## 21 Citations

A chaotic lattice field theory in one dimension

- Physics
- 2022

Motivated by Gutzwiller’s semiclassical quantization, in which unstable periodic orbits of low-dimensional deterministic dynamics serve as a WKB ‘skeleton’ for chaotic quantum mechanics, we construct…

Variational method for finding periodic orbits in a general flow.

- Physics, MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

A variational principle is proposed and implemented for determining unstable periodic orbits of flows as well as unstable spatiotemporally periodic solutions of extended systems by an initial loop approximating a periodic solution by a minimization of local errors along the loop.

The statistical description of irregular eigenfunctions: A semiclassical approach

- Physics
- 2004

We present a novel approach to study the statistical properties of eigenfunctions in quantum systems with chaotic classical counterpart. The method is based on a far reaching generalization of an old…

Many-body symbolic dynamics of a classical oscillator chain

- Physics
- 2002

We study a certain type of the celebrated Fermi-Pasta-Ulam particle chain, namely the inverted FPU model, where the interparticle potential has the form of a quartic double well. Numerical evidence…

Collectivity and Periodic Orbits in a Chain of Interacting, Kicked Spins

- Physics
- 2017

The field of quantum chaos originated in the study of spectral statistics for interacting many-body systems, but this heritage was almost forgotten when single-particle systems moved into the focus.…

An empirical approach to the theory of particle and nuclear phenomena: Review and some new ideas

- Physics
- 2001

Experimental data on masses and lifetimes of unstable particles falls into a pattern, a brief review of some interesting consequences is presented here. From the experience in semiclassical methods…

Strange attractors in dissipative Nambu mechanics: classical and quantum aspects

- Physics
- 2010

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in R3 phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems…

Relative Periodic Solutions of the Complex Ginzburg-Landau Equation

- Mathematics, PhysicsSIAM J. Appl. Dyn. Syst.
- 2005

A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the…

A Dynamical Zeta Function for Pseudo Riemannian Foliations

- Mathematics
- 2008

We investigate a generalization of geodesic random walks to pseudo Riemannian foliations. The main application we have in mind is to consider the logarithm of the associated zeta function as grand…

## References

SHOWING 1-10 OF 41 REFERENCES

Trace Formulas for Stochastic Evolution Operators: Weak Noise Perturbation Theory

- Physics
- 1998

Periodic orbit theory is all effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with…

Spectrum of stochastic evolution operators: local matrix representation approach.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999

The results are perturbative corrections to a stochastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stoChastic and quantum-mechanical applications.

[h-bar] expansion for the periodic-orbit quantization of hyperbolic systems.

- Physics, MathematicsPhysical review. A, Atomic, molecular, and optical physics
- 1993

Using Feynman path integrals and the stationary-phase method, we develop a semiclassical theory for quantum trace formulas in classically hyperbolic systems. In this way, we obtain corrections to the…

Periodic orbit quantization beyond the semiclassical theory.

- PhysicsPhysical review letters
- 1996

A quantum generalization of the semiclassical theory of Gutzwiller leads to systematic orbit-by-orbit inclusion of higher $\ensuremath{\Elzxh}$ contributions to the spectral determinant, and is applied to billiard systems.

Chaos in classical and quantum mechanics

- Physics
- 1990

Contents: Introduction.- The Mechanics of Lagrange.- The Mechanics of Hamilton and Jacobi.- Integrable Systems.- The Three-Body Problem: Moon-Earth-Sun.- Three Methods of Section.- Periodic Orbits.-…

Trace formulae for stochastic evolution operators: smooth conjugation method

- Mathematics
- 1999

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 neighbourhood of a given…

The correlation spectrum for hyperbolic analytic maps

- Mathematics
- 1992

The author introduces a class of analytic hyperbolic maps and prove that the time correlation functions associated with analytic observables have a well-defined spectrum satisfying exponential…

Bohr-Sommerfeld quantization of periodic orbits.

- PhysicsPhysical review letters
- 1996

The information content of the classical action and stability can be used more effectively than in the usual treatment and the improvement of precision is demonstrated on the example of the three disk scattering system.

Confinement of Quarks

- Physics
- 1974

A mechanism for total confinement of quarks, similar to that of Schwinger, is defined which requires the existence of Abelian or non-Abelian gauge fields. It is shown how to quantize a gauge field…