Related papers: A quantum pseudo-integrable Hamiltonian impact sys…

Exact results are derived on the averaged dynamics of a class of random quantum-dynamical systems in continuous space. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is…

We study the energy distribution in the extended resonant level model at equilibrium. Previous investigations [Phys. Rev. B {\bf 89}, 161306 (2014), Phys. Rev. B {\bf 93}, 115318 (2016)] have found, for a resonant electronic level…

Previous experimental realizations of Dicke model in atomic or ionic systems are based on global observables assuming uniform spin-boson coupling, while inevitable experimental nonuniformity on the one hand requires site-resolved…

Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of…

We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their…

A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…

We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…

The Weyl-Wigner formulation of quantum confined systems poses several interesting problems. The energy stargenvalue equation, as well as the dynamical equation does not display the expected solutions. In this paper we review some previous…

The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems…

We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the…

A local and distributive algorithm is proposed to find an optimal trial wave-function minimizing the Hamiltonian expectation in a quantum system. To this end, the quantum state of the system is connected to the Gibbs state of a classical…

In this thesis, the quantum Hamilton Jacobi (QHJ) formalism is used to study various exactly solvable (ES) and quasi -exactly solvable (QES) models. Using this method, we obtain the bound state eigenvalues and the eigenfunctions for the…

The electromagnetic characteristics of bilayer quantum Hall systems in the presence of interlayer coherence and tunneling are studied by means of a pseudospin-texture effective theory and an algebraic framework of the single-mode…

It is known that ab initio molecular dynamics based on the electron ground state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temperature is low compared to the first electron eigenvalue gap.…

A quantum statistical random system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble of random matrices. The eigenenergies of…

Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…

The characterization of quantum correlations is crucial to the development of new quantum technologies and to understand how dramatically quantum theory departs from classical physics. Here we systematically study single- and multiparticle…

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical…

Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and…

The fractional quantum Hall effect is a well-known demonstration of strongly correlated topological phases in two dimensions. However, the extension of this phenomenon into a three-dimensional context has yet to be achieved. Recently, the…