Related papers: Wegner-type bounds for a two-particle Anderson mod…
The main ideas behind a research plan to use the Wigner formulation as a bridge between classical and quantum probabilistic algorithms are presented, focusing on a particular case: the Quantum analog of Stochastic Gradient Descent in its…
Following [7,8], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with infinite-range interactions and arbitrary…
Anderson-Witting model is a relaxational model equation of the relativistic Boltzmann equation, which sees a wide application in physics. In this paper, we study the existence of classical solutions and its asymptotic behavior when the…
We investigate a Hamiltonian lattice version of the two-dimensional Wess-Zumino model by Quantum Monte Carlo simulations. In order to study the pattern of supersymmetry breaking, we measure the ground state energy and the correlation length…
The effect of random shooting of particles is considered on the basis of solution of the Schrodinger equation and in terms of the Wigner function. Two-particles description shows, in particular, that initial correlation leads to high…
We study quantum field theories with boundary by utilizing non-invertible symmetries. We consider three kinds of boundary conditions of the four dimensional $\mathbb{Z}_2$ lattice gauge theory at the critical point as examples. The weights…
In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by…
We propose a realization of a synthetic Random Flux Model in a two-dimensional optical lattice. Starting from Bose-Hubbard Hamiltonian for two atom species we show how to use fast-periodic modulation of the system parameters to construct…
We extend methods of Ding and Smart from their breakthrough paper in 2020 which showed Anderson localization for certain random Schr\"odinger operators on $\ell^2(\mathbb{Z}^2)$ via a quantitative unique continuation principle and Wegner…
We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…
In the present article, we discuss the role played by the interaction in the Anderson localization problem, for a system of interacting fermions in a one-dimensional disordered lattice, described by the Fermi Hubbard Hamiltonian, in…
Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
A new type of kinetic models with non-instantaneous binary collisions is considered. Collisions are described by a transport process in the joint state space of a pair of particles. The interactions are of alignment type, where the states…
The Wigner function of a dynamical infinite dimensional lattice is studied. A closed differential equation without diffusion terms for this function is obtained and solved. We map atom-photon interaction systems, such as the Jaynes-Cummings…
In the case of compact quantum graphs, many-particle models with singular two-particle interactions where introduced in [arXiv:1207.5648, arXiv:1112.4751] to provide a paradigm for further studies on many-particle quantum chaos. In this…
We present a complete derivation of two-particle states of the one-dimensional extended Hubbard model involving attractive or repulsive on-site and nearest-neighbour interactions. We find that this system possesses scattering resonances and…
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…
We investigate the entanglement for a model of a particle moving in the lattice (many-body system). The interaction between the particle and the lattice is modelled using Hooke's law. The Feynman path integral approach is applied to compute…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…