Acta Polytechnica. 2022, vol. 62
Recent Submissions

Orthonormal polynomial projection quantization: an algebraic eigenenergy bounding method
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)The ability to generate tight eigenenergy bounds for low dimension bosonic or ferminonic, hermitian or nonhermitian, Schrödinger operator problems is an important objective in the computation of quantum systems. Very few ... 
Linearised coherent states for nonrational SUSY extensions of the harmonic oscillator
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)In this work, we derive two equivalent nonrational extensions of the quantum harmonic oscillator using two different supersymmetric transformations. For these extensions, we built ladder operators as the product of the ... 
Generalized threebody harmonic oscillator system: ground state
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)In this work we report on a 3body system in a d−dimensional space ℝd with a quadratic harmonic potential in the relative distances rij = ri −rj between particles. Our study considers unequal masses, different spring ... 
Timedependent mass oscillators: constants of motion and semiclasical states
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)This work reports the construction of constants of motion for a family of timedependent mass oscillators, achieved by implementing the formalism of formpreserving point transformations. The latter allows obtaining a ... 
Photonic graphene under strain with positiondependent gain and loss
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)We work with photonic graphene lattices under strain with gain and loss, modeled by the Dirac equation with an imaginary mass term. To construct such Hamiltonians and their solutions, we use the freeparticle Dirac equation ... 
From quartic anharmonic oscillator to double well potential
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)Quantum quartic singlewell anharmonic oscillator Vao(x) = x2 + g2x4 and doublewell anharmonic oscillator Vdw(x) = x2(1−gx)2 are essentially oneparametric, they depend on a combination (g2ℏ). Hence, these problems are ... 
Timedependent steplike potential with a freezable bound state in the continuum
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)In this work, we construct a timedependent steplike potential supporting a normalizable state with energy embedded in the continuum. The potential is allowed to evolve until a stopping time ti, where it becomes static. ... 
About the time evolution of coherent electron states in monolayers of boron allotropes
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)In this paper, we theoretically analyze the massless Dirac fermion dynamics in twodimensional monolayers of boron allotropes, 8B and 2BH − pmmn borophene, interacting with external electric and magnetic fields. We study ... 
Modified Kortewegde Vries equation as a system with benign ghosts
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)We consider the modified Kortewegde Vries equation, uxxx + 6u2ux + ut = 0, and explore its dynamics in spatial direction. Higher x derivatives bring about the ghosts. We argue that these ghosts are benign, i.e., the ... 
Quantization of rationally deformed Morse potentials by Wronskian transforms of RomanovskiBessel polynomials
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)The paper advances Odake and Sasaki’s idea to rewrite eigenfunctions of rationally deformed Morse potentials in terms of Wronskians of Laguerre polynomials in the reciprocal argument. It is shown that the constructed ... 
On some algebraic formulations within universal enveloping algebras related to superintegrability
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)We report on some recent purely algebraic approaches to superintegrable systems from the perspective of subspaces of commuting polynomials in the enveloping algebras of Lie algebras that generate quadratic (and eventually ... 
A note on entanglement classification for tripartite mixed states
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)We study the classification of entanglement in tripartite systems by using Belltype inequalities and principal basis. By using Bell unctions and the generalized three dimensional Pauli operators, we present a set of Bell ... 
On generalized Heun equation with some mathematical properties
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)We study the analytic solutions of the generalized Heun equation, (α0 + α1 r + α2 r2 + α3 r3) y′′ + (β0 + β1 r + β2 r2) y′ + (ε0 + ε1 r) y = 0, where α3 + β2≠ 0, and {αi}3i=0, {βi}2i=0, {εi}1i=0 are real parameters. ... 
MaxwellChernSimonsHiggs theory
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)We consider the three dimensional electrodynamics described by a complex scalar field coupled with the U(1) gauge field in the presence of a Maxwell term, a ChernSimons term and the Higgs potential. The ChernSimons term ... 
On the WessZumino Model: a supersymmetric field theory
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)We consider the free massless WessZumino Model in 4D which describes a supersymmetric field theory that is invariant under the rigid or global supersymmetry transformations where the transformation parameter ϵ (or ϵ ) ... 
Swanson Hamiltonian revisited through the complex scaling method
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)In this work, we study the nonhermitian PTsymmetry Swanson Hamiltonian in the framework of the Complex Scaling Method. We show that by applying this method we can work with eigenfunctions that are squareintegrable both ... 
Complex topological soliton with real energy in particle physics
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)We summarise the procedure used to find the classical masses of Higgs particle, massive gauge boson and t’HooftPolyakov monopole in nonHermitian gauge field theory. Their physical regions are explored, and the mechanism ... 
Conserved quantities in nonhermitian systems via vectorization method
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by nonHermitian Hamiltonians with paritytime (PT) symmetry that are best understood as systems ... 
How to understand the structure of beta functions in sixderivative Quantum Gravity?
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)We extensively motivate the studies of higherderivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical ... 
Rational extension of many particle systems
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)In this talk, we briefly review the rational extension of many particle systems, and is based on a couple of our recent works. In the first model, the rational extension of the truncated CalogeroSutherland (TCS) model is ...