scholarly journals Path integral for confined Dirac fermions in a constant magnetic field

2015 ◽  
Vol 30 (27) ◽  
pp. 1550174 ◽  
Author(s):  
Abdeldjalil Merdaci ◽  
Ahmed Jellal ◽  
Lyazid Chetouani
Keyword(s):  
Magnetic Field ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Laguerre Polynomials ◽  
Nonrelativistic Limit ◽  
Dirac Fermion ◽  
Physical Parameters ◽  
Dirac Fermions ◽  
Quantum Numbers ◽  
The Green Function

In this paper, we consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a symmetric global projection, which provides a symmetric form for the Green function. Based on this, we show that it is possible to end up with the propagator of the harmonic oscillator for one charged particle. After some transformations, we derive the normalized wave functions and the eigenvalues in terms of different physical parameters and quantum numbers. By interchanging quantum numbers, we show that our solutions have interesting properties. The density of current and the nonrelativistic limit are analyzed where different conclusions are obtained. Finally, the completeness of the Dirac oscillator eigenfunctions is proved by using the standard properties of the generalized Laguerre polynomials.

scholarly journals Confined Dirac fermions in a constant magnetic field

2009 ◽  
Vol 80 (1) ◽  
Author(s):  
Ahmed Jellal ◽  
Abdulaziz D. Alhaidari ◽  
Hocine Bahlouli
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Dirac Fermions

THE RELATIVISTIC LANDAU PROBLEM FOR FERMIONS

1992 ◽  
Vol 07 (29) ◽  
pp. 2731-2739
Author(s):  
J. GAMBOA
Keyword(s):  
Magnetic Field ◽  
Conservation Laws ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Exact Expression ◽  
Integral Formalism ◽  
Planar Case ◽  
Spinning Particle ◽  
Relativistic Models ◽  
Popov Method

Using the Faddeev-Popov method an exact expression for the propagator of a relativistic spinning particle in a constant magnetic field is found. The conservation laws and the generators of the magnetic group are obtained in the path integral formalism. Both the relativistic and non-relativistic models are discussed in the planar case.

RADIATIVE EFFECTS IN A CONSTANT MAGNETIC FIELD USING THE QUANTUM MECHANICAL PATH-INTEGRAL

1994 ◽  
Vol 09 (23) ◽  
pp. 2167-2178 ◽  
Author(s):  
D.G.C. MCKEON ◽  
T.N. SHERRY
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Quantum Field Theory ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Quantum Mechanical ◽  
Quantum Field ◽  
Matrix Elements ◽  
Loop Momentum ◽  
Background Magnetic Field

It has been shown how evaluation of matrix elements of the form <x| exp −iHt|y> using the quantum mechanical path-integral allows one to determine radiative corrections in quantum field theory without encountering loop momentum integrals. In this paper we show how this technique can be applied when there is a constant background magnetic field contributing to the “Hamiltonian” H.

Dirac Particle in a Constant Magnetic Field: Path Integral Treatment

2008 ◽  
Vol 63 (5-6) ◽  
pp. 283-290 ◽  
Author(s):  
Abdeldjalil Merdaci ◽  
Nadira Boudiaf ◽  
Lyazid Chetouani
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Dirac Particle ◽  
Wave Functions ◽  
Green Functions ◽  
Integral Treatment ◽  
Global And Local

The Green functions related to a Dirac particle in a constant magnetic field are calculated via two methods, global and local, by using the supersymmetric formalism of Fradkin and Gitman. The energy spectrum as well as the corresponding wave functions are extracted following these two approaches.

scholarly journals Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Federico Finkel ◽  
Artemio González-López
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Asymptotic Approximation ◽  
Entanglement Entropy ◽  
Inhomogeneous Magnetic Field ◽  
Spin Chains ◽  
Dirac Fermion ◽  
Krawtchouk Polynomials ◽  
Rough Approximation ◽  
Half Filling

