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Qiong-gui Lin

Publications and source records attributed to Qiong-gui Lin.

17 recordsLinked to original sources
arXiv2002

Geometric phases for neutral and charged particles in a time-dependent magnetic field

It is well known that any cyclic solution of a spin 1/2 neutral particle moving in an arbitrary magnetic field has a nonadiabatic geometric phase proportional to the solid angle subtended by the trace of the spin. For neutral particles with higher spin, this is true for cyclic solutions with special initial conditions. For more general cyclic solutions, however, this does not hold. As an example, we consider the most general solutions of such particles moving in a rotating magnetic field. If the parameters of the system are appropriately chosen, all solutions are cyclic. The nonadiabatic geometric phase and the solid angle are both calculated explicitly. It turns out that the nonadiabatic geometric phase contains an extra term in addition to the one proportional to the solid angle. The extra term vanishes automatically for spin 1/2. For higher spin, however, it depends on the initial condition. We also consider the valence electron of an alkaline atom. For cyclic solutions with special initial conditions in an arbitrary strong magnetic field, we prove that the nonadiabatic geometric phase is a linear combination of the two solid angles subtended by the traces of the orbit and spin angular momenta. For more general cyclic solutions in a strong rotating magnetic field, the nonadiabatic geometric phase also contains extra terms in addition to the linear combination.

quant-ph↗
arXiv2001

Dirac particles in a rotating magnetic field

We study a relativistic charged Dirac particle moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Dirac equation with the time-dependent Hamiltonian can be reduced to a Dirac-like equation with a time-independent effective Hamiltonian. Eigenstates of the effective Hamiltonian correspond to cyclic solutions of the original Dirac equation. The nonadiabatic geometric phase of a cyclic solution can be expressed in terms of the expectation value of the component of the total angular momentum along the rotating axis, regardless of whether the solution is explictly available. For a slowly rotating magnetic field, the eigenvalue problem of the effective Hamiltonian is solved approximately and the geometric phases are calculated. The same problem for a charged or neutral Dirac particle with an anomalous magnetic moment is discussed briefly.

quant-ph↗
arXiv2001

Scattering by a contact potential in three and lower dimensions

We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $Ω\hbar^2δ(r)/ 2μr^α$ which is defined as the $a\to 0$ limit of $Ω\hbar^2δ(r-a)/2μr^α$. It is surprising that it gives a nonvanishing cross section when $α=1$ and $Ω=-1$. When the contact potential is approached by a spherical square well potential instead of the above spherical shell one, one obtains basically the same result except that the parameter $Ω$ that gives a nonvanishing cross section is different. Similar problems in two and one dimensions are studied and results of the same nature are obtained.

quant-ph↗
arXiv2001

Charged particles in a rotating magnetic field

We study the valence electron of an alkaline atom or a general charged particle with arbitrary spin and with magnetic moment moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Schrödinger equation with the time-dependent Hamiltonian can be reduced to a Schrödinger-like equation with a time-independent effective Hamiltonian. Eigenstates of the effective Hamiltonian correspond to cyclic solutions of the original Schrödinger equation. The nonadiabatic geometric phase of a cyclic solution can be expressed in terms of the expectation value of the component of the total angular momentum along the rotating axis, regardless of whether the solution is explicitly available. For the alkaline atomic electron and a strong magnetic field, the eigenvalue problem of the effective Hamiltonian is completely solved, and the geometric phase turns out to be a linear combination of two solid angles. For a weak magnetic field, the same problem is solved partly. For a general charged particle, the problem is solved approximately in a slowly rotating magnetic field, and the geometric phases are also calculated.

quant-ph↗
arXiv2000

Scattering of relativistic particles with Aharonov-Bohm-Coulomb interaction in two dimensions

The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the interaction between two particles carrying electric charge and magnetic flux, say, Chern--Simons solitons, or so called anyons. The scattering problem for such two-body systems is extended to the relativistic case, and the scattering amplitude is obtained as a partial wave series. The electric charge and magnetic flux is ($-q$, $-ϕ/Z$) for one particle and ($Zq$, $ϕ$) for the other. When $(Zq^2/\hbar c)^2\ll 1$, and $qϕ/2π\hbar c$ takes on integer or half integer values, the partial wave series is summed up approximately to give a closed form. The results exhibit some nonperturbative features and cannot be obtained from perturbative quantum electrodynamics at the tree level.

quant-ph↗
arXiv2000

Vacuum polarization for neutral particles in 2+1 dimensions

In 2+1 dimensions there exists a duality between a charged Dirac particle coupled minimally to a background vector potential and a neutral one coupled nonminimally to a background electromagnetic field strength. A constant uniform background electric current induces in the vacuum of the neutral particle a fermion current which is proportional to the background one. A background electromagnetic plane wave induces no current in the vacuum. For constant but nonuniform background electric charge, known results for charged particles can be translated to give the induced fermion number. Some new examples with infinite background electric charge are presented. The induced spin and total angular momentum are also discussed.

