Related papers: Random Partitions and the Quantum Benjamin-Ono Hie…
A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight…
The probability operator is derived from first principles for an equilibrium quantum system. It is also shown that the superposition states collapse into a mixture of states giving the conventional von Neumann trace form for the quantum…
In this thesis, we investigate the asymptotics of random partitions chosen according to probability measures coming from the representation theory of the symmetric groups $S_n$ and of the finite Chevalley groups $GL(n,F_q)$ and…
Phase-space versions of quantum mechanics -- from Wigner's original distribution to modern discrete-qudit constructions -- represent some states with negative quasi-probabilities. Conventional Shannon and R\'enyi entropies become…
We introduce $k$-local quasi-quantum states: a superset of the regular quantum states, defined by relaxing the positivity constraint. We show that a $k$-local quasi-quantum state on $n$ qubits can be 1-1 mapped to a distribution of…
The electronic density \rho(r) in atoms, molecules and solids is, in general, a distribution that can be observed experimentally, containing spatial information projected from the total wave function. These density distributions can be…
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single site potential is slow. The leading…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
One-particle energy eigenfunctions are used to obtain quantum averages in many particle systems. These are based on the effective local field due to fixed neighbors in classical phase space, while the averages account for the…
Studies of random organization models of monodisperse spherical particles have shown that a hyperuniform state is achievable when the system goes through an absorbing phase transition to a critical state. Here we investigate to what extent…
In a recent Letter [Phys. Rev. Lett. 125, 180604 (2020)], we introduced a closed-form analytic expression for the average bipartite von Neumann entanglement entropy of many-body eigenstates of random quadratic Hamiltonians. Namely, of…
We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium.…
We study non-equilibrium dynamics of integrable and non-integrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate $r$, that project the system to its initial state. We…
We derive the form of the Belavkin-Kushner-Stratonovich equation describing the filtering of a continuous observed quantum system via non-demolition measurements when the statistics of the input field used for the indirect measurement are…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…
The correspondence principle states that the quantum system will approach to the classical system in high quantum numbers. Indeed, the average of the probability density distribution reflects a classical-like distribution. However, the…
We analyze the so-called classical limit of the quantum-mechanical canonical partition function. In order to do that, we define accurately the density matrix for symmetrized and antisymmetrized wave functions only (Bose-Einstein and…
The Fisher-Shannon statistical measure of complexity is analyzed for a continuous manifold of quantum observables. It is probed then than calculating it only in the configuration and momentum spaces will not give a complete description for…
I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the…