Related papers: Wannier basis method for KAM effect in quantum mec…
The periodically $\delta$-kicked quantum linear rotor is known to experience non-classical bounded energy growth due to quantum dynamical localization in angular momentum space. We study the effect of random deviations of the kick period in…
The quantum dynamics of atoms subjected to pairs of closely-spaced $\delta$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$\delta$-kicked system. We find the unitary…
We present a first-principles scheme that allows the orbital magnetization of a magnetic crystal to be evaluated accurately and efficiently even in the presence of complex Fermi surfaces. Starting from an initial electronic-structure…
In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically…
The phenomenon of Anderson localization, occurring in a disordered medium, significantly influences the dynamics of quantum particles. A fascinating manifestation of this is the "quantum boomerang effect" (QBE), observed when a quantum…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
For a large class of physically relevant operators on a manifold with discrete group action, we prove general results on the (non-)existence of a basis of smooth well-localised Wannier functions for their spectral subspaces. This turns out…
The atomic Quantum Kicked Rotor is an outstanding "quantum simulator" for the exploration of transport in disordered quantum systems. Here we study experimentally the phase-shifted quantum kicked rotor, which we show to display properties…
In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
We propose a method for calculating Wannier functions of periodic solids directly from a modified variational principle for the energy, subject to the requirement that the Wannier functions are orthogonal to all their translations…
We describe a method to calculate the electronic properties of an insulator under an applied electric field. It is based on the minimization of an electric enthalpy functional with respect to the orbitals, which behave as Wannier functions…
In this paper we consider nonlinear Schrodinger systems with periodic boundary condition in high dimension. We establish an abstract infinite dimensional KAM theorem and apply it to the nonlinear Schrodinger equation systems with real…
The three-nucleon ground state and the N--d scattering states are obtained using variational principles. The wave function of the system is decomposed into angular-spin-isospin channels and the corresponding two dimensional spatial…
We present a computational scheme to study spin excitations in magnetic materials from first principles. The central quantity is the transverse spin susceptibility, from which the complete excitation spectrum, including single-particle…
The essentials of quantum theory, the Schr\"odinger equation and the Planck constant, are derived using classical statistical mechanics within the non-local Machan model. The appearance of complex wave function is connected with the…
The Kolmogorov-Arnold network (KAN) is a regression model that is based on a representation of an arbitrary continuous multivariate function by a composition of functions of a single variable. Experimentally-obtained datasets for regression…
The new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner representation of quantum statistical mechanics has been developed.…
In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of…