相关论文: Multiple-Scale Analysis of Quantum Systems
Accurate solution of the many-electron problem including correlations remains intractable except for few-electron systems. Describing interacting electrons as a superposition of independent electron configurations results in an apparent…
For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
Classical and quantum annealing is discussed for a kinetically constrained chain of $N$ non-interacting asymmetric double wells, represented by Ising spins in a longitudinal field $h$. It is shown that in certain cases, where the kinetic…
With an underlying common theme of competing length scales, we study the many-body Schr\"{o}dinger equation in a quasiperiodic potential and discuss its connection with the Kolmogorov-Arnold-Moser (KAM) problem of classical mechanics. We…
The theory of large deviations is already the natural language for the statistical physics of equilibrium and non-equilibrium. In the field of disordered systems, the analysis via large deviations is even more useful to describe within a…
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…
Two categories of results regarding quantum measurements are derived in this work and applied to the problem of collapse. The first category is concerned with local and transient features of the entanglement between a macroscopic measuring…
Quantum computers use quantum resources to carry out computational tasks and may outperform classical computers in solving certain computational problems. Special-purpose quantum computers such as quantum annealers employ quantum adiabatic…
We derive rigorously the non-linear macroscopic system associated to a microscopic system of coupled quintic Schr\"odinger equations in the framework of discrete wave turbulence under a particular scaling law that describes the limiting…
Recently developed strong-coupling theory open up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum…
We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the…
Amorphous solids, i.e., systems which feature well-defined short-range properties but lack long-range order, constitute an important research topic in condensed matter. While their microscopic structure is known to differ from their…
The Helmholtz equation is a prototypical model for time-harmonic wave propagation. Numerical solutions become increasingly challenging as the wave number $k$ grows, due to the equation's elliptic yet noncoercive character and the highly…
The Schr\"odinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schr\"odinger equation leads to a coupled linear system, whereby…