Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0706.3329 · Physical Review Letters

Mesoscopic Superposition States in Relativistic Landau Levels

A. Bermúdez, Miguel Angel Martin-Delgado, E. Solano

Published Sep 18, 2007• 95 citations
arXivHTMLPDF

Abstract

We show that a linear superposition of mesoscopic states in relativistic Landau levels can be built when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily superpositions of coherent states involving the particle orbital quanta in a well-defined mesoscopic regime. We demonstrate that these mesoscopic superpositions have a purely relativistic origin and disappear in the nonrelativistic limit.

DOI
10.1103/physrevlett.99.123602

Related papers

Relativistic Landau levels via Feynman-Gell-Mann formulation

V. B. Mendrot, Antonio S. de Castro

Relativistic energy levels for a spin-1/2 fermion in a stationary and homogeneous magnetic field, namely the Landau levels, are obtained via the Feynman-Gell-Mann formulation of the Dirac equation using the axially symmetric gauge, such that the radial functions obey a similar equation to the one of a singular harmonic oscillator in the nonrelativistic theory.

International Workshop on Hadron Physics•Aug 1, 2022•0 citations

Coherent states of a relativistic particle in an external electromagnetic field

Vladislav G. Bagrov, I. L. Buchbinder, Dmitri M Gitman

The problem of the construction of coherent states of relativistic particles (bosons and fermions) in electromagnetic fields has been solved. The states discovered are exact solutions to the Klein-Gordon and Dirac equations; the wavefunctions of the particles are found in the homogeneous magnetic and electric fields and the Redmond configuration field, as well as in the plane-wave field. The formulation of relativistic quantum mechanics is used on the 'null' plane.

Journal of Physics A Mathematical and General•Nov 1, 1976•21 citations

On the correspondence between classical geometric phase of gyro-motion and quantum Berry phase

Hongxuan Zhu, Hong Qin

We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the Schrödinger equation or the Dirac equation. This correspondence is established by constructing coherent states for a particle using the energy eigenstates on the Landau levels and proving that the coherent states can maintain their status of coherent states during the slow varying of the magnetic field. It is discovered that the orbital Berry phases of the eigenstates interfere coherently to produce an observable effect (which we termed “coherent Berry phase”), which is exactly the geometric phase of the classical gyro-motion. This technique works for the particles with and without spin. For particles with spin, on each of the eigenstates that make up the coherent states, the Berry phase consists of two parts that can be identified as those due to the orbital and the spin motion. It is the orbital Berry phases that interfere coherently to produce a coherent Berry phase corresponding to the classical geometric phase of the gyro-motion. The spin Berry phases of the eigenstates, on the other hand, remain to be quantum phase factors for the coherent states and have no classical counterpart.

arXiv:1609.02522•Physics of Plasmas•Feb 1, 2017•1 citation

1 Quantum Mechanics of Klein-Gordon Fields II: Relativistic Coherent States

Alí Mostafazadeh, Farhad Zamani

We use the formulation of the quantum mechanics of first quantized Klein-Gordon fields given in the first of this series of papers to study relativistic coherent states. In particular, we offer an explicit construction of coherent states for both charged and neutral (real) free Klein-Gordon fields as well as for charged fields interacting with a constant magnetic field. Our construction is free from the problems associated with charge-superselection rule that complicated the previous studies. We compute various physical quantities associated with our coherent states and present a detailed investigation of their classical (nonquantum) and nonrelativistic limits. 1

•Jan 1, 2006•14 citations

Supersymmetric Quantum Mechanics and SUSY Dependent SU(2) Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

Jia Wen-Zhi, Shun-Jin Wang

We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SU τ (2) ⊗ SU σ (2) symmetry in the context of the relativistic Pauli Hamiltonian squared. We show that there exists also an SU(2) symmetry associated with the supersymmetry of the Dirac particle.

Communications in Theoretical Physics•Aug 1, 2008•2 citations

Non-Relativistic Limit of the Dirac Equation

Muhammad Adeel Ajaib

We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local gauge invariance. In addition, we study the problem of a spin up particle incident on a finite potential barrier and show that the known quantum mechanical results are obtained. Finally, we consider the symmetric potential well and show that the quantum mechanical expression for the quantized energy levels of a particle is obtained with periodic boundary conditions. Based on these conclusions, we propose that the equation introduced in [1] is the non-relativistic limit of the Dirac equation and more appropriately describes spin 1/2 particles in the non-relativistic limit.

arXiv:1511.07901•Nov 24, 2015•5 citations
We show that a linear superposition of mesoscopic states in relativistic Landau levels can be built when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily superpositions of coherent states involving the particle orbital quanta in a well-defined mesoscopic regime. We demonstrate that these mesoscopic superpositions have a purely relativistic origin and disappear in the nonrelativistic limit.
We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the Schrödinger equation or the Dirac equation. This correspondence is established by constructing coherent states for a particle using the energy eigenstates on the Landau levels and proving that the coherent states can maintain their status of coherent states during the slow varying of the magnetic field. It is discovered that the orbital Berry phases of the eigenstates interfere coherently to produce an observable effect (which we termed “coherent Berry phase”), which is exactly the geometric phase of the classical gyro-motion. This technique works for the particles with and without spin. For particles with spin, on each of the eigenstates that make up the coherent states, the Berry phase consists of two parts that can be identified as those due to the orbital and the spin motion. It is the orbital Berry phases that interfere coherently to produce a coherent Berry phase corresponding to the classical geometric phase of the gyro-motion. The spin Berry phases of the eigenstates, on the other hand, remain to be quantum phase factors for the coherent states and have no classical counterpart.
We use the formulation of the quantum mechanics of first quantized Klein-Gordon fields given in the first of this series of papers to study relativistic coherent states. In particular, we offer an explicit construction of coherent states for both charged and neutral (real) free Klein-Gordon fields as well as for charged fields interacting with a constant magnetic field. Our construction is free from the problems associated with charge-superselection rule that complicated the previous studies. We compute various physical quantities associated with our coherent states and present a detailed investigation of their classical (nonquantum) and nonrelativistic limits. 1
We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SU τ (2) ⊗ SU σ (2) symmetry in the context of the relativistic Pauli Hamiltonian squared. We show that there exists also an SU(2) symmetry associated with the supersymmetry of the Dirac particle.
We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local gauge invariance. In addition, we study the problem of a spin up particle incident on a finite potential barrier and show that the known quantum mechanical results are obtained. Finally, we consider the symmetric potential well and show that the quantum mechanical expression for the quantized energy levels of a particle is obtained with periodic boundary conditions. Based on these conclusions, we propose that the equation introduced in [1] is the non-relativistic limit of the Dirac equation and more appropriately describes spin 1/2 particles in the non-relativistic limit.