Wave functions for high-symmetry, thin microstrip antennas and
two-dimensional quantum boxes
- URL: http://arxiv.org/abs/2108.07916v1
- Date: Wed, 18 Aug 2021 00:57:42 GMT
- Title: Wave functions for high-symmetry, thin microstrip antennas and
two-dimensional quantum boxes
- Authors: Joseph R. Rain, PeiYu Cai, Alexander Baekey, Matthew A. Reinhard,
Roman I. Vasquez, Andrew C. Silverman, Christopher L. Cain, and Richard A.
Klemm
- Abstract summary: For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions.
In two spatial dimensions, the symmetry of the box or microstrip antenna is an important feature that has often been overlooked in the literature.
- Score: 48.7576911714538
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: For a spinless quantum particle in a one-dimensional box or an
electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and
Neumann boundary conditions both lead to non-degenerate wave functions.
However, in two spatial dimensions, the symmetry of the box or microstrip
antenna is an important feature that has often been overlooked in the
literature. In the high-symmetry cases of a disk, square, or equilateral
triangle, the wave functions for each of those two boundary conditions are
grouped into two distinct classes, which are one- and two-dimensional
representations of the respective point groups, $C_{\infty v}$, $C_{4v}$, and
$C_{3v}$. Here we present visualizations of representative wave functions for
both boundary conditions and both one- and two-dimensional representations of
those point groups. For the one-dimensional representations, color contour
plots of the wave functions are presented. For the two-dimensional
representations, the infinite degeneracies are presented as common nodal points
and/or lines, the patterns of which are invariant under all operations of the
respective point group. The wave functions with the Neumann boundary conditions
have important consequences for the coherent terahertz emission from the
intrinsic Josephson junctions in the high-temperature superconductor
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$: the enhancement of the output power from
electromagnetic cavity resonances is only strong for wave functions that are
not degenerate.
Related papers
- Two-dimensional lattice with an imaginary magnetic field [0.0]
We introduce a two-dimensional non-Hermitian lattice model with an imaginary magnetic field.
We show that the energy spectrum does not converge as lattice size is made larger, which comes from the intrinsic nonperiodicity of the model.
We also find an analog of the Aharonov-Bohm effect; the net change of the norm of the wave function upon adiabatically forming a closed path is determined by the imaginary magnetic flux enclosed by the path.
arXiv Detail & Related papers (2023-07-27T05:50:24Z) - Double-scale theory [77.34726150561087]
We present a new interpretation of quantum mechanics, called the double-scale theory.
It is based on the simultaneous existence of two wave functions in the laboratory reference frame.
The external wave function corresponds to a field that pilots the center-of-mass of the quantum system.
The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
arXiv Detail & Related papers (2023-05-29T14:28:31Z) - Topological multi-mode waveguide QED [49.1574468325115]
We show how to take advantage of topologically protected propagating modes by interfacing them with quantum emitters.
Such capabilities pave the way for generating quantum gates among topologically protected photons as well as generating more complex entangled states of light in topological channels.
arXiv Detail & Related papers (2022-07-05T14:48:50Z) - Experimental study of closed and open microwave waveguide graphs with
preserved and partially violated time-reversal invariance [3.0383898736649115]
Microwave waveguide systems may serve as a model for closed and open quantum graphs.
Quantum graphs with incommensurate bond lengths attracted interest within the field of quantum chaos.
arXiv Detail & Related papers (2022-06-16T01:43:46Z) - Quantum Simulation of Molecules without Fermionic Encoding of the Wave
Function [62.997667081978825]
fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations.
An application to computing the ground-state energy and 2-RDM of H$_4$ is presented.
arXiv Detail & Related papers (2021-01-27T18:57:11Z) - Constructing tensor network wavefunction for a generic two-dimensional
quantum phase transition via thermofield double states [2.416375474510521]
Two-dimensional quantum Rokhsar-Kivelson (RK) type models can be mapped into the partition functions of two-dimensional statistical models.
We introduce the universality of the thermofield double (TFD) state, which is a purification of the equilibrium density operator.
By expressing the TFD state in terms of the projected entangled pair state, its $N$-order of R'enyi entropy results in a three-dimensional statistical model in Euclidian spacetime.
arXiv Detail & Related papers (2020-12-28T09:05:55Z) - Non-Hermitian effects of the intrinsic signs in topologically ordered
wavefunctions [12.453831188907797]
Ground-state wavefunction of double semion model on a two-dimensional hexagonal lattice contains an intrinsic sign.
A connection has established between the intrinsic signs in the topologically ordered wavefunction and the PT-symmetric non-Hermitian statistical model.
arXiv Detail & Related papers (2020-05-08T03:57:21Z) - Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide.
For open boundary condition, we find exotic topological bound-pair edge states with radiative losses.
By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
arXiv Detail & Related papers (2020-02-24T04:44:12Z) - External and internal wave functions: de Broglie's double-solution
theory? [77.34726150561087]
We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory.
The principle is to decompose the evolution of a quantum system into two wave functions.
For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
arXiv Detail & Related papers (2020-01-13T13:41:24Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.