相关论文: Stability of driven systems with growing gaps, Qua…
We study the dynamics of electrons in crystalline solids in the presence of inhomogeneous external electric and magnetic fields. We present a manifestly gauge-invariant operator-based approach without relying on a semiclassical wavepacket…
A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a…
While electric power grids play a key role in the decarbonization of society, it remains unclear how recent trends, such as the strong integration of renewable energies, can affect their stability. Power oscillation modes, which are key to…
Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the…
We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In…
An otherwise free classical particle moving through an extended spatially homogeneous medium with which it may exchange energy and momentum will undergo a frictional drag force in the direction opposite to its velocity with a magnitude…
The band gap, a key concept in solid-state physics, is traditionally explained by the Bragg diffraction of electron waves in the periodic potential of a crystal. Although widely accepted, this framework raises fundamental issues in…
It is demonstrated that in contrast to the well-known case with a quantum particle moving freely in a real line, the wave packets corresponding to the coherent states for a free quantum particle on a circle do not spread but develop…
In this letter, we provide evidence for a classical sector of states in the Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of states whose the minimum bound of position -momentum uncertainty (equivalent to an…
We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several…
We study the spread of a quantum-mechanical wavepacket in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
An oscillating, compact Friedmann universe with a massive conformally coupled scalar field is studied in the framework of quantum cosmology. The scalar field is treated as a perturbation and we look for solutions of the Wheeler-DeWitt…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…
We investigate the stability of plane wave solutions of equations describing quantum particles interacting with a complex environment. The models take the form of PDE systems with a non local (in space or in space and time) self-consistent…
Some long standing issues concerning the quantum nature of the big bang are resolved in the context of homogeneous isotropic models with a scalar field. Specifically, the known results on the resolution of the big bang singularity in loop…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
We prove various notions of uniform continuity for compact-quantum-group representations on Hilbert or Banach spaces equivalent to having finite spectrum, i.e. finitely many isotypic components. This generalizes the classical analogue for…
We analyze the behavior of a non-Hermitian opened one-dimensional quantum system with $\mathcal{PT}$ symmetry. This system is built by a dimer, with balanced gains and losses described by a parameter $\gamma$. By varying $\gamma$ the system…