Related papers: Quantum Well in Fractional Quantum Mechanics
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
The structure of the energy levels in a deep triple well is analyzed using simple quantum mechanical considerations. The resultant spectra of the first three energy levels are found to be composed of a ground state localized at the central…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
In this work the gravitational quantum well is used to model an effective two level system and to perform two thermodynamic cycles, the isogravitational and the isoenergetic ones. It is shown that the isogravitational is independent of the…
A procedure to find optimal regimes for quantum thermal engines (QTMs) is described and demonstrated. The QTMs are modelled as the periodically-driven non-equilibrium steady states of open quantum systems, whose dynamics is approximated in…
Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…
We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…
Non-commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non-commutative configuration space. Within this framework an unambiguous definition can be given for the…
This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…
The fractal character of some quantum properties has been shown for systems described by continuous variables. Here, a definition of quantum fractal states is given that suits the discrete systems used in quantum information processing,…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
There are both practical and foundational motivations to consider the thermodynamics of quantum systems at small scales. Here we address the issue of autonomous quantum thermal machines that are tailored to achieve some specific…
We explore the energy spectrum of a non-relativistic particle bound in a linear finite range, attractive potential, envisaged as a quark-confining potential. The intricate transcendental eigenvalue equation is solved numerically to obtain…
We analyze here the energy states and associated wave functions available to a particle acted upon by a delta function potential of arbitrary strength and sign and fixed anywhere within a one-dimensional infinite well. We consider how the…
We apply a method recently devised by one of the authors to obtain an approximate analytical formula for the spectrum of a quantum anharmonic potential. Due to its general features the method can be applied with minimal effort to general…
A purely imaginary potential can provide a phenomenological description of creation and absorption of quantum mechanical particles. PT-invariance of such a potential ensures that the non-unitary phenomena occur in a balanced manner. In…
Time-resolved Faraday rotation studies of CdS/CdSe/CdS quantum-dot quantum wells have recently shown that the Faraday rotation angle exhibits several well-defined resonances as a function of probe energy close to the absorption edge. Here,…
The bound state energies of a 1-dimensional finite quantum square well (FSW) can be determined using a geometric method, involving a smooth mapping between two copies of the complex plane. The method allows one to identify particular…
Fractional evolution equations lack generally accessible and well-converged codes excepting anomalous diffusion. A particular equation of strong interest to the growing intersection of applied mathematics and quantum information science and…
Classical and quantum annealing is discussed for a kinetically constrained chain of $N$ non-interacting asymmetric double wells, represented by Ising spins in a longitudinal field $h$. It is shown that in certain cases, where the kinetic…