Related papers: Wannier basis method for KAM effect in quantum mec…
Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in…
We construct time quasi-periodic vortex patch solutions with one hole for the planar Euler equations. These structures are captured close to any annulus provided that its modulus belongs to a massive Borel set. The proof is based on…
An observer at rest with the expanding universe experiences some extra noise in the quantum vacuum, and so does an accelerated observer in a vacuum at rest (in Minkowski space). The literature mainly focuses on the ideal cases of…
A new variational technique for investigation of the ground state and correlation functions in 1D quantum magnets is proposed. A spin Hamiltonian is reduced to a fermionic representation by the Jordan-Wigner transformation. The ground state…
This article is about the proof of the celebrated KAM theorem as sketched out in \cite{KOL} Kolmogorov's original presentation to the ICM. The proof presented here has been detailed as an effort to clarify if Kolmogorov's argument can be…
We illustrate Heisenberg's method of matrix mechanics using the planar quantum rotor example. We show how to find the spectrum of this simple model without the need to use the eigenstates of the system. This then leads us to speculate on…
In this work, we develop a theoretical description of the collective behavior of interacting dipolar planar rotors by using time independent perturbation theory and a small angle quadratic approximation. The ground state properties for both…
The phase space representation for a q-deformed model of the quantum harmonic oscillator is constructed. We have found explicit expressions for both the Wigner and Husimi distribution functions for the stationary states of the…
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…
We present an investigation into effects exhibited by the two-frequency kicked rotor. Experiments were performed and in addition quantum and classical dynamics were simulated and compared with the experimental results. The experiments…
The work of Kolmogorov, Arnold and Moser appeared just before the renormalization group approach to statistical mechanics was proposed by Wilson: it can be classified as a multiscale approach which also appeared in works on the convergence…
We investigate the possibility of an Anderson type transition in the quantum kicked rotor with a smooth potential due to dynamical localization of the wavefunctions. Our results show the typical characteristics of a critical behavior i.e…
We develop a system consisting of a quantum kicked rotor with an additional degree of freedom. This models a single two-level atom with internal ground and excited states, and it is characterized by its quantum resonances with ballistic…
A kink-based expression for the canonical partition function is developed using Feynman's path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on…
We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization and Anderson transition can be…
This paper is a follow-up of our earlier work [11] where a uniform exponential Anderson localization was proved for a class of deterministic (including quasi-periodic) Hamiltonians with the help of a variant of the KAM…
Rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approach. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the…
Matrix mechanics is developed to describe the bound state spectra in few- and many-electron atoms, ions and molecules. Our method is based on the matrix factorization of many-electron (or many-particle) Coulomb Hamiltonians which are…
This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the…
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…