Related papers: Semiclassical matrix elements for a chaotic propag…
The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…
We describe an iterative approach to computing long-time semiclassical dynamics in the presence of chaos, which eliminates the need for summing over an exponentially large number of classical paths, and has good convergence properties even…
Random matrix theory can be used to describe the transport properties of a chaotic quantum dot coupled to leads. In such a description, two approaches have been taken in the literature, considering either the Hamiltonian of the dot or its…
We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex…
We develop a semiclassical approximation for the spectral Wigner and Husimi functions in the neighbourhood of a classically unstable periodic orbit of chaotic two dimensional maps. The prediction of hyperbolic fringes for the Wigner…
We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the…
The semiclassical structure of resonance states of classically chaotic scattering systems with partial escape is investigated. We introduce a local randomization on phase space for the baker map with escape, which separates the smallest…
The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system…
In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…
We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical…
The work distribution is a fundamental quantity in nonequilibrium thermodynamics mainly due to its connection with fluctuations theorems. Here we develop a semiclassical approximation to the work distribution for a quench process in chaotic…
We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across…
The standard semiclassical calculation of transmission correlation functions for chaotic systems is severely influenced by unitarity problems. We show that unitarity alone imposes a set of relationships between cross sections correlation…
A trajectory segment in an energy shell, which combines to form a closed curve with a segment in another canonically driven energy shell, adds an oscillatory semiclassical contribution to the smooth classical background of the quantum…
We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are…
We extend former results for coherent states on the circle in the literature in two ways. On the one hand, we show that expectation values of fractional powers of momentum operators can be computed exactly analytically by means of Kummer's…
Gutzwiller's trace formula has a central place in quantum chaos because it provides semiclassical approximations for quantum energy levels in classically chaotic systems by linking them to classical periodic orbits. In this didactic…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
The statistics of quantum transport through chaotic cavities with two leads is encoded in transport moments $M_m={\rm Tr}[(t^\dag t)^m]$, where $t$ is the transmission matrix, which have a known universal expression for systems without…
We study a chaotic quantum transport in the presence of a weak spin-orbit interaction. Our theory covers the whole symmetry crossover regime between time-reversal invariant systems with and without a spin-orbit interaction. This situation…