Related papers: Weyl's problem: A computational approach
The van der Waals (VDW) equation of state is a simple and popular model to describe the pressure function in equilibrium systems of particles with both repulsive and attractive interactions. This equation predicts an existence of a…
The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the…
The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatible with the constraint…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two…
Weyl functions conveniently describe the evolution of wave coherences in periodic or quadratic potentials. In this work we use Weyl functions to study the ``Talbot-Lau effect'' in a time-domain matter-wave interferometer. A ``displacement…
An algebraic treatment of shape-invariant potentials is discussed. By introducing an operator which reparametrizes wavefunctions, the shape-invariance condition can be related to a generalized Heisenberg- Weyl algebra. It is shown that this…
In this work, we consider the propagation of acoustic waves in unbounded domains characterized by a constant wavenumber, except possibly in a bounded region. The geometry of this inhomogeneity is assumed to be uncertain, and we are…
Many-particle systems pose commonly known computational challenges in quantum theory. The obstacles arise from the difficulty in finding sets of eigenvalues and eigenvectors of the underlying Hamiltonian while enforcing fermion or boson…
We consider the inverse conductivity problem of identifying embedded objects in unbounded domains. The main tool is a set of special solutions to the Schroedinger equation, the complex spherical waves, which are constructed by a Carleman…
An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The…
Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum…
The hypothetical Weyl particles in high-energy physics have been discovered in three-dimensional crystals as collective quasiparticle excitations near two-fold degenerate Weyl points. Such momentum-space Weyl particles carry quantized…
A local UV cutoff $\Lambda(x)$ transforming under Weyl rescalings allows to construct Weyl invariant kinetic terms for scalar fields including Wilsonian cutoff functions. First we consider scalar fields in curved space-time with local bare…
The density operator for a quantum system in thermal equilibrium with its environment depends on Planck's constant, as well as the temperature. At high temperatures, the Weyl representation, that is, the thermal Wigner function, becomes…
Variational perturbation theory is used to determine the decay rates of metastable states across a cubic barrier of arbitrary height. For high barriers, a variational resummation procedure is applied to the complex energy eigenvalues…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum…
We consider a quadratic matrix boundary value problem with equations and boundary conditions dependent on a spectral parameter. We study an inverse problem that consists in recovering the differential pencil by the so-called Weyl matrix. We…
Steady-state solutions of the Poisson-Nernst-Planck model are studied in the asymptotic limit of large, but finite domains. By using asymptotic matching for integrals, we derive an approximate solution for the steady-state equation with…