相关论文: Multiple-Scale Analysis of Quantum Systems
A reliable and efficient computation of the entire single-particle spectrum of correlated molecules is an outstanding challenge in the field of quantum chemistry, with standard density functional theory approaches often giving an inadequate…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
The main issue of this work consists in extracting one or several finite values for the sum of series involved in perturbation theories. It is supposed to work for all cases in which two physical parameters are involved, and makes thorough…
An emergent theory of quantum measurement arises directly by considering the particular subset of many body wavefunctions that can be associated with classical condensed matter and its interaction with delocalized wavefunctions. This…
Long periodic orbits constitute a serious drawback in Gutzwiller's theory of chaotic systems, and then it would be desirable that other classical invariants, not suffering from the same problem, could be used in the quantization of such…
Quantum systems are dynamic systems restricted by the principles of quantum mechanics (linearity of dynamic equations, linear transformation of the wave function etc.). One suggests to investigate the quantum systems simply as dynamic…
In this paper we introduce a generalization to the algebraic Bender-Wu recursion relation for the eigenvalues and the eigenfunctions of the anharmonic oscillator. We extend this well known formalism to the time-dependent quantum statistical…
The Discrete Nonlinear Schroedinger Equation with a random potential in one dimension is studied as a dynamical system. It is characterized by the length, the strength of the random potential and by the field density that determines the…
Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the…
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…
Resonant solutions of the quantum Schr\"odinger equation occur at complex energies where the S-matrix becomes singular. Knowledge of such resonances is important in the study of the underlying physical system. Often the Schr\"odinger…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
Quantum correlations are key information about the structures and dynamics of quantum many-body systems. There are many types of high-order quantum correlations with different time orderings, but only a few of them are accessible to the…
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
The goal of this manuscript is to provide an introduction to the multi-scale entanglement renormalization ansatz (MERA) and its application to the study of quantum critical systems. Only systems in one spatial dimension are considered. The…
We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrodinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the…
With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…
We investigate multicritical phenomena in O(N)+O(M)-models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To…
We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function,…