Related papers: Quantum Realization of the Wallis Formula
We construct approximate solutions of the hybrid quantum Gowdy cosmology with three-torus topology, linear polarization, and local rotational symmetry, in the presence of a massless scalar field. More specifically, we determine some…
We investigate the quantum cosmology of a closed spatially homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker (FLRW) minisuperspace model with electromagnetic radiation as matter content. We solve the corresponding…
We consider dynamics of a flat anisotropic Universe filled by a perfect fluid near a cosmological singularity in quadratic gravity. Two possible regimes are described -- the Kasner anisotropic solution and an isotropic "vacuum radiation"…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…
We use the canonical quantization of spherically symetric dust universes, and calculate the expectation value of the quantized metric, $<\Psi|\hat{g}|\Psi>$. Though the classical solutions are singular, and the wave functions have no zero…
We investigate the properties of a quantum Robertson - Walker universe described by the Wheeler -- DeWitt equation. The universe is filled with a quantum Yang -- Mills uniform field. This is then a quantum mini copy of the standard model of…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one, which is an anharmonic oscillator with $n+1$ known eigenstates for any $n\in \N$. It is also proved that the Hamiltonian of the…
Calculations in a (3+1)-dimensional model indicate that Pauli-Villars regularization can be combined with discrete light-cone quantization (DLCQ) to solve at least some field theories nonperturbatively. Discrete momentum states of…
The problem of particle creation from vacuum in a flat Robertson-Walker space-time is studied. Two sets of exact solutions for the Klein Gordon equation are given. Then the canonical method based on Bogoliubov transformation is applied to…
We consider fractional quantum Hall states built on Laughlin's original N-body wave-functions, i.e., they are of the form holomorphic times gaussian and vanish when two particles come close, with a given polynomial rate. Such states appear…
For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where spectrum…
We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates (BECs). The system is modeled by the Gross-Pitaevskii (GP) equation with the cubic term…
We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return…
A Quantum Walk (QW) simulating the flat $(1 + 2)$D Dirac Eq.\ on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group, but rather of its double…
In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…
We apply Pauli-Villars regularization and discrete light-cone quantization to the nonperturbative solution of a (3+1)-dimensional model field theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of the complex…
The dynamics of open quantum systems is formulated in a minimally extended state space comprising the degrees of freedom of a system of interest and a finite set of non-unitary, pure-state reservoir modes. This formal structure, derived…
Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…
In their activity, the traders approximate the rate of return by integer multiples of a minimal one. Therefore, it can be regarded as a quantized variable. On the other hand, there is the impossibility of observing the rate of return and…