Related papers: Multifractality of open quantum systems
We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic…
Eigenstate multifractality, a hallmark of non-interacting disordered metals, which may also be observed in many-body localized states, is characterized by anomalous slow dynamics and appears relevant for many areas of quantum physics, from…
By analyzing a paradigmatic example of the theory of dissipative systems -- the classical and quantum dissipative standard map -- we are able to explain the main features of the decay to the quantum equilibrium state. The classical…
We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wavefunction amplitudes in a real-space basis. For single-particle 'quantum billiards', these real-space amplitudes are known to have Gaussian…
In the theory of open quantum systems, divisibility of the system dynamical maps is related to memory effects in the dynamics. By decomposing the system Hilbert space as a direct sum of several Hilbert spaces, we study the relationship…
Multifractal states offer a "third way" for quantum matter, neither fully localized nor ergodic, exhibiting singular continuous spectra, self-similar wavefunctions, and transport and entanglement scaling exponents intermediate between…
We show that the autocorrelation of quantum spectra of an open chaotic system is well described by the classical Ruelle-Pollicott resonances of the associated chaotic strange repeller. This correspondence is demonstrated utilizing microwave…
We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system…
We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via spectral analysis of the corresponding time dependent…
While quantum multifractality has been widely studied in the physics literature and is by now well understood from the point of view of physics, there is little work on this subject in the mathematical literature. I will report on a proof…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum $p$ direction of the 2-torus phase space, modelling an open chaotic cavity. We study briefly the classical forward…
The distribution function of local amplitudes of eigenstates of a two-dimensional disordered metal is calculated. Although the distribution of comparatively small amplitudes is governed by laws similar to those known from the random matrix…
We experimentally studied evolution of quasi-eigenmodes as classical dynamics undergoing a transition from being regular to chaotic in open quantum billiards. In a deformation-variable microcavity we traced all high-Q cavity modes in a wide…
We investigate different one-dimensional quantum spin-1/2 chain models and by combining analytical and numerical calculations prove that their ground state wave functions in the natural spin basis are multifractals with, in general,…
Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…
We have computed the low energy quantum states and low frequency dynamical susceptibility of complex quantum spin systems in the limit of strong interactions, obtaining exact results for system sizes enormously larger than accessible…
Quantum-classical correspondence for the shape of eigenfunctions, local spectral density of states and occupation number distribution is studied in a chaotic model of two coupled quartic oscillators. In particular, it is shown that both…
Semiclassical methods have been applied very successfully to describe the nontrivial transition from the quantum to the classical regime in $\textit{single}$-particle or at least $\textit{few}$-particle systems. Challenges on the way to an…
In classical systems, chaos is clearly defined via the behavior of trajectories. In quantum systems with a classical analogue one finds that the transition from regular to chaotic dynamics is signified by a change in the spectral…