107 citations · 814 across the 36 of their papers we have counts for
12 papers · 1 filter
Periodic orbit sum rules for billiards: Accelerating cycle expansions
Sune F. Nielsen, Per Dahlqvist, Predrag Cvitanovic
We show that the periodic orbit sums for 2-dimensional billiards satisfy an infinity of exact sum rules. We test such sum rules and demonstrate that they can be used to accelerate…
Trace formulas for stochastic evolution operators: Smooth conjugation method
Predrag Cvitanovic, C. P. Dettmann, Ronnie Mainieri +1
The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neigh…
Trace formulas for stochastic evolution operators: Weak noise perturbation theory
Predrag Cvitanovic', C. P. Dettmann, Ronnie Mainieri +1
Periodic orbit theory is an effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to…
Beyond the periodic orbit theory
Predrag Cvitanovic, Kim Hansen, Juri Rolf +1
The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum…
Cycle expansions for intermittent diffusion
Carl Dettmann, Predrag Cvitanovic'
We investigate intermittent diffusion using cycle expansions, and show that a truncation based on cycle stability achieves reasonable convergence.
Quantum Fluids and Classical Determinants
Predrag Cvitanovic, Gabor Vattay, Andreas Wirzba
A "quasiclassical" approximation to the quantum spectrum of the Schroedinger equation is obtained from the trace of a quasiclassical evolution operator for the "hydrodynamical" ver…
Symbolic Dynamics and Markov Partitions for the Stadium Billiard
Kai T. Hansen, Predrag Cvitanovic
We investigate the Bunimovich stadium dynamics and find that in the limit of infinitely long stadium the symbolic dynamics is a subshift of finite type. For a stadium of finite len…
Transport Properties of the Lorentz Gas in Terms of Periodic Orbits
P. Cvitanović, J. -P. Eckmann, P. Gaspard
We establish a formula relating global diffusion in a space periodic dynamical system to cycles in the elementary cell which tiles the space under translations.
A Fredholm Determinant for Semi-classical Quantization
Predrag Cvitanović, Per E. Rosenqvist, Gábor Vattay +1
We investigate a new type of approximation to quantum determinants, the ``\qFd", and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larg…
Advection of vector fields by chaotic flows
N. J. BALMFORTH, P. CVITANOVIC, G. R. IERLEY +2
We have introduced a new transfer operator for chaotic flows whose leading eigenvalue yields the dynamo rate of the fast kinematic dynamo and applied cycle expansion of the Fredhol…
A New Determinant for Quantum Chaos
Predrag Cvitanović, Per E. Rosenqvist
We propose a new type of approximation to quantum determinants, ``quantum Fredholm determinant", and conjecture that, compared to the quantum Selberg zeta functions derived from Gu…
Symmetry Decomposition of Chaotic Dynamics
Predrag Cvitanović, Bruno Eckhardt
Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. Th…