Related papers: A quantum pseudo-integrable Hamiltonian impact sys…
We discuss the localization of wavefunctions along planes containing the shortest periodic orbits in a three-dimensional billiard system with axial symmetry. This model mimicks the self-consistent mean field of a heavy nucleus at…
We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…
We present a uniform framework for the treatment of a large class of toy models of quantum theory. Specifically, we will be interested in theories of wavefunctions valued in commutative involutive semirings, and which give rise to some…
We investigate decoherence in the limit where the interaction with the environment is weak and the evolution is dominated by the self Hamiltonian of the system. We show that in this case quantized eigenstates of energy emerge as pointer…
In this work we present the results of a numerical and semiclassical analysis of high lying states in a Hamiltonian system, whose classical mechanics is of a generic, mixed type, where the energy surface is split into regions of regular and…
We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded…
A local, deterministic toy model for quantum mechanics is introduced and discussed. It is demonstrated that, when averaged over the hidden variables, the model produces the same predictions as quantum mechanics. In the model considered…
A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher $\hbar$ contributions to the spectral determinant. We apply the theory to billiard…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling…
We investigate two-dimensional canonical systems $y'=zJHy$ on an interval, with positive semi-definite Hamiltonian $H$, such that limit circle case prevails at the left endpoint and limit point case at the right . Let $q_H$ be the Weyl…
In this thesis, we investigate quantum ergodicity for two classes of Hamiltonian systems satisfying intermediate dynamical hypotheses between the well understood extremes of ergodic flow and quantum completely integrable flow. These two…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
An impossibility theorem on approximately simulating quantum non-integrable Hamiltonian systems is presented here. This result shows that there is a trade-off between the unitary property and the energy expectation conservation law in…
In quantum/classical (QM/CM) partitioning methods for multi-scale modeling, one is often forced to introduce uncontrolled phenomenological effects of the environment (CM) in the quantum (QM) domain as ab initio quantum calculations are…
The statistics of energy levels of a rectangular billiard, that is perturbed by a strong localized potential, are studied analytically and numerically, when this perturbation is at the center or at a typical position. Different results are…
The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy.…
Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this…
We derive a semi-classical nonequilibrium work identity by applying the Wigner-Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us, to the leading order in $\hbar$, to overcome the problem of…