Related papers: Symmetry deduction from spectral fluctuations in c…
In order to study the resonance spectra of chaotic cavities subject to some damping (which can be due to absorption or partial reflection at the boundaries), we use a model of damped quantum maps. In the high-frequency limit, the…
Quantum groups have a long and fruitful history of applications in integrable systems. Can quantum group symmetries exist in the absence of integrability? We provide an explicit example of a system with quantum group global symmetry which…
We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…
Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the…
Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry…
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide…
Any quantum system interacting with a complex environment undergoes decoherence. Empty space is filled with vacuum energy due to matter fields in their ground state and represents an underlying environment that any quantum particle has to…
Quantum mechanical systems with some degree of complexity due to multiple scattering behave as if their Hamiltonians were random matrices. Such behavior, while originally surmised for the interacting many-body system of highly excited…
We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
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…
Decoherence of a quantum system induced by the interaction with its environment (measuring medium) may be presented phenomenologically as a continuous (or repeated) fuzzy quantum measurement. The dynamics of the system subject to continuous…
Recent developments in many-body quantum chaos have raised the issue of correlations between different families of levels in the spectra of random fermionic systems. It seems that rotational invariance is sufficient to force an otherwise…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
Measurement choices in weakly-measured open quantum systems can affect quantum trajectory chaos. We consider this scenario semi-classically and show that measurement acts as nonlinear generalized fluctuation and dissipation forces. These…
Symmetries are ubiquitous in physics and play a pivotal role in light-matter interactions, where they determine the selection rules governing allowed atomic transitions and define the associated conserved quantities. For the up-conversion…
The power law $1/f^{\alpha}$ in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of…
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…
The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that when $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics are not changed by the…