Related papers: Hilbert-space geometry of random-matrix eigenstate…
We consider the geometry of quantum states associated with different classes of random matrix Hamiltonians, in particular ensembles that show integrability to chaotic transition in terms of the nearest neighbour energy level spacing…
We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini-Study metric of the projective Hilbert space of a multi-qubit quantum system, endowing it with a Riemannian metric…
We develop a unified quantum geometric framework to understand reactive quantum dynamics. The critical roles of the quantum geometry of adiabatic electronic states in both adiabatic and non-adiabatic quantum dynamics are unveiled. A…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical…
The space of quantum states can be endowed with a metric structure using the second order derivatives of the relative entropy, giving rise to the so-called Kubo-Mori-Bogoliubov inner product. We explore its geometric properties on the…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
Insomuch as statistical mechanics circumvents the formidable task of addressing many-body dynamics, it remains a challenge to derive macroscopic properties from a solution to Hamiltonian equations for microscopic motion of an isolated…
Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the…
Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring a…
We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types…
We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is driven by a purely combinatorial version of Ricci…
A quantum statistical system with energy dissipation is studied. Its statisitics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble. The eigenenergies are shown to form stable structure in…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
By the example of a Fourier transform, the possibilities of Hilbert space geometry applications for statistical model construction are analyzed. In accordance with Bohr's complementarity principle, mutually-complementary coordinate and…
We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points in the complex plane. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum…