Quantization and coherent states for a time-dependent Landau problem
- URL: http://arxiv.org/abs/2111.05163v1
- Date: Tue, 9 Nov 2021 14:22:11 GMT
- Title: Quantization and coherent states for a time-dependent Landau problem
- Authors: Lat\'evi Mohamed Lawson
- Abstract summary: The spectrum of a Hamiltonian describing this system is obtained.
We construct the coresponding coherent states and the associated photon added and nonlinear coherent states.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: The ordinary Landau problem consists of describing a charged particle in
time-independent magnetic field. In the present case the problem is generalized
onto time-dependent uniform electric fields with time-dependent mass and
harmonic frequency [1].The spectrum of a Hamiltonian describing this system is
obtained. The configuration space wave functions of the model is expressed in
terms of the generalised Laguerre polynomials. To diagonalize the
time-dependent Hamiltonian we employ the Lewis-Riesenfeld method of invariants.
To this end, we introduce an unitary transformation in the framework of the
algebraic formalism to construct the invariant operator of the system and then
to obtain the exact solution of the Hamiltonian. We recover the solutions of
the ordinary Landau problem in the absence of the electric and harmonic fields,
for a constant particle mass. The quantization of this system exhibits many
symmetries such as $U(1), SU(2), SU(1,1)$. We therefore construct the
coresponding coherent states and the associated photon added and nonlinear
coherent states.
Related papers
- Integral quantization based on the Heisenberg-Weyl group [39.58317527488534]
We develop a framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime.
The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group.
A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.
arXiv Detail & Related papers (2024-10-31T14:36:38Z) - Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations.
We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
arXiv Detail & Related papers (2024-10-04T18:06:12Z) - Quantum Circuits for the heat equation with physical boundary conditions via Schrodingerisation [33.76659022113328]
This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions.
We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions.
We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension.
arXiv Detail & Related papers (2024-07-22T03:52:14Z) - Canonical equivalence of a charge in a time dependent,
spatially-homogeneous electromagnetic field to a time-dependent perturbed
oscillator [0.0]
We prove that the classical (respectively, quantum) system is equivalent to a harmonic oscillator by a spatially homogeneous force field.
The eigenstates of the initial problem turn out to be entangled states of the harmonic oscillator.
The unitary transformations between the quantum systems are a representation of the canonical transformations by unitary transformations of the corresponding Hilbert spaces.
arXiv Detail & Related papers (2023-06-26T12:29:36Z) - Free expansion of a Gaussian wavepacket using operator manipulations [77.34726150561087]
The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes.
We provide an alternative way to calculate the free expansion by recognizing that the Gaussian wavepacket can be thought of as the ground state of a harmonic oscillator.
As quantum instruction evolves to include more quantum information science applications, reworking this well known problem using a squeezing formalism will help students develop intuition for how squeezed states are used in quantum sensing.
arXiv Detail & Related papers (2023-04-28T19:20:52Z) - Measurement phase transitions in the no-click limit as quantum phase
transitions of a non-hermitean vacuum [77.34726150561087]
We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians.
We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
arXiv Detail & Related papers (2023-01-18T09:26:02Z) - On the two-dimensional time-dependent anisotropic harmonic oscillator in
a magnetic field [0.0]
We have considered a two-dimensional anisotropic harmonic oscillator placed in a time-dependent magnetic field.
An orthonormal basis of the Hilbert space consisting of the eigenvectors of $hatmathcalI$ is obtained.
Separability Criterion for the bipartite coherent states corresponding to our system has been demonstrated.
arXiv Detail & Related papers (2022-06-30T17:19:09Z) - Exact solution of damped harmonic oscillator with a magnetic field in a
time dependent noncommutative space [0.32771631221674324]
We have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in the presence of an external magnetic field.
The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation.
arXiv Detail & Related papers (2021-05-14T17:07:50Z) - Photon-added BarutGirardello like coherent states of time-dependent
Landau problem [0.0]
We study the time-dependent Landau problem into the context of coherent states.
We construct coherent states a la Barut-Girardello.
We find that these states are sub-Poissonian in nature.
arXiv Detail & Related papers (2021-01-07T10:06:43Z) - New approach to describe two coupled spins in a variable magnetic field [55.41644538483948]
We describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field.
We modify the time-dependent Schr"odinger equation through a change of representation.
The solution is highly simplified when an adiabatically varying magnetic field perturbs the system.
arXiv Detail & Related papers (2020-11-23T17:29:31Z) - Exact solutions of a damped harmonic oscillator in a time dependent
noncommutative space [0.32771631221674324]
We have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in time dependent noncommutative space.
The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation.
arXiv Detail & Related papers (2020-06-15T08:30:25Z)
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.