Related papers: Quantum and Arithmetical Chaos
Quantum chaos is linked to Brownian diffusion of the underlying quantum energy level-spacing sequences. The level-spacings viewed as functions of their order execute random walks which imply uncorrelated random increments of the…
A number of studies have shown that chaos occurs in scattering: the outgoing deflection angle is seen to be an erratic function of the impact parameter. We propose to extend this to quantum field theory, and to use erratic behavior of the…
Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical chaotic Duffing oscillator. The similarities and the differences from the classical oscillator are examined; in…
To treat the spectral statistics of quantum maps and flows that are fully chaotic classically, we use the rigorous Riemann-Siegel lookalike available for the spectral determinant of unitary time evolution operators $F$. Concentrating on…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…
This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic.…
Quantum dots pose a problem where one must confront three obstacles: randomness, interactions and finite size. Yet it is this confluence that allows one to make some theoretical advances by invoking three theoretical tools: Random Matrix…
The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…
We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the…
The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, non-unitary conformal field theories with logarithmic correlations. The nature and the physical…
These lecture notes provide an introduction to quantum cluster methods for strongly correlated systems. Cluster Perturbation Theory (CPT), the Variational Cluster Approximation (VCA) and Cellular Dynamical Mean Field Theory (CDMFT) are…
This paper describes perturbative framework, on the basis of closed-time-path formalism, for studying quasiuniform relativistic quantum field systems near equilibrium and nonequilibrium quasistationary systems. At the first part, starting…
This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point…
We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to…
We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that…
Relaxation in the time correlation between operators is studied. Quantized chaotic systems are shown to have distinct relaxation fluctuations that are universal and can be usefully modelled by Random Matrix Theory. Various quantized maps…
In the framework of the random matrix approach, we apply the theory of Selberg's integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order.…