Abstract We introduce a family of inhomogeneous XX spin chains whose squared couplings are a polynomial of degree at most four in the site index. We show how to obtain an asymptotic approximation for the Rényi entanglement entropy of all such chains in a constant magnetic field at half filling by exploiting their connection with the conformal field theory of a massless Dirac fermion in a suitably curved static background. We study the above approximation for three particular chains in the family, two of them related to well-known quasi-exactly solvable quantum models on the line and the third one to classical Krawtchouk polynomials, finding an excellent agreement with the exact value obtained numerically when the Rényi parameter α is less than one. When α ≥ 1 we find parity oscillations, as expected from the homogeneous case, and show that they are very accurately reproduced by a modification of the Fagotti-Calabrese formula. We have also analyzed the asymptotic behavior of the Rényi entanglement entropy in the non-standard situation of arbitrary filling and/or inhomogeneous magnetic field. Our numerical results show that in this case a block of spins at each end of the chain becomes disentangled from the rest. Moreover, the asymptotic approximation for the case of half filling and constant magnetic field, when suitably rescaled to the region of non-vanishing entropy, provides a rough approximation to the entanglement entropy also in this general case.

scholarly journals On the (2 + 1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty

2015 ◽  
Vol 24 (02) ◽  
pp. 1550016 ◽  
Author(s):  
P. Pedram ◽  
M. Amirfakhrian ◽  
H. Shababi
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Dirac Equation ◽  
General Solution ◽  
Harmonic Oscillator ◽  
Constant Magnetic Field ◽  
Minimal Length ◽  
Two Dimensional ◽  
Quantum Numbers ◽  
Dirac Hamiltonian

In this paper, we exactly solve the (2 + 1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two two-dimensional nonrelativistic harmonic oscillator and obtain the solutions without directly solving the corresponding differential equations which are presented by Menculini et al. [Phys. Rev. D 87 (2013) 065017]. We also show that Menculini et al. solution is a subset of the general solution which is related to the even quantum numbers.

THE FADDEEV–POPOV METHOD FOR THE RELATIVISTIC LANDAU PROBLEM

1992 ◽  
Vol 07 (12) ◽  
pp. 2825-2839
Author(s):  
C. FARINA ◽  
J. GAMBOA
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Conservation Laws ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Proper Time ◽  
Landau Levels ◽  
Integral Approach ◽  
Relativistic Problem ◽  
Popov Method

We use the Faddeev–Popov method to calculate explicitly the path integral propagator for a relativistic spinless charged particle in the presence of a constant magnetic field. We obtain the conservation laws in the path integral approach. We also establish the equivalence between the Faddeev–Popov method and the Fock–Schwinger proper time approach. Finally, after proposing a suitable regularization prescription for the non-relativistic problem, we obtain the Landau levels directly from the path integral result.

TUNNELING FOR DIRAC FERMIONS IN CONSTANT MAGNETIC FIELD

2010 ◽  
Vol 07 (06) ◽  
pp. 909-931 ◽  
Author(s):  
EL BOUÂZZAOUI CHOUBABI ◽  
MOHAMED EL BOUZIANI ◽  
AHMED JELLAL
Keyword(s):  
Magnetic Field ◽  
Constant Magnetic Field ◽  
Resonant Tunneling ◽  
Continuity Equation ◽  
Energy Gap ◽  
Tunneling Effect ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Transmission Coefficients ◽  
Total Transmission

The tunneling effect of two-dimensional Dirac fermions in a constant magnetic field is studied. This can be done by using the continuity equation at some points to determine the corresponding reflexion and transmission coefficients. For this, we consider a system made of graphene as superposition of two different regions where the second is characterized by an energy gap t'. In fact, we treat concrete systems to practically give two illustrations: barrier and diode. For each case, we discuss the transmission in terms of the ratio of the energy conservation and t'. Moreover, we analyze the resonant tunneling by introducing a scalar Lorentz potential where it is shown that a total transmission is possible.

Sign in / Sign up

Export Citation Format

Share Document