hep-th↗
arXiv2000

Bound states of neutral particles in external electric fields

Neutral fermions of spin $\frac 12$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be reduced to two simultaneous ordinary differential equations by separation of variables in spherical coordinates. For a wide variety of central electric fields, bound-state solutions of critical energy values can be found analytically. The degeneracy of these energy levels turns out to be numerably infinite. This reveals the possibility of condensing infinitely many fermions into a single energy level. For radially constant and radially linear electric fields, the system of ordinary differential equations can be completely solved, and all bound-state solutions are obtained in closed forms. The radially constant field supports scattering solutions as well. For radially linear fields, more energy levels (in addition to the critical one) are infinitely degenerate. The simultaneous presence of central magnetic and electric fields is discussed.

quant-ph↗
arXiv1999

Levinson theorem for Dirac particles in one dimension

The scattering of Dirac particles by symmetric potentials in one dimension is studied. A Levinson theorem is established. By this theorem, the number of bound states with even (odd) parity, $n_+$ ($n_-$), is related to the phase shifts $η_+(\pm E_k)$ [$η_-(\pm E_k)$] of scattering states with the same parity at zero momentum as follows: $$η_\pm(μ)+η_\pm(-μ)\pm{π\over 2}[\sin^2η_\pm(μ) -\sin^2η_\pm(-μ)]=n_\pmπ.$$ The theorem is verified by several simple examples.

quant-ph↗
arXiv1999

Scattering of relativistic particles by a Coulomb field in two dimensions

The scattering of relativistic Dirac particles by a Coulomb field $\pm Ze^2/r$ in two dimensions is studied and the scattering amplitude is obtained as a partial wave series. For small $Z$ the series can be summed up approximately to give a closed form. The result, though being aproximate, exhibites some nonperturbative feature and cannot be obtained from perturbative quantum electrodynamics at the tree level.

quant-ph↗
arXiv1999

Pair creation of neutral particles in a vacuum by external electromagnetic fields in 2+1 dimensions

Neutral fermions of spin 1/2 with magnetic moment can interact with electromagnetic fields through nonminimal coupling. In 2+1 dimensions the electromagnetic field strength plays the same role to the magnetic moment as the vector potential to the electric charge. This duality enables one to obtain physical results for neutral particles from known ones for charged particles. We give the probability of neutral particle-antiparticle pair creation in the vacuum by non-uniform electromagnetic fields produced by constant uniform charge and current densities.

hep-th↗
arXiv1999

Quantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensions

We propose a simple quantum mechanical equation for $n$ particles in two dimensions, each particle carrying electric charge and magnetic flux. Such particles appear in (2+1)-dimensional Chern-Simons field theories as charged vortex soliton solutions, where the ratio of charge to flux is a constant independent of the specific solution. As an approximation, the charge-flux interaction is described here by the Aharonov-Bohm potential, and the charge-charge interaction by the Coulomb one. The equation for two particles, one with charge and flux ($q, Φ/Z$) and the other with ($-Zq, -Φ$) where $Z$ is a pure number is studied in detail. The bound state problem is solved exactly for arbitrary $q$ and $Φ$ when $Z>0$. The scattering problem is exactly solved in parabolic coordinates in special cases when $qΦ/2π\hbar c$ takes integers or half integers. In both cases the cross sections obtained are rather different from that for pure Coulomb scattering.

quant-ph↗
arXiv1998

Nonlocal scalar electrodynamics from Chern-Simons theory

The theory of a complex scalar interacting with a pure Chern-Simons gauge field is quantized canonically. Dynamical and nondynamical variables are separated in a gauge-independent way. In the physical subspace of the full Hilbert space, this theory reduces to a pure scalar theory with nonlocal interaction. Several scattering processes are studied and the cross sections are calculated.

hep-th↗
arXiv1998

Nonlocal electrodynamics in 2+1 dimensions from Chern-Simons theory

The theory of a spinor field interacting with a pure Chern-Simons gauge field in 2+1 dimensions is quantized. Dynamical and nondynamical variables are separated in a gauge-independent way. After the nondynamical variables are dropped, this theory reduces to a pure spinor field theory with nonlocal interaction. Several two-body scattering processes are studied and the cross sections are obtained in explicitly Lorentz invariant forms.

hep-th↗
arXiv1998

Levinson theorem in two dimensions

A two-dimensional analogue of Levinson's theorem for nonrelativistic quantum mechanics is established, which relates the phase shift at threshold(zero momentum) for the $m$th partial wave to the total number of bound states with angular momentum $m\hbar(m=0,1,2,...)$ in an attractive central field.

quant-ph↗
arXiv1998

Levinson theorem for Dirac particles in two dimensions

The Levinson theorem for nonrelativistic quantum mechanics in two spatial dimensions is generalized to Dirac particles moving in a central field. The theorem relates the total number of bound states with angular momentum $j$ ($j=\pm 1/2, \pm 3/2, ... $), $n_j$, to the phase shifts $η_j(\pm E_k)$ of scattering states at zero momentum as follows: $η_j(μ)+η_j(-μ)= n_jπ$.

quant-ph↗