. The method is applied e.g. to demonstrate how an initially coherent out-of-equlibrium state approaches equlibrium through decoherence and thermalization.

Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature

2021

This work concerns the theoretical description of the quantum dynamics of molecular junctions with thermal fluctuations and probability losses. To this end, we propose a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. Along the lines discussed in [A. Sergi et al., Symmetry 10 518 (2018)], we adopt the operator-valued Wigner formulation of quantum mechanics (wherein the density matrix depends on the points of the Wigner phase space associated to the system) and derive a non-linear equation of motion. Moreover, we introduce a model for a non-Hermitian quantum single-molecule junction (nHQSMJ). In this model the leads are mapped to a tunneling…