Related papers: Description of resonances within the rigged Hilber…
Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…
At the heart of quantum many-body physics lies the understanding of mechanisms that avoid quantum thermalization in an isolated system quenched far from equilibrium. A prominent example is Hilbert space fragmentation, which has recently…
In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values…
We consider a quantum system with a finite number of distinguishable quantum states, which may be partitioned freely by a number of quantum particles, assumed to be maximally entangled. We show that if we partition the system into a number…
We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and…
Even if the motion of a quantum (quasi-)particle proceeds along a left-right-symmetric (PT-symmetric) curved path in complex plane, the spectrum of bound states may remain physical, i.e., real and bounded below). We propose a…
It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown…
We argue that the quantum-theoretical structures studied in several recent lines of research cannot be adequately described within the standard framework of quantum circuits. This is in particular the case whenever the combination of…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…
We consider a 2D quantum spin model with ring-exchange interaction that has subsystem symmetries associated to conserved magnetization along rows and columns of a square lattice, which implies the conservation of the global dipole moment.…
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…
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…
The classical and quantum mechanics of isolated, nonlinear resonances in integrable systems with N>=2 degrees of freedom is discussed in terms of geometry in the space of action variables. Energy surfaces and frequencies are calculated and…
We study the resonant divergences that occur in quantum scattering cross-sections in the presence of a strong external magnetic field. We demonstrate that all such divergences may be eliminated by introducing radiative corrections to the…
The purpose of these lectures is to give an accessible and self contained introduction to quantum scattering theory in one dimension. Part A defines the theoretical playground, and develops basic concepts of scattering theory in the time…
The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed…
Excited hadrons are seen as resonances in the scattering of lighter stable hadrons like $\pi$, $K$ and $\eta$. Many decay into multiple final states necessitating coupled-channel analyses. Recently it has become possible to obtain…
The relationship between the boundaries for Hill and Lagrange stability in orbital element space is modified in the case of resonantly interacting planets. Hill stability requires the ordering of the planets to remain constant while…
In even dimensional Euclidean scattering, the resonances lie on the logarithmic cover of the complex plane. This paper studies resonances for obstacle scattering in ${\mathbb R}^d$ with Dirchlet or admissable Robin boundary conditions, when…