Related papers: Random Matrix Ensembles For Many-Body Quantum Syst…
The model of Fermi particles with random two-body interaction is investigated. This model allows to study the origin and accuracy of statistical laws in few-body systems, the role of interaction and chaos in thermalization, Fermi-Dirac…
The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations, relevant to condensed matter physics,…
This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles. The idea of the random batch method is to replace the total interaction of each particle with the $N-1$ other particles by…
We derive a quantum master equation which describes the dynamics of the ensemble-averaged state of homogeneous disorder models at short times, and mediates a transition from coherent superpositions into classical mixtures. While each single…
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…
We study the dynamics of the entanglement between two qubits coupled to a common chaotic environment, described by the quantum kicked rotator model. We show that the kicked rotator, which is a single-particle deterministic dynamical system,…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from $O(N^2)$ per time step to…
We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…
Embedded random matrix ensembles with $k$-body interactions are well established to be appropriate for many quantum systems. For these ensemble the two point correlation function is not yet derived though these ensembles are introduced 50…
There is significant interest in exploring novel phenomena in quantum light-matter interfaces, which are driven by the combination of structured dissipation and long-range interactions that are typical in such systems. To this end, it is…
Integrable differential identities, together with ensemble-specific initial conditions, provide an effective approach for the characterisation of relevant observables and state functions in random matrix theory. We develop this approach for…
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of…
In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…
One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application…
Understanding the non-equilibrium dynamics of extended quantum systems after the trigger of a sudden, global perturbation (quench) represents a daunting challenge, especially in the presence of interactions. The main difficulties stem from…
An "almost diagonal" reduced density matrix (in coordinate representation) is usually a result of environment induced decoherence and is considered the sign of classical behavior. We point out that the proton of a ground state hydrogen atom…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to…